We apply Learning Vector Quantization (LVQ) in automated boar semen quality assessment. The classification of single boar sperm heads into healthy (normal) and non-normal ones is based on grey-scale microscopic images only. Sample data was classified by veterinary experts and is used for training a system with a number of prototypes for each class. We apply as training schemes Kohonen’s LVQ1 and the variants Generalized LVQ (GLVQ) and Generalized Relevance LVQ (GRLVQ). We compare their performance and study the influence of the employed metric

Biehl, Michael

Pasma, Piter

Petkov, Nicolai

Pijl, Marten

Sánchez, Lidia

Verleysen, Michel

University of Groningen Research Database

  
 University of Groningen
Classification of Boar Sperm Head Images using Learning Vector Quantization
Biehl, Michael; Pasma, Piter; Pijl, Marten; Sánchez, Lidia; Petkov, Nicolai
Published in:
Proc. European Symposium on Artificial Neural Networks
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Biehl, M., Pasma, P., Pijl, M., Sánchez, L., & Petkov, N. (2006). Classification of Boar Sperm Head Images
using Learning Vector Quantization. In M. Verleysen (Ed.), Proc. European Symposium on Artificial Neural
Networks: ESANN 2006 d-side publishing.
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Classification of Boar Sperm Head Images using
Learning Vector Quantization
Michael Biehl1, Piter Pasma1, Marten Pijl1, Lidia Sa´nchez2 and Nicolai Petkov1
1- Rijksuniversiteit Groningen - Mathematics and Computing Science
P.O. Box 800, NL-9700 AV Groningen - The Netherlands
2- University of Leo´n - Department of Electrical and Electronics Engineering
Campus de Vegazana s/n, 24071 Leo´n - Spain
Abstract. We apply Learning Vector Quantization (LVQ) in automated
boar semen quality assessment. The classification of single boar sperm
heads into healthy (normal) and non-normal ones is based on grey-scale
microscopic images only. Sample data was classified by veterinary experts
and is used for training a system with a number of prototypes for each
class. We apply as training schemes Kohonen’s LVQ1 and the variants
Generalized LVQ (GLVQ) and Generalized Relevance LVQ (GRLVQ).
We compare their performance and study the influence of the employed
metric.
1 Introduction
Semen quality assessment constitutes an important problem in fertility studies.
Existing, relatively costly methods rely on staining or motility measurements.
Mostly they have originally been developed for the analysis of human semen and
clinical purposes. Here, the aim is a fast and relatively cheap reliable method
for the inspection of boar semen samples on the basis of microscopic images.
We apply methods of prototype based clustering and classification. Learning
vector quantization (LVQ) as originally proposed by Kohonen is widely used in
a variety of areas due to its flexibility and conceptual simplicity [1, 4]. LVQ
provides a particularly intuitive and clear approach: the classification of data
is based on a set of so-called prototype vectors and a feature vector is assigned
to the class represented by the closest prototype.
Frequently, distances are evaluated in terms of simple Euclidean metrics, but
alternative measures can easily be incorporated into the standard LVQ schemes.
The choice of an appropriate distance measure can indeed be crucial in practical
problems. Recent variations of LVQ have been suggested in which an adaptive
metric is modified in the course of learning.
One of the most attractive features of LVQ learning is that the parameter-
ization in terms of prototype vectors allows for an immediate interpretation of
the classifier. Prototypes are defined in the same space as the data; they are, for
instance, images themselves and provide direct information about the achieved
clustering and the features that it is based on. This is in contrast to other
methods, including feed-forward neural networks and the support vector ma-
chine which in general cannot be interpreted as easily. The paper is organized
as follows: in the next section we outline the problem and summarize how the
data has been acquired and pre-processed. In section 3, we describe the LVQ
classifier and training algorithms. The results are presented and discussed in
section 4 and we conclude with a brief summary in 5.
2 Classification problem and data acquisition
Computer assisted analysis of semen fertility has been used to save costs and im-
prove quality in artificial insemination. Sperm analysis is a complex task which
allows to identify the males with the best reproductive features and control the
fertility of the samples. Some approaches have used image analysis techniques
to detect shape abnormalities in sperm heads [6] or classify subpopulations in a
sample. However, only very few methods use the information of the acrosome
integrity or the intracellular distribution to evaluate the sperm quality [7, 8].
Several commercial systems have been developed, which were designed specif-
ically for human sperm cells and have been adapted to other species later. They
do not consider the intracellular density distribution which provides information
about the cell status.
Veterinary experts hypothesize that there are certain patterns of cytoplasm
density distributions which can be correlated with alive and dead sperm cells.
Techniques such as fluorescence staining protocols mark sperm heads depending
on if they are alive of dead. However, these methods are expensive and require
more work in the sample preparation. The goal of this work is to classify the
sperm head images without using staining techniques in order to speed up the
process and reduce the costs.
The 1360 images used in this project are obtained from boar semen samples
by use of a phase-contrast microscope. The first processing and segmentation
steps provide aligned images of isolated sperm heads as grey-level distributions
on a black (empty) background. For details of acquisition and pre-processing
see [7].
Sperm heads typically display an oval shape which we approximate by an
ellipse. We determine its principal axes and align all images. Using nearest-
neighbor interpolation, we re-scale all head images to the same aspect ratio of
19 x 35 pixels. Finally, we consider an array of grey-levels which lie inside the
ellipse with main axes 19 and 35 pixels.
Intracellular intensities in heads which were labelled as normal by veterinary
experts display three areas: a darker region corresponding to the post nucleus
cap where the tail develops from, an intermediate light area and the acrosome
which is covering the nucleus region, see Fig. 1 for example images. As the illu-
mination of the samples under the microscope is controlled manually, brightness
and contrast can vary significantly across different images. To cope with this
problem, we perform a linear transformation which results in the same mean,
µ = 100, and standard deviation, σ = 8, of the grey-levels in all images.
We represent example images as vectors ξµ ∈ IRN where the N = 35 ×
19 = 665 components correspond to a rectangle. All pixels outside the above
mentioned ellipsoidal regions are the same in every ξµ and will play no role in
the LVQ training and classification performance. Due to variations in shape,
also the ellipses can contain pixels or entire regions which do not correspond
Fig. 1: Examples of sperm heads which were labelled as normal (left panel)
or non-normal (right panel), respectively. For clarity, background pixels are
displayed black while for the classification they are set to the overall mean value
of all non-background pixels, see the discussion in section 2.
to intracellular densities but are part of the black background in Fig. 1. In
[7], such pixels were explicitly excluded when comparing different heads, which
essentially disregards differences in shape. Here, we have chosen to replace
them by a constant value, i.e. the total mean of non-background grey-scales
over all example images. Thus, we are taking into account deformations but
avoid artificially large differences between corresponding pixels. By choice of
the constant one could vary the emphasis that is put on shape, the effect of this
will be studied in a forthcoming project.
3 LVQ system and training algorithms
Training is based on the repeated random sequential presentation of example
images drawn from a given (sub-) set of data ID = {ξµ, SµT }
P
µ=1
. Here the class
membership label as provided by the veterinary experts is
SµT = +1 if ξ
µ is marked as normal and SµT = −1 else. (1)
In the set of M prototypes
{
w1,w2, . . . ,wM
}
a vector wk is supposed to repre-
sent data from class Sk ∈ {−1,+1}. Upon presentation of the pair (ξµ, SµT ) at
time step t, we evaluate the distance of ξµ from the current prototypes wj(t).
In the following we will use three different distance measures d(j, µ):
a) (squared) Euclidean: d2(j, µ) =
(
ξµ −wj(t)
)2
=
∑N
i=1
(
ξµi − w
j
i (t)
)2
b) generalized (squared) Euclidean: d2,λ(j, µ) =
∑N
i=1 λi
(
ξµi − w
j
i (t)
)2
with the positive and normalized relevances λi > 0,
∑
i λ
2
i = 1
c) L1 metric: d1(j, µ) =
∑N
i=1
∣∣∣ξµi − wji (t)∣∣∣ .
In any case we identify the minimal distances d(j, µ) among prototypes with
class labels SjT = +1 and S
j
T = −1 separately and use the notation{
wJ(t) (correct winner) with d(J, µ) = min
k
{
d(k, µ)|Sk = +SµT
}
wK(t) (wrong winner) with d(K,µ) = min
k
{
d(k, µ)|Sk = −SµT
}
.
(2)
Further, the total winner is denoted aswL(t) =
{
wJ (t) if d(J, µ) < d(K,µ)
wK(t) else.
We consider the following training schemes:
Fig. 2: Left panel: The upper (lower) row displays prototypes in LVQ1 for
normal (non-normal) heads, respectively. Right panel: Relevances as obtained
by GRLVQ: the classification is based on very few components with considerable
λi, corresponding to the dark region in the figure.
a) LVQ1
At each learning step, only the total winner wL(t) is updated:
wL(t+ 1) = wL(t) + η(t)[SµT S
L]
(
ξ
µ −wL(t)
)
(3)
The update is towards (away from) the input ξµ if the class label of the
winning prototype and that of the example agree (disagree). In LVQ1 we
have considered the use of the distance measures d2(j, µ) and d1(j, µ).
b) GLVQ
In this learning scheme we restrict our implementation to the Euclidean
distance measure d(j, µ) = d2(j, µ). Both winning prototypes, w
J and
wK , are modified. Defining zµ = (d(J, µ) − d(K,µ))/ (d(J, µ) + d(K,µ))
the update of wJ can be written as
wJ(t+ 1) = wJ (t) + η(t)[SµTS
J ]f ′ (zµ)
d(K,µ)
(d(J, µ) + d(K,µ))2
(
ξµ −wJ (t)
)
(4)
and that of wK is of the same form with indices K and J exchanged.
This corresponds to a step in the direction of the negative gradient of
the function f(zµ) w.r.t. wK and wL. The function f has been set to
f(x) = (1 + e−x)−1 in [2, 3]. For the limited range of possible arguments
−1 ≤ zµ ≤ 1 the sigmoidal is very close to linear, however, and we replace
it by the simpler f(x) = x, f ′(x) = 1 in the following.
c) GRLVQ
In GRLVQ as suggested in [3], the distance measure d(j, µ) = d2,λ(j, µ) is
used and the cost function f(zµ) = zµ of GLVQ is re-defined accordingly.
Both prototypes wJ (t), wK(t) and also the relevances λi are updated in
the direction of the respective negative gradient, see [3] for details.
In all considered algorithms the learning rate should gradually decrease in the
course of learning. We have implemented a schedule of the form
η(t) = ηo for τ < τo and η(t) = ηo/[1 + b(τ − τo)] for τ ≥ τo.
Here, τ counts the number of randomly shuﬄed sweeps through the actual
training set. In each training process we have performed 80 such sweeps and
used the values τo = 10, ηo = 0.1, and b = 0.3.
4 Results
In order to evaluate the quality of the obtained classification we have performed
ten-fold cross-validation: We split the set of 1360 available data into ten disjoint
subsets IDi of equal size. For a given number of prototypes each of ten identi-
cally designed LVQ systems (n = 1, 2, . . . 10) was trained from ∪i6=nIDi, while
IDn served as a test set. The following table summarizes some of our results:
# of prototypes: 3 / 3 (normal/non-normal) 1 / 7
LVQ1 (L1 measure) test = 0.232 (σ = 0.037) test = 0.215 (σ = 0.058)
LVQ1 (Euclidean) test = 0.186 (σ = 0.040) test = 0.184 (σ = 0.045)
GLVQ (Euclidean) test = 0.244 (σ = 0.041) test = 0.236 (σ = 0.038)
GRLVQ (Euclidean) test = 0.185 (σ = 0.035) test = 0.183 (σ = 0.037)
Here test is the mean test error and σ denotes its standard deviation over the
ten (statistically dependent) training sets. Note that a training error of 0.20
comparable with the above test error was achieved for the same data set using a
single normal cell prototype and a distance threshold [7, 8]. We are not aware of
other published results for boar sperm head classification based on microscopic
images only.
As a first result we note that the performance depends only weakly on the
number of prototypes. Relatively low test errors can be achieved by using a
single prototype for the class of normal heads while the non-normal sperms
are represented by several prototypes. We observe only weak variations and no
indication of significant over–fitting in the considered range of 1−10 normal and
3−16 non-normal prototypes. We have studied the performance of LVQ1 using
the squared Euclidean distance as well as the L1-metric. In all considered cases
we have found a lower classification error when using the Euclidean measure
and, hence, we restrict our comparison of different algorithms to this case.
An important observation is that the performance of GLVQ is inferior to that
of LVQ1 (with Euclidean distances). One attractive feature of GLVQ is that it
can be interpreted as a gradient descent with respect to a plausible cost function.
However, the relation of the latter with the goal of good generalization is not
obvious. Indeed, we observe that, here, training and test error typically increase
in the course of GLVQ training while the associated cost function decreases.
By introducing adaptive relevances, the good performance of LVQ1 is recov-
ered in GRLVQ. It is interesting to note that only very few relevances λi remain
significantly different from zero in the training process. Fig. 2 (right panel) dis-
plays a typical vector of relevances in grey-scale. GRLVQ selects mainly those
pixels which correspond to the pronounced light region in normal head images.
Apparently, the achieved performance could be obtained from a comparison of
these regions only, while the acrosome and post nucleus cap densities are essen-
tially disregarded. This seems to indicate that the resolution of the obtained
images might be insufficient to exploit the latter information.
5 Summary and Outlook
We have applied several LVQ schemes in the classification of boar sperm head
images. Unlike other more sophisticated and more expensive approaches, we
aim at a classification which is based on grey-scale microscopic images only. We
are aware of only two earlier publications [7, 8] which report results based on
similar data and we find that plausible LVQ algorithms yield comparable, if not
superior performance. It is very well feasible that a more careful fine-tuning of
the LVQ algorithms, e.g. with respect to the learning rate schedule, will yield
an even lower classification error.
Cross validation estimates of test display a rather weak dependence on the
number of employed prototypes. When comparing the use of L1- vs. Euclidean
distances in LVQ1, we find the latter to be superior and restrict the further
analysis to this case. While the heuristic LVQ1 yields relatively low test error,
here, the cost function based GLVQ is clearly inferior. Better performance is
recovered when introducing adaptive relevance factors in the frame of GRLVQ.
The training of relevance factors reveals insight into what features the clas-
sification is based on. We find that a test error of about 0.20 can be achieved
by comparing a small characteristic region of the grey-scale data. The latter
corresponds to a pronounced low density region in images of normal sperm
heads. While acrosome density is believed to carry relevant information, they
are essentially disregarded here. In forthcoming investigations we will aim at
further optimization of the training process and LVQ architectures. For now, it
remains an open question if the data in its current form is sufficient to achieve
significantly better classification schemes.
Finally, we would like to point out that the goal in semen quality assessment
is not necessarily a low error rate with respect to single image classification.
The aim is to estimate with high precision the fraction of non-normal heads in
a sample of unknown composition [8]. The design of a classifier appropriate for
this purpose will be aimed at in a forthcoming project.
References
[1] Bibliography on the Self-Organizing Map (SOM) and Learning Vector Quantization
(LVQ), Neural Networks Research Centre, Helsinki University of Technology, 2002.
[2] A.S. Sato and K. Yamada, Generalized learning vector quantization. In: G. Tesauro,
D. Touretzky, and T. Leen, eds., Advances in Neural Information Processing Systems 7
(MIT Press, 1995)
[3] B. Hammer and T. Villmann, Generalized relevance learning vector quantization, Neural
Networks 15: 1059-1068, 2002.
[4] T. Kohonen, Self-organizing maps, Springer, Berlin, 1995.
[5] L. Thurston, W. Holt, and P. Watson. Post-thaw functional status of boar spermatozoa
cryopreserved using three rate freezers: a comparison. Theriogenology, 60:101–113, 2003.
[6] M. Hirai et, A. Boersma, A. Hoeflich, E. Wolf, J. Foll, T.R. Aumuller, and J. Braun.
Objectively measured sperm motility and sperm head morphometry in boars (Sus scrofa):
relation to fertility and seminal plasma growth factors. J. Androl, 22:104–110, 2001.
[7] L. Sa´nchez, N. Petkov, and E. Alegre. Statistical Approach to Boar Semen Head Classi-
fication Based on Intracellular Intensity Distribution. In A. Gagalowicz and W. Philips,
editors, Proceedings of 11th International Conference, CAIP 2005, Lecture Notes in
Computer Science, Vol. 3691, pages 88–95. Springer-Verlag, 2005.
[8] L. Sa´nchez, N. Petkov, and E. Alegre. Classification of boar spermatozoid head images
using a model intracellular density distribution. In M. Lazo and A. Sanfeliu, edi-
tors, Progress in Pattern Recognition, Image Analysis and Applications: Proc. 10th
Iberoamerican Congress on Pattern Recognition, CIARP 2005, pages 154-160. Springer-
Verlag, 2005.


Classification of Boar Sperm Head Images using Learning Vector Quantization

University of Groningen

   University of GroningenClassification of Boar Sperm Head Images using Learning Vector QuantizationBiehl, Michael; Pasma, Piter; Pijl, Marten; Sánchez, Lidia; Petkov, NicolaiPublished in:Proc. European Symposium on Artificial Neural NetworksIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2006Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Biehl, M., Pasma, P., Pijl, M., Sánchez, L., & Petkov, N. (2006). Classification of Boar Sperm Head Imagesusing Learning Vector Quantization. In M. Verleysen (Ed.), Proc. European Symposium on Artificial NeuralNetworks: ESANN 2006 d-side publishing.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 12-11-2019Classification of Boar Sperm Head Images usingLearning Vector QuantizationMichael Biehl1, Piter Pasma1, Marten Pijl1, Lidia Sa´nchez2 and Nicolai Petkov11- Rijksuniversiteit Groningen - Mathematics and Computing ScienceP.O. Box 800, NL-9700 AV Groningen - The Netherlands2- University of Leo´n - Department of Electrical and Electronics EngineeringCampus de Vegazana s/n, 24071 Leo´n - SpainAbstract. We apply Learning Vector Quantization (LVQ) in automatedboar semen quality assessment. The classification of single boar spermheads into healthy (normal) and non-normal ones is based on grey-scalemicroscopic images only. Sample data was classified by veterinary expertsand is used for training a system with a number of prototypes for eachclass. We apply as training schemes Kohonen’s LVQ1 and the variantsGeneralized LVQ (GLVQ) and Generalized Relevance LVQ (GRLVQ).We compare their performance and study the influence of the employedmetric.1 IntroductionSemen quality assessment constitutes an important problem in fertility studies.Existing, relatively costly methods rely on staining or motility measurements.Mostly they have originally been developed for the analysis of human semen andclinical purposes. Here, the aim is a fast and relatively cheap reliable methodfor the inspection of boar semen samples on the basis of microscopic images.We apply methods of prototype based clustering and classification. Learningvector quantization (LVQ) as originally proposed by Kohonen is widely used ina variety of areas due to its flexibility and conceptual simplicity [1, 4]. LVQprovides a particularly intuitive and clear approach: the classification of datais based on a set of so-called prototype vectors and a feature vector is assignedto the class represented by the closest prototype.Frequently, distances are evaluated in terms of simple Euclidean metrics, butalternative measures can easily be incorporated into the standard LVQ schemes.The choice of an appropriate distance measure can indeed be crucial in practicalproblems. Recent variations of LVQ have been suggested in which an adaptivemetric is modified in the course of learning.One of the most attractive features of LVQ learning is that the parameter-ization in terms of prototype vectors allows for an immediate interpretation ofthe classifier. Prototypes are defined in the same space as the data; they are, forinstance, images themselves and provide direct information about the achievedclustering and the features that it is based on. This is in contrast to othermethods, including feed-forward neural networks and the support vector ma-chine which in general cannot be interpreted as easily. The paper is organizedas follows: in the next section we outline the problem and summarize how thedata has been acquired and pre-processed. In section 3, we describe the LVQclassifier and training algorithms. The results are presented and discussed insection 4 and we conclude with a brief summary in 5.2 Classification problem and data acquisitionComputer assisted analysis of semen fertility has been used to save costs and im-prove quality in artificial insemination. Sperm analysis is a complex task whichallows to identify the males with the best reproductive features and control thefertility of the samples. Some approaches have used image analysis techniquesto detect shape abnormalities in sperm heads [6] or classify subpopulations in asample. However, only very few methods use the information of the acrosomeintegrity or the intracellular distribution to evaluate the sperm quality [7, 8].Several commercial systems have been developed, which were designed specif-ically for human sperm cells and have been adapted to other species later. Theydo not consider the intracellular density distribution which provides informationabout the cell status.Veterinary experts hypothesize that there are certain patterns of cytoplasmdensity distributions which can be correlated with alive and dead sperm cells.Techniques such as fluorescence staining protocols mark sperm heads dependingon if they are alive of dead. However, these methods are expensive and requiremore work in the sample preparation. The goal of this work is to classify thesperm head images without using staining techniques in order to speed up theprocess and reduce the costs.The 1360 images used in this project are obtained from boar semen samplesby use of a phase-contrast microscope. The first processing and segmentationsteps provide aligned images of isolated sperm heads as grey-level distributionson a black (empty) background. For details of acquisition and pre-processingsee [7].Sperm heads typically display an oval shape which we approximate by anellipse. We determine its principal axes and align all images. Using nearest-neighbor interpolation, we re-scale all head images to the same aspect ratio of19 x 35 pixels. Finally, we consider an array of grey-levels which lie inside theellipse with main axes 19 and 35 pixels.Intracellular intensities in heads which were labelled as normal by veterinaryexperts display three areas: a darker region corresponding to the post nucleuscap where the tail develops from, an intermediate light area and the acrosomewhich is covering the nucleus region, see Fig. 1 for example images. As the illu-mination of the samples under the microscope is controlled manually, brightnessand contrast can vary significantly across different images. To cope with thisproblem, we perform a linear transformation which results in the same mean,µ = 100, and standard deviation, σ = 8, of the grey-levels in all images.We represent example images as vectors ξµ ∈ IRN where the N = 35 ×19 = 665 components correspond to a rectangle. All pixels outside the abovementioned ellipsoidal regions are the same in every ξµ and will play no role inthe LVQ training and classification performance. Due to variations in shape,also the ellipses can contain pixels or entire regions which do not correspondFig. 1: Examples of sperm heads which were labelled as normal (left panel)or non-normal (right panel), respectively. For clarity, background pixels aredisplayed black while for the classification they are set to the overall mean valueof all non-background pixels, see the discussion in section 2.to intracellular densities but are part of the black background in Fig. 1. In[7], such pixels were explicitly excluded when comparing different heads, whichessentially disregards differences in shape. Here, we have chosen to replacethem by a constant value, i.e. the total mean of non-background grey-scalesover all example images. Thus, we are taking into account deformations butavoid artificially large differences between corresponding pixels. By choice ofthe constant one could vary the emphasis that is put on shape, the effect of thiswill be studied in a forthcoming project.3 LVQ system and training algorithmsTraining is based on the repeated random sequential presentation of exampleimages drawn from a given (sub-) set of data ID = {ξµ, SµT }Pµ=1. Here the classmembership label as provided by the veterinary experts isSµT = +1 if ξµ is marked as normal and SµT = −1 else. (1)In the set of M prototypes{w1,w2, . . . ,wM}a vector wk is supposed to repre-sent data from class Sk ∈ {−1,+1}. Upon presentation of the pair (ξµ, SµT ) attime step t, we evaluate the distance of ξµ from the current prototypes wj(t).In the following we will use three different distance measures d(j, µ):a) (squared) Euclidean: d2(j, µ) =(ξµ −wj(t))2=∑Ni=1(ξµi − wji (t))2b) generalized (squared) Euclidean: d2,λ(j, µ) =∑Ni=1 λi(ξµi − wji (t))2with the positive and normalized relevances λi > 0,∑i λ2i = 1c) L1 metric: d1(j, µ) =∑Ni=1∣∣∣ξµi − wji (t)∣∣∣ .In any case we identify the minimal distances d(j, µ) among prototypes withclass labels SjT = +1 and SjT = −1 separately and use the notation{wJ(t) (correct winner) with d(J, µ) = mink{d(k, µ)|Sk = +SµT}wK(t) (wrong winner) with d(K,µ) = mink{d(k, µ)|Sk = −SµT}.(2)Further, the total winner is denoted aswL(t) ={wJ (t) if d(J, µ) < d(K,µ)wK(t) else.We consider the following training schemes:Fig. 2: Left panel: The upper (lower) row displays prototypes in LVQ1 fornormal (non-normal) heads, respectively. Right panel: Relevances as obtainedby GRLVQ: the classification is based on very few components with considerableλi, corresponding to the dark region in the figure.a) LVQ1At each learning step, only the total winner wL(t) is updated:wL(t+ 1) = wL(t) + η(t)[SµT SL](ξµ −wL(t))(3)The update is towards (away from) the input ξµ if the class label of thewinning prototype and that of the example agree (disagree). In LVQ1 wehave considered the use of the distance measures d2(j, µ) and d1(j, µ).b) GLVQIn this learning scheme we restrict our implementation to the Euclideandistance measure d(j, µ) = d2(j, µ). Both winning prototypes, wJ andwK , are modified. Defining zµ = (d(J, µ) − d(K,µ))/ (d(J, µ) + d(K,µ))the update of wJ can be written aswJ(t+ 1) = wJ (t) + η(t)[SµTSJ ]f ′ (zµ)d(K,µ)(d(J, µ) + d(K,µ))2(ξµ −wJ (t))(4)and that of wK is of the same form with indices K and J exchanged.This corresponds to a step in the direction of the negative gradient ofthe function f(zµ) w.r.t. wK and wL. The function f has been set tof(x) = (1 + e−x)−1 in [2, 3]. For the limited range of possible arguments−1 ≤ zµ ≤ 1 the sigmoidal is very close to linear, however, and we replaceit by the simpler f(x) = x, f ′(x) = 1 in the following.c) GRLVQIn GRLVQ as suggested in [3], the distance measure d(j, µ) = d2,λ(j, µ) isused and the cost function f(zµ) = zµ of GLVQ is re-defined accordingly.Both prototypes wJ (t), wK(t) and also the relevances λi are updated inthe direction of the respective negative gradient, see [3] for details.In all considered algorithms the learning rate should gradually decrease in thecourse of learning. We have implemented a schedule of the formη(t) = ηo for τ < τo and η(t) = ηo/[1 + b(τ − τo)] for τ ≥ τo.Here, τ counts the number of randomly shuﬄed sweeps through the actualtraining set. In each training process we have performed 80 such sweeps andused the values τo = 10, ηo = 0.1, and b = 0.3.4 ResultsIn order to evaluate the quality of the obtained classification we have performedten-fold cross-validation: We split the set of 1360 available data into ten disjointsubsets IDi of equal size. For a given number of prototypes each of ten identi-cally designed LVQ systems (n = 1, 2, . . . 10) was trained from ∪i6=nIDi, whileIDn served as a test set. The following table summarizes some of our results:# of prototypes: 3 / 3 (normal/non-normal) 1 / 7LVQ1 (L1 measure) test = 0.232 (σ = 0.037) test = 0.215 (σ = 0.058)LVQ1 (Euclidean) test = 0.186 (σ = 0.040) test = 0.184 (σ = 0.045)GLVQ (Euclidean) test = 0.244 (σ = 0.041) test = 0.236 (σ = 0.038)GRLVQ (Euclidean) test = 0.185 (σ = 0.035) test = 0.183 (σ = 0.037)Here test is the mean test error and σ denotes its standard deviation over theten (statistically dependent) training sets. Note that a training error of 0.20comparable with the above test error was achieved for the same data set using asingle normal cell prototype and a distance threshold [7, 8]. We are not aware ofother published results for boar sperm head classification based on microscopicimages only.As a first result we note that the performance depends only weakly on thenumber of prototypes. Relatively low test errors can be achieved by using asingle prototype for the class of normal heads while the non-normal spermsare represented by several prototypes. We observe only weak variations and noindication of significant over–fitting in the considered range of 1−10 normal and3−16 non-normal prototypes. We have studied the performance of LVQ1 usingthe squared Euclidean distance as well as the L1-metric. In all considered caseswe have found a lower classification error when using the Euclidean measureand, hence, we restrict our comparison of different algorithms to this case.An important observation is that the performance of GLVQ is inferior to thatof LVQ1 (with Euclidean distances). One attractive feature of GLVQ is that itcan be interpreted as a gradient descent with respect to a plausible cost function.However, the relation of the latter with the goal of good generalization is notobvious. Indeed, we observe that, here, training and test error typically increasein the course of GLVQ training while the associated cost function decreases.By introducing adaptive relevances, the good performance of LVQ1 is recov-ered in GRLVQ. It is interesting to note that only very few relevances λi remainsignificantly different from zero in the training process. Fig. 2 (right panel) dis-plays a typical vector of relevances in grey-scale. GRLVQ selects mainly thosepixels which correspond to the pronounced light region in normal head images.Apparently, the achieved performance could be obtained from a comparison ofthese regions only, while the acrosome and post nucleus cap densities are essen-tially disregarded. This seems to indicate that the resolution of the obtainedimages might be insufficient to exploit the latter information.5 Summary and OutlookWe have applied several LVQ schemes in the classification of boar sperm headimages. Unlike other more sophisticated and more expensive approaches, weaim at a classification which is based on grey-scale microscopic images only. Weare aware of only two earlier publications [7, 8] which report results based onsimilar data and we find that plausible LVQ algorithms yield comparable, if notsuperior performance. It is very well feasible that a more careful fine-tuning ofthe LVQ algorithms, e.g. with respect to the learning rate schedule, will yieldan even lower classification error.Cross validation estimates of test display a rather weak dependence on thenumber of employed prototypes. When comparing the use of L1- vs. Euclideandistances in LVQ1, we find the latter to be superior and restrict the furtheranalysis to this case. While the heuristic LVQ1 yields relatively low test error,here, the cost function based GLVQ is clearly inferior. Better performance isrecovered when introducing adaptive relevance factors in the frame of GRLVQ.The training of relevance factors reveals insight into what features the clas-sification is based on. We find that a test error of about 0.20 can be achievedby comparing a small characteristic region of the grey-scale data. The lattercorresponds to a pronounced low density region in images of normal spermheads. While acrosome density is believed to carry relevant information, theyare essentially disregarded here. In forthcoming investigations we will aim atfurther optimization of the training process and LVQ architectures. For now, itremains an open question if the data in its current form is sufficient to achievesignificantly better classification schemes.Finally, we would like to point out that the goal in semen quality assessmentis not necessarily a low error rate with respect to single image classification.The aim is to estimate with high precision the fraction of non-normal heads ina sample of unknown composition [8]. The design of a classifier appropriate forthis purpose will be aimed at in a forthcoming project.References[1] Bibliography on the Self-Organizing Map (SOM) and Learning Vector Quantization(LVQ), Neural Networks Research Centre, Helsinki University of Technology, 2002.[2] A.S. Sato and K. Yamada, Generalized learning vector quantization. In: G. Tesauro,D. Touretzky, and T. Leen, eds., Advances in Neural Information Processing Systems 7(MIT Press, 1995)[3] B. Hammer and T. Villmann, Generalized relevance learning vector quantization, NeuralNetworks 15: 1059-1068, 2002.[4] T. Kohonen, Self-organizing maps, Springer, Berlin, 1995.[5] L. Thurston, W. Holt, and P. Watson. Post-thaw functional status of boar spermatozoacryopreserved using three rate freezers: a comparison. Theriogenology, 60:101–113, 2003.[6] M. Hirai et, A. Boersma, A. Hoeflich, E. Wolf, J. Foll, T.R. Aumuller, and J. Braun.Objectively measured sperm motility and sperm head morphometry in boars (Sus scrofa):relation to fertility and seminal plasma growth factors. J. Androl, 22:104–110, 2001.[7] L. Sa´nchez, N. Petkov, and E. Alegre. Statistical Approach to Boar Semen Head Classi-fication Based on Intracellular Intensity Distribution. In A. Gagalowicz and W. Philips,editors, Proceedings of 11th International Conference, CAIP 2005, Lecture Notes inComputer Science, Vol. 3691, pages 88–95. Springer-Verlag, 2005.[8] L. Sa´nchez, N. Petkov, and E. Alegre. Classification of boar spermatozoid head imagesusing a model intracellular density distribution. In M. Lazo and A. Sanfeliu, edi-tors, Progress in Pattern Recognition, Image Analysis and Applications: Proc. 10thIberoamerican Congress on Pattern Recognition, CIARP 2005, pages 154-160. Springer-Verlag, 2005.

ARTS repository - University of Groningen

   University of GroningenClassification of Boar Sperm Head Images using Learning Vector QuantizationBiehl, Michael; Pasma, Piter; Pijl, Marten; Sánchez, Lidia; Petkov, NicolaiPublished in:Proc. European Symposium on Artificial Neural NetworksIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2006Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Biehl, M., Pasma, P., Pijl, M., Sánchez, L., & Petkov, N. (2006). Classification of Boar Sperm Head Imagesusing Learning Vector Quantization. In M. Verleysen (Ed.), Proc. European Symposium on Artificial NeuralNetworks: ESANN 2006 d-side publishing.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 20-06-2022Classification of Boar Sperm Head Images usingLearning Vector QuantizationMichael Biehl1, Piter Pasma1, Marten Pijl1, Lidia Sánchez2 and Nicolai Petkov11- Rijksuniversiteit Groningen - Mathematics and Computing ScienceP.O. Box 800, NL-9700 AV Groningen - The Netherlands2- University of León - Department of Electrical and Electronics EngineeringCampus de Vegazana s/n, 24071 León - SpainAbstract. We apply Learning Vector Quantization (LVQ) in automatedboar semen quality assessment. The classification of single boar spermheads into healthy (normal) and non-normal ones is based on grey-scalemicroscopic images only. Sample data was classified by veterinary expertsand is used for training a system with a number of prototypes for eachclass. We apply as training schemes Kohonen’s LVQ1 and the variantsGeneralized LVQ (GLVQ) and Generalized Relevance LVQ (GRLVQ).We compare their performance and study the influence of the employedmetric.1 IntroductionSemen quality assessment constitutes an important problem in fertility studies.Existing, relatively costly methods rely on staining or motility measurements.Mostly they have originally been developed for the analysis of human semen andclinical purposes. Here, the aim is a fast and relatively cheap reliable methodfor the inspection of boar semen samples on the basis of microscopic images.We apply methods of prototype based clustering and classification. Learningvector quantization (LVQ) as originally proposed by Kohonen is widely used ina variety of areas due to its flexibility and conceptual simplicity [1, 4]. LVQprovides a particularly intuitive and clear approach: the classification of datais based on a set of so-called prototype vectors and a feature vector is assignedto the class represented by the closest prototype.Frequently, distances are evaluated in terms of simple Euclidean metrics, butalternative measures can easily be incorporated into the standard LVQ schemes.The choice of an appropriate distance measure can indeed be crucial in practicalproblems. Recent variations of LVQ have been suggested in which an adaptivemetric is modified in the course of learning.One of the most attractive features of LVQ learning is that the parameter-ization in terms of prototype vectors allows for an immediate interpretation ofthe classifier. Prototypes are defined in the same space as the data; they are, forinstance, images themselves and provide direct information about the achievedclustering and the features that it is based on. This is in contrast to othermethods, including feed-forward neural networks and the support vector ma-chine which in general cannot be interpreted as easily. The paper is organizedas follows: in the next section we outline the problem and summarize how thedata has been acquired and pre-processed. In section 3, we describe the LVQclassifier and training algorithms. The results are presented and discussed insection 4 and we conclude with a brief summary in 5.2 Classification problem and data acquisitionComputer assisted analysis of semen fertility has been used to save costs and im-prove quality in artificial insemination. Sperm analysis is a complex task whichallows to identify the males with the best reproductive features and control thefertility of the samples. Some approaches have used image analysis techniquesto detect shape abnormalities in sperm heads [6] or classify subpopulations in asample. However, only very few methods use the information of the acrosomeintegrity or the intracellular distribution to evaluate the sperm quality [7, 8].Several commercial systems have been developed, which were designed specif-ically for human sperm cells and have been adapted to other species later. Theydo not consider the intracellular density distribution which provides informationabout the cell status.Veterinary experts hypothesize that there are certain patterns of cytoplasmdensity distributions which can be correlated with alive and dead sperm cells.Techniques such as fluorescence staining protocols mark sperm heads dependingon if they are alive of dead. However, these methods are expensive and requiremore work in the sample preparation. The goal of this work is to classify thesperm head images without using staining techniques in order to speed up theprocess and reduce the costs.The 1360 images used in this project are obtained from boar semen samplesby use of a phase-contrast microscope. The first processing and segmentationsteps provide aligned images of isolated sperm heads as grey-level distributionson a black (empty) background. For details of acquisition and pre-processingsee [7].Sperm heads typically display an oval shape which we approximate by anellipse. We determine its principal axes and align all images. Using nearest-neighbor interpolation, we re-scale all head images to the same aspect ratio of19 x 35 pixels. Finally, we consider an array of grey-levels which lie inside theellipse with main axes 19 and 35 pixels.Intracellular intensities in heads which were labelled as normal by veterinaryexperts display three areas: a darker region corresponding to the post nucleuscap where the tail develops from, an intermediate light area and the acrosomewhich is covering the nucleus region, see Fig. 1 for example images. As the illu-mination of the samples under the microscope is controlled manually, brightnessand contrast can vary significantly across different images. To cope with thisproblem, we perform a linear transformation which results in the same mean,µ = 100, and standard deviation, σ = 8, of the grey-levels in all images.We represent example images as vectors ξµ ∈ IRN where the N = 35 ×19 = 665 components correspond to a rectangle. All pixels outside the abovementioned ellipsoidal regions are the same in every ξµ and will play no role inthe LVQ training and classification performance. Due to variations in shape,also the ellipses can contain pixels or entire regions which do not correspondFig. 1: Examples of sperm heads which were labelled as normal (left panel)or non-normal (right panel), respectively. For clarity, background pixels aredisplayed black while for the classification they are set to the overall mean valueof all non-background pixels, see the discussion in section 2.to intracellular densities but are part of the black background in Fig. 1. In[7], such pixels were explicitly excluded when comparing different heads, whichessentially disregards differences in shape. Here, we have chosen to replacethem by a constant value, i.e. the total mean of non-background grey-scalesover all example images. Thus, we are taking into account deformations butavoid artificially large differences between corresponding pixels. By choice ofthe constant one could vary the emphasis that is put on shape, the effect of thiswill be studied in a forthcoming project.3 LVQ system and training algorithmsTraining is based on the repeated random sequential presentation of exampleimages drawn from a given (sub-) set of data ID = {ξµ, SµT }Pµ=1. Here the classmembership label as provided by the veterinary experts isSµT = +1 if ξµ is marked as normal and SµT = −1 else. (1)In the set of M prototypes{w1,w2, . . . ,wM}a vector wk is supposed to repre-sent data from class Sk ∈ {−1, +1}. Upon presentation of the pair (ξµ, SµT ) attime step t, we evaluate the distance of ξµ from the current prototypes wj(t).In the following we will use three different distance measures d(j, µ):a) (squared) Euclidean: d2(j, µ) =(ξµ − wj(t))2=∑Ni=1(ξµi − wji (t))2b) generalized (squared) Euclidean: d2,λ(j, µ) =∑Ni=1 λi(ξµi − wji (t))2with the positive and normalized relevances λi > 0,∑i λ2i = 1c) L1 metric: d1(j, µ) =∑Ni=1∣∣∣ξµi − wji (t)∣∣∣.In any case we identify the minimal distances d(j, µ) among prototypes withclass labels SjT = +1 and SjT = −1 separately and use the notation{wJ(t) (correct winner) with d(J, µ) = mink{d(k, µ)|Sk = +SµT}wK(t) (wrong winner) with d(K, µ) = mink{d(k, µ)|Sk = −SµT}.(2)Further, the total winner is denoted as wL(t) ={wJ (t) if d(J, µ) < d(K, µ)wK(t) else.We consider the following training schemes:Fig. 2: Left panel: The upper (lower) row displays prototypes in LVQ1 fornormal (non-normal) heads, respectively. Right panel: Relevances as obtainedby GRLVQ: the classification is based on very few components with considerableλi, corresponding to the dark region in the figure.a) LVQ1At each learning step, only the total winner wL(t) is updated:wL(t + 1) = wL(t) + η(t)[SµT SL](ξµ − wL(t))(3)The update is towards (away from) the input ξµ if the class label of thewinning prototype and that of the example agree (disagree). In LVQ1 wehave considered the use of the distance measures d2(j, µ) and d1(j, µ).b) GLVQIn this learning scheme we restrict our implementation to the Euclideandistance measure d(j, µ) = d2(j, µ). Both winning prototypes, wJ andwK , are modified. Defining zµ = (d(J, µ) − d(K, µ))/ (d(J, µ) + d(K, µ))the update of wJ can be written aswJ(t + 1) = wJ (t) + η(t)[SµT SJ ]f ′ (zµ)d(K, µ)(d(J, µ) + d(K, µ))2(ξµ − wJ (t))(4)and that of wK is of the same form with indices K and J exchanged.This corresponds to a step in the direction of the negative gradient ofthe function f(zµ) w.r.t. wK and wL. The function f has been set tof(x) = (1 + e−x)−1 in [2, 3]. For the limited range of possible arguments−1 ≤ zµ ≤ 1 the sigmoidal is very close to linear, however, and we replaceit by the simpler f(x) = x, f ′(x) = 1 in the following.c) GRLVQIn GRLVQ as suggested in [3], the distance measure d(j, µ) = d2,λ(j, µ) isused and the cost function f(zµ) = zµ of GLVQ is re-defined accordingly.Both prototypes wJ (t), wK(t) and also the relevances λi are updated inthe direction of the respective negative gradient, see [3] for details.In all considered algorithms the learning rate should gradually decrease in thecourse of learning. We have implemented a schedule of the formη(t) = ηo for τ < τo and η(t) = ηo/[1 + b(τ − τo)] for τ ≥ τo.Here, τ counts the number of randomly shuffled sweeps through the actualtraining set. In each training process we have performed 80 such sweeps andused the values τo = 10, ηo = 0.1, and b = 0.3.4 ResultsIn order to evaluate the quality of the obtained classification we have performedten-fold cross-validation: We split the set of 1360 available data into ten disjointsubsets IDi of equal size. For a given number of prototypes each of ten identi-cally designed LVQ systems (n = 1, 2, . . . 10) was trained from ∪i6=nIDi, whileIDn served as a test set. The following table summarizes some of our results:# of prototypes: 3 / 3 (normal/non-normal) 1 / 7LVQ1 (L1 measure) εtest = 0.232 (σ = 0.037) εtest = 0.215 (σ = 0.058)LVQ1 (Euclidean) εtest = 0.186 (σ = 0.040) εtest = 0.184 (σ = 0.045)GLVQ (Euclidean) εtest = 0.244 (σ = 0.041) εtest = 0.236 (σ = 0.038)GRLVQ (Euclidean) εtest = 0.185 (σ = 0.035) εtest = 0.183 (σ = 0.037)Here εtest is the mean test error and σ denotes its standard deviation over theten (statistically dependent) training sets. Note that a training error of 0.20comparable with the above test error was achieved for the same data set using asingle normal cell prototype and a distance threshold [7, 8]. We are not aware ofother published results for boar sperm head classification based on microscopicimages only.As a first result we note that the performance depends only weakly on thenumber of prototypes. Relatively low test errors can be achieved by using asingle prototype for the class of normal heads while the non-normal spermsare represented by several prototypes. We observe only weak variations and noindication of significant over–fitting in the considered range of 1−10 normal and3−16 non-normal prototypes. We have studied the performance of LVQ1 usingthe squared Euclidean distance as well as the L1-metric. In all considered caseswe have found a lower classification error when using the Euclidean measureand, hence, we restrict our comparison of different algorithms to this case.An important observation is that the performance of GLVQ is inferior to thatof LVQ1 (with Euclidean distances). One attractive feature of GLVQ is that itcan be interpreted as a gradient descent with respect to a plausible cost function.However, the relation of the latter with the goal of good generalization is notobvious. Indeed, we observe that, here, training and test error typically increasein the course of GLVQ training while the associated cost function decreases.By introducing adaptive relevances, the good performance of LVQ1 is recov-ered in GRLVQ. It is interesting to note that only very few relevances λi remainsignificantly different from zero in the training process. Fig. 2 (right panel) dis-plays a typical vector of relevances in grey-scale. GRLVQ selects mainly thosepixels which correspond to the pronounced light region in normal head images.Apparently, the achieved performance could be obtained from a comparison ofthese regions only, while the acrosome and post nucleus cap densities are essen-tially disregarded. This seems to indicate that the resolution of the obtainedimages might be insufficient to exploit the latter information.5 Summary and OutlookWe have applied several LVQ schemes in the classification of boar sperm headimages. Unlike other more sophisticated and more expensive approaches, weaim at a classification which is based on grey-scale microscopic images only. Weare aware of only two earlier publications [7, 8] which report results based onsimilar data and we find that plausible LVQ algorithms yield comparable, if notsuperior performance. It is very well feasible that a more careful fine-tuning ofthe LVQ algorithms, e.g. with respect to the learning rate schedule, will yieldan even lower classification error.Cross validation estimates of εtest display a rather weak dependence on thenumber of employed prototypes. When comparing the use of L1- vs. Euclideandistances in LVQ1, we find the latter to be superior and restrict the furtheranalysis to this case. While the heuristic LVQ1 yields relatively low test error,here, the cost function based GLVQ is clearly inferior. Better performance isrecovered when introducing adaptive relevance factors in the frame of GRLVQ.The training of relevance factors reveals insight into what features the clas-sification is based on. We find that a test error of about 0.20 can be achievedby comparing a small characteristic region of the grey-scale data. The lattercorresponds to a pronounced low density region in images of normal spermheads. While acrosome density is believed to carry relevant information, theyare essentially disregarded here. In forthcoming investigations we will aim atfurther optimization of the training process and LVQ architectures. For now, itremains an open question if the data in its current form is sufficient to achievesignificantly better classification schemes.Finally, we would like to point out that the goal in semen quality assessmentis not necessarily a low error rate with respect to single image classification.The aim is to estimate with high precision the fraction of non-normal heads ina sample of unknown composition [8]. The design of a classifier appropriate forthis purpose will be aimed at in a forthcoming project.References[1] Bibliography on the Self-Organizing Map (SOM) and Learning Vector Quantization(LVQ), Neural Networks Research Centre, Helsinki University of Technology, 2002.[2] A.S. Sato and K. Yamada, Generalized learning vector quantization. In: G. Tesauro,D. Touretzky, and T. Leen, eds., Advances in Neural Information Processing Systems 7(MIT Press, 1995)[3] B. Hammer and T. Villmann, Generalized relevance learning vector quantization, NeuralNetworks 15: 1059-1068, 2002.[4] T. Kohonen, Self-organizing maps, Springer, Berlin, 1995.[5] L. Thurston, W. Holt, and P. Watson. Post-thaw functional status of boar spermatozoacryopreserved using three rate freezers: a comparison. Theriogenology, 60:101–113, 2003.[6] M. Hirai et, A. Boersma, A. Hoeflich, E. Wolf, J. Foll, T.R. Aumuller, and J. Braun.Objectively measured sperm motility and sperm head morphometry in boars (Sus scrofa):relation to fertility and seminal plasma growth factors. J. Androl, 22:104–110, 2001.[7] L. Sánchez, N. Petkov, and E. Alegre. Statistical Approach to Boar Semen Head Classi-fication Based on Intracellular Intensity Distribution. In A. Gagalowicz and W. Philips,editors, Proceedings of 11th International Conference, CAIP 2005, Lecture Notes inComputer Science, Vol. 3691, pages 88–95. Springer-Verlag, 2005.[8] L. Sánchez, N. Petkov, and E. Alegre. Classification of boar spermatozoid head imagesusing a model intracellular density distribution. In M. Lazo and A. Sanfeliu, edi-tors, Progress in Pattern Recognition, Image Analysis and Applications: Proc. 10thIberoamerican Congress on Pattern Recognition, CIARP 2005, pages 154-160. Springer-Verlag, 2005.

English

Proceedings - University of Groningen

   University of GroningenClassification of Boar Sperm Head Images using Learning Vector QuantizationBiehl, Michael; Pasma, Piter; Pijl, Marten; Sánchez, Lidia; Petkov, NicolaiPublished in:Proc. European Symposium on Artificial Neural NetworksIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2006Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Biehl, M., Pasma, P., Pijl, M., Sánchez, L., & Petkov, N. (2006). Classification of Boar Sperm Head Imagesusing Learning Vector Quantization. In M. Verleysen (Ed.), Proc. European Symposium on Artificial NeuralNetworks: ESANN 2006 d-side publishing.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 09-09-2023Classification of Boar Sperm Head Images usingLearning Vector QuantizationMichael Biehl1, Piter Pasma1, Marten Pijl1, Lidia Sánchez2 and Nicolai Petkov11- Rijksuniversiteit Groningen - Mathematics and Computing ScienceP.O. Box 800, NL-9700 AV Groningen - The Netherlands2- University of León - Department of Electrical and Electronics EngineeringCampus de Vegazana s/n, 24071 León - SpainAbstract. We apply Learning Vector Quantization (LVQ) in automatedboar semen quality assessment. The classification of single boar spermheads into healthy (normal) and non-normal ones is based on grey-scalemicroscopic images only. Sample data was classified by veterinary expertsand is used for training a system with a number of prototypes for eachclass. We apply as training schemes Kohonen’s LVQ1 and the variantsGeneralized LVQ (GLVQ) and Generalized Relevance LVQ (GRLVQ).We compare their performance and study the influence of the employedmetric.1 IntroductionSemen quality assessment constitutes an important problem in fertility studies.Existing, relatively costly methods rely on staining or motility measurements.Mostly they have originally been developed for the analysis of human semen andclinical purposes. Here, the aim is a fast and relatively cheap reliable methodfor the inspection of boar semen samples on the basis of microscopic images.We apply methods of prototype based clustering and classification. Learningvector quantization (LVQ) as originally proposed by Kohonen is widely used ina variety of areas due to its flexibility and conceptual simplicity [1, 4]. LVQprovides a particularly intuitive and clear approach: the classification of datais based on a set of so-called prototype vectors and a feature vector is assignedto the class represented by the closest prototype.Frequently, distances are evaluated in terms of simple Euclidean metrics, butalternative measures can easily be incorporated into the standard LVQ schemes.The choice of an appropriate distance measure can indeed be crucial in practicalproblems. Recent variations of LVQ have been suggested in which an adaptivemetric is modified in the course of learning.One of the most attractive features of LVQ learning is that the parameter-ization in terms of prototype vectors allows for an immediate interpretation ofthe classifier. Prototypes are defined in the same space as the data; they are, forinstance, images themselves and provide direct information about the achievedclustering and the features that it is based on. This is in contrast to othermethods, including feed-forward neural networks and the support vector ma-chine which in general cannot be interpreted as easily. The paper is organizedas follows: in the next section we outline the problem and summarize how thedata has been acquired and pre-processed. In section 3, we describe the LVQclassifier and training algorithms. The results are presented and discussed insection 4 and we conclude with a brief summary in 5.2 Classification problem and data acquisitionComputer assisted analysis of semen fertility has been used to save costs and im-prove quality in artificial insemination. Sperm analysis is a complex task whichallows to identify the males with the best reproductive features and control thefertility of the samples. Some approaches have used image analysis techniquesto detect shape abnormalities in sperm heads [6] or classify subpopulations in asample. However, only very few methods use the information of the acrosomeintegrity or the intracellular distribution to evaluate the sperm quality [7, 8].Several commercial systems have been developed, which were designed specif-ically for human sperm cells and have been adapted to other species later. Theydo not consider the intracellular density distribution which provides informationabout the cell status.Veterinary experts hypothesize that there are certain patterns of cytoplasmdensity distributions which can be correlated with alive and dead sperm cells.Techniques such as fluorescence staining protocols mark sperm heads dependingon if they are alive of dead. However, these methods are expensive and requiremore work in the sample preparation. The goal of this work is to classify thesperm head images without using staining techniques in order to speed up theprocess and reduce the costs.The 1360 images used in this project are obtained from boar semen samplesby use of a phase-contrast microscope. The first processing and segmentationsteps provide aligned images of isolated sperm heads as grey-level distributionson a black (empty) background. For details of acquisition and pre-processingsee [7].Sperm heads typically display an oval shape which we approximate by anellipse. We determine its principal axes and align all images. Using nearest-neighbor interpolation, we re-scale all head images to the same aspect ratio of19 x 35 pixels. Finally, we consider an array of grey-levels which lie inside theellipse with main axes 19 and 35 pixels.Intracellular intensities in heads which were labelled as normal by veterinaryexperts display three areas: a darker region corresponding to the post nucleuscap where the tail develops from, an intermediate light area and the acrosomewhich is covering the nucleus region, see Fig. 1 for example images. As the illu-mination of the samples under the microscope is controlled manually, brightnessand contrast can vary significantly across different images. To cope with thisproblem, we perform a linear transformation which results in the same mean,µ = 100, and standard deviation, σ = 8, of the grey-levels in all images.We represent example images as vectors ξµ ∈ IRN where the N = 35 ×19 = 665 components correspond to a rectangle. All pixels outside the abovementioned ellipsoidal regions are the same in every ξµ and will play no role inthe LVQ training and classification performance. Due to variations in shape,also the ellipses can contain pixels or entire regions which do not correspondFig. 1: Examples of sperm heads which were labelled as normal (left panel)or non-normal (right panel), respectively. For clarity, background pixels aredisplayed black while for the classification they are set to the overall mean valueof all non-background pixels, see the discussion in section 2.to intracellular densities but are part of the black background in Fig. 1. In[7], such pixels were explicitly excluded when comparing different heads, whichessentially disregards differences in shape. Here, we have chosen to replacethem by a constant value, i.e. the total mean of non-background grey-scalesover all example images. Thus, we are taking into account deformations butavoid artificially large differences between corresponding pixels. By choice ofthe constant one could vary the emphasis that is put on shape, the effect of thiswill be studied in a forthcoming project.3 LVQ system and training algorithmsTraining is based on the repeated random sequential presentation of exampleimages drawn from a given (sub-) set of data ID = {ξµ, SµT }Pµ=1. Here the classmembership label as provided by the veterinary experts isSµT = +1 if ξµ is marked as normal and SµT = −1 else. (1)In the set of M prototypes{w1,w2, . . . ,wM}a vector wk is supposed to repre-sent data from class Sk ∈ {−1, +1}. Upon presentation of the pair (ξµ, SµT ) attime step t, we evaluate the distance of ξµ from the current prototypes wj(t).In the following we will use three different distance measures d(j, µ):a) (squared) Euclidean: d2(j, µ) =(ξµ − wj(t))2=∑Ni=1(ξµi − wji (t))2b) generalized (squared) Euclidean: d2,λ(j, µ) =∑Ni=1 λi(ξµi − wji (t))2with the positive and normalized relevances λi > 0,∑i λ2i = 1c) L1 metric: d1(j, µ) =∑Ni=1∣∣∣ξµi − wji (t)∣∣∣.In any case we identify the minimal distances d(j, µ) among prototypes withclass labels SjT = +1 and SjT = −1 separately and use the notation{wJ(t) (correct winner) with d(J, µ) = mink{d(k, µ)|Sk = +SµT}wK(t) (wrong winner) with d(K, µ) = mink{d(k, µ)|Sk = −SµT}.(2)Further, the total winner is denoted as wL(t) ={wJ (t) if d(J, µ) < d(K, µ)wK(t) else.We consider the following training schemes:Fig. 2: Left panel: The upper (lower) row displays prototypes in LVQ1 fornormal (non-normal) heads, respectively. Right panel: Relevances as obtainedby GRLVQ: the classification is based on very few components with considerableλi, corresponding to the dark region in the figure.a) LVQ1At each learning step, only the total winner wL(t) is updated:wL(t + 1) = wL(t) + η(t)[SµT SL](ξµ − wL(t))(3)The update is towards (away from) the input ξµ if the class label of thewinning prototype and that of the example agree (disagree). In LVQ1 wehave considered the use of the distance measures d2(j, µ) and d1(j, µ).b) GLVQIn this learning scheme we restrict our implementation to the Euclideandistance measure d(j, µ) = d2(j, µ). Both winning prototypes, wJ andwK , are modified. Defining zµ = (d(J, µ) − d(K, µ))/ (d(J, µ) + d(K, µ))the update of wJ can be written aswJ(t + 1) = wJ (t) + η(t)[SµT SJ ]f ′ (zµ)d(K, µ)(d(J, µ) + d(K, µ))2(ξµ − wJ (t))(4)and that of wK is of the same form with indices K and J exchanged.This corresponds to a step in the direction of the negative gradient ofthe function f(zµ) w.r.t. wK and wL. The function f has been set tof(x) = (1 + e−x)−1 in [2, 3]. For the limited range of possible arguments−1 ≤ zµ ≤ 1 the sigmoidal is very close to linear, however, and we replaceit by the simpler f(x) = x, f ′(x) = 1 in the following.c) GRLVQIn GRLVQ as suggested in [3], the distance measure d(j, µ) = d2,λ(j, µ) isused and the cost function f(zµ) = zµ of GLVQ is re-defined accordingly.Both prototypes wJ (t), wK(t) and also the relevances λi are updated inthe direction of the respective negative gradient, see [3] for details.In all considered algorithms the learning rate should gradually decrease in thecourse of learning. We have implemented a schedule of the formη(t) = ηo for τ < τo and η(t) = ηo/[1 + b(τ − τo)] for τ ≥ τo.Here, τ counts the number of randomly shuffled sweeps through the actualtraining set. In each training process we have performed 80 such sweeps andused the values τo = 10, ηo = 0.1, and b = 0.3.4 ResultsIn order to evaluate the quality of the obtained classification we have performedten-fold cross-validation: We split the set of 1360 available data into ten disjointsubsets IDi of equal size. For a given number of prototypes each of ten identi-cally designed LVQ systems (n = 1, 2, . . . 10) was trained from ∪i6=nIDi, whileIDn served as a test set. The following table summarizes some of our results:# of prototypes: 3 / 3 (normal/non-normal) 1 / 7LVQ1 (L1 measure) εtest = 0.232 (σ = 0.037) εtest = 0.215 (σ = 0.058)LVQ1 (Euclidean) εtest = 0.186 (σ = 0.040) εtest = 0.184 (σ = 0.045)GLVQ (Euclidean) εtest = 0.244 (σ = 0.041) εtest = 0.236 (σ = 0.038)GRLVQ (Euclidean) εtest = 0.185 (σ = 0.035) εtest = 0.183 (σ = 0.037)Here εtest is the mean test error and σ denotes its standard deviation over theten (statistically dependent) training sets. Note that a training error of 0.20comparable with the above test error was achieved for the same data set using asingle normal cell prototype and a distance threshold [7, 8]. We are not aware ofother published results for boar sperm head classification based on microscopicimages only.As a first result we note that the performance depends only weakly on thenumber of prototypes. Relatively low test errors can be achieved by using asingle prototype for the class of normal heads while the non-normal spermsare represented by several prototypes. We observe only weak variations and noindication of significant over–fitting in the considered range of 1−10 normal and3−16 non-normal prototypes. We have studied the performance of LVQ1 usingthe squared Euclidean distance as well as the L1-metric. In all considered caseswe have found a lower classification error when using the Euclidean measureand, hence, we restrict our comparison of different algorithms to this case.An important observation is that the performance of GLVQ is inferior to thatof LVQ1 (with Euclidean distances). One attractive feature of GLVQ is that itcan be interpreted as a gradient descent with respect to a plausible cost function.However, the relation of the latter with the goal of good generalization is notobvious. Indeed, we observe that, here, training and test error typically increasein the course of GLVQ training while the associated cost function decreases.By introducing adaptive relevances, the good performance of LVQ1 is recov-ered in GRLVQ. It is interesting to note that only very few relevances λi remainsignificantly different from zero in the training process. Fig. 2 (right panel) dis-plays a typical vector of relevances in grey-scale. GRLVQ selects mainly thosepixels which correspond to the pronounced light region in normal head images.Apparently, the achieved performance could be obtained from a comparison ofthese regions only, while the acrosome and post nucleus cap densities are essen-tially disregarded. This seems to indicate that the resolution of the obtainedimages might be insufficient to exploit the latter information.5 Summary and OutlookWe have applied several LVQ schemes in the classification of boar sperm headimages. Unlike other more sophisticated and more expensive approaches, weaim at a classification which is based on grey-scale microscopic images only. Weare aware of only two earlier publications [7, 8] which report results based onsimilar data and we find that plausible LVQ algorithms yield comparable, if notsuperior performance. It is very well feasible that a more careful fine-tuning ofthe LVQ algorithms, e.g. with respect to the learning rate schedule, will yieldan even lower classification error.Cross validation estimates of εtest display a rather weak dependence on thenumber of employed prototypes. When comparing the use of L1- vs. Euclideandistances in LVQ1, we find the latter to be superior and restrict the furtheranalysis to this case. While the heuristic LVQ1 yields relatively low test error,here, the cost function based GLVQ is clearly inferior. Better performance isrecovered when introducing adaptive relevance factors in the frame of GRLVQ.The training of relevance factors reveals insight into what features the clas-sification is based on. We find that a test error of about 0.20 can be achievedby comparing a small characteristic region of the grey-scale data. The lattercorresponds to a pronounced low density region in images of normal spermheads. While acrosome density is believed to carry relevant information, theyare essentially disregarded here. In forthcoming investigations we will aim atfurther optimization of the training process and LVQ architectures. For now, itremains an open question if the data in its current form is sufficient to achievesignificantly better classification schemes.Finally, we would like to point out that the goal in semen quality assessmentis not necessarily a low error rate with respect to single image classification.The aim is to estimate with high precision the fraction of non-normal heads ina sample of unknown composition [8]. The design of a classifier appropriate forthis purpose will be aimed at in a forthcoming project.References[1] Bibliography on the Self-Organizing Map (SOM) and Learning Vector Quantization(LVQ), Neural Networks Research Centre, Helsinki University of Technology, 2002.[2] A.S. Sato and K. Yamada, Generalized learning vector quantization. In: G. Tesauro,D. Touretzky, and T. Leen, eds., Advances in Neural Information Processing Systems 7(MIT Press, 1995)[3] B. Hammer and T. Villmann, Generalized relevance learning vector quantization, NeuralNetworks 15: 1059-1068, 2002.[4] T. Kohonen, Self-organizing maps, Springer, Berlin, 1995.[5] L. Thurston, W. Holt, and P. Watson. Post-thaw functional status of boar spermatozoacryopreserved using three rate freezers: a comparison. Theriogenology, 60:101–113, 2003.[6] M. Hirai et, A. Boersma, A. Hoeflich, E. Wolf, J. Foll, T.R. Aumuller, and J. Braun.Objectively measured sperm motility and sperm head morphometry in boars (Sus scrofa):relation to fertility and seminal plasma growth factors. J. Androl, 22:104–110, 2001.[7] L. Sánchez, N. Petkov, and E. Alegre. Statistical Approach to Boar Semen Head Classi-fication Based on Intracellular Intensity Distribution. In A. Gagalowicz and W. Philips,editors, Proceedings of 11th International Conference, CAIP 2005, Lecture Notes inComputer Science, Vol. 3691, pages 88–95. Springer-Verlag, 2005.[8] L. Sánchez, N. Petkov, and E. Alegre. Classification of boar spermatozoid head imagesusing a model intracellular density distribution. In M. Lazo and A. Sanfeliu, edi-tors, Progress in Pattern Recognition, Image Analysis and Applications: Proc. 10thIberoamerican Congress on Pattern Recognition, CIARP 2005, pages 154-160. Springer-Verlag, 2005.

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   University of GroningenClassification of Boar Sperm Head Images using Learning Vector QuantizationBiehl, Michael; Pasma, Piter; Pijl, Marten; Sánchez, Lidia; Petkov, NicolaiPublished in:Proc. European Symposium on Artificial Neural NetworksIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2006Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Biehl, M., Pasma, P., Pijl, M., Sánchez, L., & Petkov, N. (2006). Classification of Boar Sperm Head Imagesusing Learning Vector Quantization. In M. Verleysen (Ed.), Proc. European Symposium on Artificial NeuralNetworks: ESANN 2006 d-side publishing.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 28-12-2022Classification of Boar Sperm Head Images usingLearning Vector QuantizationMichael Biehl1, Piter Pasma1, Marten Pijl1, Lidia Sánchez2 and Nicolai Petkov11- Rijksuniversiteit Groningen - Mathematics and Computing ScienceP.O. Box 800, NL-9700 AV Groningen - The Netherlands2- University of León - Department of Electrical and Electronics EngineeringCampus de Vegazana s/n, 24071 León - SpainAbstract. We apply Learning Vector Quantization (LVQ) in automatedboar semen quality assessment. The classification of single boar spermheads into healthy (normal) and non-normal ones is based on grey-scalemicroscopic images only. Sample data was classified by veterinary expertsand is used for training a system with a number of prototypes for eachclass. We apply as training schemes Kohonen’s LVQ1 and the variantsGeneralized LVQ (GLVQ) and Generalized Relevance LVQ (GRLVQ).We compare their performance and study the influence of the employedmetric.1 IntroductionSemen quality assessment constitutes an important problem in fertility studies.Existing, relatively costly methods rely on staining or motility measurements.Mostly they have originally been developed for the analysis of human semen andclinical purposes. Here, the aim is a fast and relatively cheap reliable methodfor the inspection of boar semen samples on the basis of microscopic images.We apply methods of prototype based clustering and classification. Learningvector quantization (LVQ) as originally proposed by Kohonen is widely used ina variety of areas due to its flexibility and conceptual simplicity [1, 4]. LVQprovides a particularly intuitive and clear approach: the classification of datais based on a set of so-called prototype vectors and a feature vector is assignedto the class represented by the closest prototype.Frequently, distances are evaluated in terms of simple Euclidean metrics, butalternative measures can easily be incorporated into the standard LVQ schemes.The choice of an appropriate distance measure can indeed be crucial in practicalproblems. Recent variations of LVQ have been suggested in which an adaptivemetric is modified in the course of learning.One of the most attractive features of LVQ learning is that the parameter-ization in terms of prototype vectors allows for an immediate interpretation ofthe classifier. Prototypes are defined in the same space as the data; they are, forinstance, images themselves and provide direct information about the achievedclustering and the features that it is based on. This is in contrast to othermethods, including feed-forward neural networks and the support vector ma-chine which in general cannot be interpreted as easily. The paper is organizedas follows: in the next section we outline the problem and summarize how thedata has been acquired and pre-processed. In section 3, we describe the LVQclassifier and training algorithms. The results are presented and discussed insection 4 and we conclude with a brief summary in 5.2 Classification problem and data acquisitionComputer assisted analysis of semen fertility has been used to save costs and im-prove quality in artificial insemination. Sperm analysis is a complex task whichallows to identify the males with the best reproductive features and control thefertility of the samples. Some approaches have used image analysis techniquesto detect shape abnormalities in sperm heads [6] or classify subpopulations in asample. However, only very few methods use the information of the acrosomeintegrity or the intracellular distribution to evaluate the sperm quality [7, 8].Several commercial systems have been developed, which were designed specif-ically for human sperm cells and have been adapted to other species later. Theydo not consider the intracellular density distribution which provides informationabout the cell status.Veterinary experts hypothesize that there are certain patterns of cytoplasmdensity distributions which can be correlated with alive and dead sperm cells.Techniques such as fluorescence staining protocols mark sperm heads dependingon if they are alive of dead. However, these methods are expensive and requiremore work in the sample preparation. The goal of this work is to classify thesperm head images without using staining techniques in order to speed up theprocess and reduce the costs.The 1360 images used in this project are obtained from boar semen samplesby use of a phase-contrast microscope. The first processing and segmentationsteps provide aligned images of isolated sperm heads as grey-level distributionson a black (empty) background. For details of acquisition and pre-processingsee [7].Sperm heads typically display an oval shape which we approximate by anellipse. We determine its principal axes and align all images. Using nearest-neighbor interpolation, we re-scale all head images to the same aspect ratio of19 x 35 pixels. Finally, we consider an array of grey-levels which lie inside theellipse with main axes 19 and 35 pixels.Intracellular intensities in heads which were labelled as normal by veterinaryexperts display three areas: a darker region corresponding to the post nucleuscap where the tail develops from, an intermediate light area and the acrosomewhich is covering the nucleus region, see Fig. 1 for example images. As the illu-mination of the samples under the microscope is controlled manually, brightnessand contrast can vary significantly across different images. To cope with thisproblem, we perform a linear transformation which results in the same mean,µ = 100, and standard deviation, σ = 8, of the grey-levels in all images.We represent example images as vectors ξµ ∈ IRN where the N = 35 ×19 = 665 components correspond to a rectangle. All pixels outside the abovementioned ellipsoidal regions are the same in every ξµ and will play no role inthe LVQ training and classification performance. Due to variations in shape,also the ellipses can contain pixels or entire regions which do not correspondFig. 1: Examples of sperm heads which were labelled as normal (left panel)or non-normal (right panel), respectively. For clarity, background pixels aredisplayed black while for the classification they are set to the overall mean valueof all non-background pixels, see the discussion in section 2.to intracellular densities but are part of the black background in Fig. 1. In[7], such pixels were explicitly excluded when comparing different heads, whichessentially disregards differences in shape. Here, we have chosen to replacethem by a constant value, i.e. the total mean of non-background grey-scalesover all example images. Thus, we are taking into account deformations butavoid artificially large differences between corresponding pixels. By choice ofthe constant one could vary the emphasis that is put on shape, the effect of thiswill be studied in a forthcoming project.3 LVQ system and training algorithmsTraining is based on the repeated random sequential presentation of exampleimages drawn from a given (sub-) set of data ID = {ξµ, SµT }Pµ=1. Here the classmembership label as provided by the veterinary experts isSµT = +1 if ξµ is marked as normal and SµT = −1 else. (1)In the set of M prototypes{w1,w2, . . . ,wM}a vector wk is supposed to repre-sent data from class Sk ∈ {−1, +1}. Upon presentation of the pair (ξµ, SµT ) attime step t, we evaluate the distance of ξµ from the current prototypes wj(t).In the following we will use three different distance measures d(j, µ):a) (squared) Euclidean: d2(j, µ) =(ξµ − wj(t))2=∑Ni=1(ξµi − wji (t))2b) generalized (squared) Euclidean: d2,λ(j, µ) =∑Ni=1 λi(ξµi − wji (t))2with the positive and normalized relevances λi > 0,∑i λ2i = 1c) L1 metric: d1(j, µ) =∑Ni=1∣∣∣ξµi − wji (t)∣∣∣.In any case we identify the minimal distances d(j, µ) among prototypes withclass labels SjT = +1 and SjT = −1 separately and use the notation{wJ(t) (correct winner) with d(J, µ) = mink{d(k, µ)|Sk = +SµT}wK(t) (wrong winner) with d(K, µ) = mink{d(k, µ)|Sk = −SµT}.(2)Further, the total winner is denoted as wL(t) ={wJ (t) if d(J, µ) < d(K, µ)wK(t) else.We consider the following training schemes:Fig. 2: Left panel: The upper (lower) row displays prototypes in LVQ1 fornormal (non-normal) heads, respectively. Right panel: Relevances as obtainedby GRLVQ: the classification is based on very few components with considerableλi, corresponding to the dark region in the figure.a) LVQ1At each learning step, only the total winner wL(t) is updated:wL(t + 1) = wL(t) + η(t)[SµT SL](ξµ − wL(t))(3)The update is towards (away from) the input ξµ if the class label of thewinning prototype and that of the example agree (disagree). In LVQ1 wehave considered the use of the distance measures d2(j, µ) and d1(j, µ).b) GLVQIn this learning scheme we restrict our implementation to the Euclideandistance measure d(j, µ) = d2(j, µ). Both winning prototypes, wJ andwK , are modified. Defining zµ = (d(J, µ) − d(K, µ))/ (d(J, µ) + d(K, µ))the update of wJ can be written aswJ(t + 1) = wJ (t) + η(t)[SµT SJ ]f ′ (zµ)d(K, µ)(d(J, µ) + d(K, µ))2(ξµ − wJ (t))(4)and that of wK is of the same form with indices K and J exchanged.This corresponds to a step in the direction of the negative gradient ofthe function f(zµ) w.r.t. wK and wL. The function f has been set tof(x) = (1 + e−x)−1 in [2, 3]. For the limited range of possible arguments−1 ≤ zµ ≤ 1 the sigmoidal is very close to linear, however, and we replaceit by the simpler f(x) = x, f ′(x) = 1 in the following.c) GRLVQIn GRLVQ as suggested in [3], the distance measure d(j, µ) = d2,λ(j, µ) isused and the cost function f(zµ) = zµ of GLVQ is re-defined accordingly.Both prototypes wJ (t), wK(t) and also the relevances λi are updated inthe direction of the respective negative gradient, see [3] for details.In all considered algorithms the learning rate should gradually decrease in thecourse of learning. We have implemented a schedule of the formη(t) = ηo for τ < τo and η(t) = ηo/[1 + b(τ − τo)] for τ ≥ τo.Here, τ counts the number of randomly shuffled sweeps through the actualtraining set. In each training process we have performed 80 such sweeps andused the values τo = 10, ηo = 0.1, and b = 0.3.4 ResultsIn order to evaluate the quality of the obtained classification we have performedten-fold cross-validation: We split the set of 1360 available data into ten disjointsubsets IDi of equal size. For a given number of prototypes each of ten identi-cally designed LVQ systems (n = 1, 2, . . . 10) was trained from ∪i6=nIDi, whileIDn served as a test set. The following table summarizes some of our results:# of prototypes: 3 / 3 (normal/non-normal) 1 / 7LVQ1 (L1 measure) εtest = 0.232 (σ = 0.037) εtest = 0.215 (σ = 0.058)LVQ1 (Euclidean) εtest = 0.186 (σ = 0.040) εtest = 0.184 (σ = 0.045)GLVQ (Euclidean) εtest = 0.244 (σ = 0.041) εtest = 0.236 (σ = 0.038)GRLVQ (Euclidean) εtest = 0.185 (σ = 0.035) εtest = 0.183 (σ = 0.037)Here εtest is the mean test error and σ denotes its standard deviation over theten (statistically dependent) training sets. Note that a training error of 0.20comparable with the above test error was achieved for the same data set using asingle normal cell prototype and a distance threshold [7, 8]. We are not aware ofother published results for boar sperm head classification based on microscopicimages only.As a first result we note that the performance depends only weakly on thenumber of prototypes. Relatively low test errors can be achieved by using asingle prototype for the class of normal heads while the non-normal spermsare represented by several prototypes. We observe only weak variations and noindication of significant over–fitting in the considered range of 1−10 normal and3−16 non-normal prototypes. We have studied the performance of LVQ1 usingthe squared Euclidean distance as well as the L1-metric. In all considered caseswe have found a lower classification error when using the Euclidean measureand, hence, we restrict our comparison of different algorithms to this case.An important observation is that the performance of GLVQ is inferior to thatof LVQ1 (with Euclidean distances). One attractive feature of GLVQ is that itcan be interpreted as a gradient descent with respect to a plausible cost function.However, the relation of the latter with the goal of good generalization is notobvious. Indeed, we observe that, here, training and test error typically increasein the course of GLVQ training while the associated cost function decreases.By introducing adaptive relevances, the good performance of LVQ1 is recov-ered in GRLVQ. It is interesting to note that only very few relevances λi remainsignificantly different from zero in the training process. Fig. 2 (right panel) dis-plays a typical vector of relevances in grey-scale. GRLVQ selects mainly thosepixels which correspond to the pronounced light region in normal head images.Apparently, the achieved performance could be obtained from a comparison ofthese regions only, while the acrosome and post nucleus cap densities are essen-tially disregarded. This seems to indicate that the resolution of the obtainedimages might be insufficient to exploit the latter information.5 Summary and OutlookWe have applied several LVQ schemes in the classification of boar sperm headimages. Unlike other more sophisticated and more expensive approaches, weaim at a classification which is based on grey-scale microscopic images only. Weare aware of only two earlier publications [7, 8] which report results based onsimilar data and we find that plausible LVQ algorithms yield comparable, if notsuperior performance. It is very well feasible that a more careful fine-tuning ofthe LVQ algorithms, e.g. with respect to the learning rate schedule, will yieldan even lower classification error.Cross validation estimates of εtest display a rather weak dependence on thenumber of employed prototypes. When comparing the use of L1- vs. Euclideandistances in LVQ1, we find the latter to be superior and restrict the furtheranalysis to this case. While the heuristic LVQ1 yields relatively low test error,here, the cost function based GLVQ is clearly inferior. Better performance isrecovered when introducing adaptive relevance factors in the frame of GRLVQ.The training of relevance factors reveals insight into what features the clas-sification is based on. We find that a test error of about 0.20 can be achievedby comparing a small characteristic region of the grey-scale data. The lattercorresponds to a pronounced low density region in images of normal spermheads. While acrosome density is believed to carry relevant information, theyare essentially disregarded here. In forthcoming investigations we will aim atfurther optimization of the training process and LVQ architectures. For now, itremains an open question if the data in its current form is sufficient to achievesignificantly better classification schemes.Finally, we would like to point out that the goal in semen quality assessmentis not necessarily a low error rate with respect to single image classification.The aim is to estimate with high precision the fraction of non-normal heads ina sample of unknown composition [8]. The design of a classifier appropriate forthis purpose will be aimed at in a forthcoming project.References[1] Bibliography on the Self-Organizing Map (SOM) and Learning Vector Quantization(LVQ), Neural Networks Research Centre, Helsinki University of Technology, 2002.[2] A.S. Sato and K. Yamada, Generalized learning vector quantization. In: G. Tesauro,D. Touretzky, and T. Leen, eds., Advances in Neural Information Processing Systems 7(MIT Press, 1995)[3] B. Hammer and T. Villmann, Generalized relevance learning vector quantization, NeuralNetworks 15: 1059-1068, 2002.[4] T. Kohonen, Self-organizing maps, Springer, Berlin, 1995.[5] L. Thurston, W. Holt, and P. Watson. Post-thaw functional status of boar spermatozoacryopreserved using three rate freezers: a comparison. Theriogenology, 60:101–113, 2003.[6] M. Hirai et, A. Boersma, A. Hoeflich, E. Wolf, J. Foll, T.R. Aumuller, and J. Braun.Objectively measured sperm motility and sperm head morphometry in boars (Sus scrofa):relation to fertility and seminal plasma growth factors. J. Androl, 22:104–110, 2001.[7] L. Sánchez, N. Petkov, and E. Alegre. Statistical Approach to Boar Semen Head Classi-fication Based on Intracellular Intensity Distribution. In A. Gagalowicz and W. Philips,editors, Proceedings of 11th International Conference, CAIP 2005, Lecture Notes inComputer Science, Vol. 3691, pages 88–95. Springer-Verlag, 2005.[8] L. Sánchez, N. Petkov, and E. Alegre. Classification of boar spermatozoid head imagesusing a model intracellular density distribution. In M. Lazo and A. Sanfeliu, edi-tors, Progress in Pattern Recognition, Image Analysis and Applications: Proc. 10thIberoamerican Congress on Pattern Recognition, CIARP 2005, pages 154-160. Springer-Verlag, 2005.

   University of GroningenClassification of Boar Sperm Head Images using Learning Vector QuantizationBiehl, Michael; Pasma, Piter; Pijl, Marten; Sánchez, Lidia; Petkov, NicolaiPublished in:Proc. European Symposium on Artificial Neural NetworksIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2006Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Biehl, M., Pasma, P., Pijl, M., Sánchez, L., & Petkov, N. (2006). Classification of Boar Sperm Head Imagesusing Learning Vector Quantization. In M. Verleysen (Ed.), Proc. European Symposium on Artificial NeuralNetworks: ESANN 2006 d-side publishing.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 16-07-2023Classification of Boar Sperm Head Images usingLearning Vector QuantizationMichael Biehl1, Piter Pasma1, Marten Pijl1, Lidia Sánchez2 and Nicolai Petkov11- Rijksuniversiteit Groningen - Mathematics and Computing ScienceP.O. Box 800, NL-9700 AV Groningen - The Netherlands2- University of León - Department of Electrical and Electronics EngineeringCampus de Vegazana s/n, 24071 León - SpainAbstract. We apply Learning Vector Quantization (LVQ) in automatedboar semen quality assessment. The classification of single boar spermheads into healthy (normal) and non-normal ones is based on grey-scalemicroscopic images only. Sample data was classified by veterinary expertsand is used for training a system with a number of prototypes for eachclass. We apply as training schemes Kohonen’s LVQ1 and the variantsGeneralized LVQ (GLVQ) and Generalized Relevance LVQ (GRLVQ).We compare their performance and study the influence of the employedmetric.1 IntroductionSemen quality assessment constitutes an important problem in fertility studies.Existing, relatively costly methods rely on staining or motility measurements.Mostly they have originally been developed for the analysis of human semen andclinical purposes. Here, the aim is a fast and relatively cheap reliable methodfor the inspection of boar semen samples on the basis of microscopic images.We apply methods of prototype based clustering and classification. Learningvector quantization (LVQ) as originally proposed by Kohonen is widely used ina variety of areas due to its flexibility and conceptual simplicity [1, 4]. LVQprovides a particularly intuitive and clear approach: the classification of datais based on a set of so-called prototype vectors and a feature vector is assignedto the class represented by the closest prototype.Frequently, distances are evaluated in terms of simple Euclidean metrics, butalternative measures can easily be incorporated into the standard LVQ schemes.The choice of an appropriate distance measure can indeed be crucial in practicalproblems. Recent variations of LVQ have been suggested in which an adaptivemetric is modified in the course of learning.One of the most attractive features of LVQ learning is that the parameter-ization in terms of prototype vectors allows for an immediate interpretation ofthe classifier. Prototypes are defined in the same space as the data; they are, forinstance, images themselves and provide direct information about the achievedclustering and the features that it is based on. This is in contrast to othermethods, including feed-forward neural networks and the support vector ma-chine which in general cannot be interpreted as easily. The paper is organizedas follows: in the next section we outline the problem and summarize how thedata has been acquired and pre-processed. In section 3, we describe the LVQclassifier and training algorithms. The results are presented and discussed insection 4 and we conclude with a brief summary in 5.2 Classification problem and data acquisitionComputer assisted analysis of semen fertility has been used to save costs and im-prove quality in artificial insemination. Sperm analysis is a complex task whichallows to identify the males with the best reproductive features and control thefertility of the samples. Some approaches have used image analysis techniquesto detect shape abnormalities in sperm heads [6] or classify subpopulations in asample. However, only very few methods use the information of the acrosomeintegrity or the intracellular distribution to evaluate the sperm quality [7, 8].Several commercial systems have been developed, which were designed specif-ically for human sperm cells and have been adapted to other species later. Theydo not consider the intracellular density distribution which provides informationabout the cell status.Veterinary experts hypothesize that there are certain patterns of cytoplasmdensity distributions which can be correlated with alive and dead sperm cells.Techniques such as fluorescence staining protocols mark sperm heads dependingon if they are alive of dead. However, these methods are expensive and requiremore work in the sample preparation. The goal of this work is to classify thesperm head images without using staining techniques in order to speed up theprocess and reduce the costs.The 1360 images used in this project are obtained from boar semen samplesby use of a phase-contrast microscope. The first processing and segmentationsteps provide aligned images of isolated sperm heads as grey-level distributionson a black (empty) background. For details of acquisition and pre-processingsee [7].Sperm heads typically display an oval shape which we approximate by anellipse. We determine its principal axes and align all images. Using nearest-neighbor interpolation, we re-scale all head images to the same aspect ratio of19 x 35 pixels. Finally, we consider an array of grey-levels which lie inside theellipse with main axes 19 and 35 pixels.Intracellular intensities in heads which were labelled as normal by veterinaryexperts display three areas: a darker region corresponding to the post nucleuscap where the tail develops from, an intermediate light area and the acrosomewhich is covering the nucleus region, see Fig. 1 for example images. As the illu-mination of the samples under the microscope is controlled manually, brightnessand contrast can vary significantly across different images. To cope with thisproblem, we perform a linear transformation which results in the same mean,µ = 100, and standard deviation, σ = 8, of the grey-levels in all images.We represent example images as vectors ξµ ∈ IRN where the N = 35 ×19 = 665 components correspond to a rectangle. All pixels outside the abovementioned ellipsoidal regions are the same in every ξµ and will play no role inthe LVQ training and classification performance. Due to variations in shape,also the ellipses can contain pixels or entire regions which do not correspondFig. 1: Examples of sperm heads which were labelled as normal (left panel)or non-normal (right panel), respectively. For clarity, background pixels aredisplayed black while for the classification they are set to the overall mean valueof all non-background pixels, see the discussion in section 2.to intracellular densities but are part of the black background in Fig. 1. In[7], such pixels were explicitly excluded when comparing different heads, whichessentially disregards differences in shape. Here, we have chosen to replacethem by a constant value, i.e. the total mean of non-background grey-scalesover all example images. Thus, we are taking into account deformations butavoid artificially large differences between corresponding pixels. By choice ofthe constant one could vary the emphasis that is put on shape, the effect of thiswill be studied in a forthcoming project.3 LVQ system and training algorithmsTraining is based on the repeated random sequential presentation of exampleimages drawn from a given (sub-) set of data ID = {ξµ, SµT }Pµ=1. Here the classmembership label as provided by the veterinary experts isSµT = +1 if ξµ is marked as normal and SµT = −1 else. (1)In the set of M prototypes{w1,w2, . . . ,wM}a vector wk is supposed to repre-sent data from class Sk ∈ {−1, +1}. Upon presentation of the pair (ξµ, SµT ) attime step t, we evaluate the distance of ξµ from the current prototypes wj(t).In the following we will use three different distance measures d(j, µ):a) (squared) Euclidean: d2(j, µ) =(ξµ − wj(t))2=∑Ni=1(ξµi − wji (t))2b) generalized (squared) Euclidean: d2,λ(j, µ) =∑Ni=1 λi(ξµi − wji (t))2with the positive and normalized relevances λi > 0,∑i λ2i = 1c) L1 metric: d1(j, µ) =∑Ni=1∣∣∣ξµi − wji (t)∣∣∣.In any case we identify the minimal distances d(j, µ) among prototypes withclass labels SjT = +1 and SjT = −1 separately and use the notation{wJ(t) (correct winner) with d(J, µ) = mink{d(k, µ)|Sk = +SµT}wK(t) (wrong winner) with d(K, µ) = mink{d(k, µ)|Sk = −SµT}.(2)Further, the total winner is denoted as wL(t) ={wJ (t) if d(J, µ) < d(K, µ)wK(t) else.We consider the following training schemes:Fig. 2: Left panel: The upper (lower) row displays prototypes in LVQ1 fornormal (non-normal) heads, respectively. Right panel: Relevances as obtainedby GRLVQ: the classification is based on very few components with considerableλi, corresponding to the dark region in the figure.a) LVQ1At each learning step, only the total winner wL(t) is updated:wL(t + 1) = wL(t) + η(t)[SµT SL](ξµ − wL(t))(3)The update is towards (away from) the input ξµ if the class label of thewinning prototype and that of the example agree (disagree). In LVQ1 wehave considered the use of the distance measures d2(j, µ) and d1(j, µ).b) GLVQIn this learning scheme we restrict our implementation to the Euclideandistance measure d(j, µ) = d2(j, µ). Both winning prototypes, wJ andwK , are modified. Defining zµ = (d(J, µ) − d(K, µ))/ (d(J, µ) + d(K, µ))the update of wJ can be written aswJ(t + 1) = wJ (t) + η(t)[SµT SJ ]f ′ (zµ)d(K, µ)(d(J, µ) + d(K, µ))2(ξµ − wJ (t))(4)and that of wK is of the same form with indices K and J exchanged.This corresponds to a step in the direction of the negative gradient ofthe function f(zµ) w.r.t. wK and wL. The function f has been set tof(x) = (1 + e−x)−1 in [2, 3]. For the limited range of possible arguments−1 ≤ zµ ≤ 1 the sigmoidal is very close to linear, however, and we replaceit by the simpler f(x) = x, f ′(x) = 1 in the following.c) GRLVQIn GRLVQ as suggested in [3], the distance measure d(j, µ) = d2,λ(j, µ) isused and the cost function f(zµ) = zµ of GLVQ is re-defined accordingly.Both prototypes wJ (t), wK(t) and also the relevances λi are updated inthe direction of the respective negative gradient, see [3] for details.In all considered algorithms the learning rate should gradually decrease in thecourse of learning. We have implemented a schedule of the formη(t) = ηo for τ < τo and η(t) = ηo/[1 + b(τ − τo)] for τ ≥ τo.Here, τ counts the number of randomly shuffled sweeps through the actualtraining set. In each training process we have performed 80 such sweeps andused the values τo = 10, ηo = 0.1, and b = 0.3.4 ResultsIn order to evaluate the quality of the obtained classification we have performedten-fold cross-validation: We split the set of 1360 available data into ten disjointsubsets IDi of equal size. For a given number of prototypes each of ten identi-cally designed LVQ systems (n = 1, 2, . . . 10) was trained from ∪i6=nIDi, whileIDn served as a test set. The following table summarizes some of our results:# of prototypes: 3 / 3 (normal/non-normal) 1 / 7LVQ1 (L1 measure) εtest = 0.232 (σ = 0.037) εtest = 0.215 (σ = 0.058)LVQ1 (Euclidean) εtest = 0.186 (σ = 0.040) εtest = 0.184 (σ = 0.045)GLVQ (Euclidean) εtest = 0.244 (σ = 0.041) εtest = 0.236 (σ = 0.038)GRLVQ (Euclidean) εtest = 0.185 (σ = 0.035) εtest = 0.183 (σ = 0.037)Here εtest is the mean test error and σ denotes its standard deviation over theten (statistically dependent) training sets. Note that a training error of 0.20comparable with the above test error was achieved for the same data set using asingle normal cell prototype and a distance threshold [7, 8]. We are not aware ofother published results for boar sperm head classification based on microscopicimages only.As a first result we note that the performance depends only weakly on thenumber of prototypes. Relatively low test errors can be achieved by using asingle prototype for the class of normal heads while the non-normal spermsare represented by several prototypes. We observe only weak variations and noindication of significant over–fitting in the considered range of 1−10 normal and3−16 non-normal prototypes. We have studied the performance of LVQ1 usingthe squared Euclidean distance as well as the L1-metric. In all considered caseswe have found a lower classification error when using the Euclidean measureand, hence, we restrict our comparison of different algorithms to this case.An important observation is that the performance of GLVQ is inferior to thatof LVQ1 (with Euclidean distances). One attractive feature of GLVQ is that itcan be interpreted as a gradient descent with respect to a plausible cost function.However, the relation of the latter with the goal of good generalization is notobvious. Indeed, we observe that, here, training and test error typically increasein the course of GLVQ training while the associated cost function decreases.By introducing adaptive relevances, the good performance of LVQ1 is recov-ered in GRLVQ. It is interesting to note that only very few relevances λi remainsignificantly different from zero in the training process. Fig. 2 (right panel) dis-plays a typical vector of relevances in grey-scale. GRLVQ selects mainly thosepixels which correspond to the pronounced light region in normal head images.Apparently, the achieved performance could be obtained from a comparison ofthese regions only, while the acrosome and post nucleus cap densities are essen-tially disregarded. This seems to indicate that the resolution of the obtainedimages might be insufficient to exploit the latter information.5 Summary and OutlookWe have applied several LVQ schemes in the classification of boar sperm headimages. Unlike other more sophisticated and more expensive approaches, weaim at a classification which is based on grey-scale microscopic images only. Weare aware of only two earlier publications [7, 8] which report results based onsimilar data and we find that plausible LVQ algorithms yield comparable, if notsuperior performance. It is very well feasible that a more careful fine-tuning ofthe LVQ algorithms, e.g. with respect to the learning rate schedule, will yieldan even lower classification error.Cross validation estimates of εtest display a rather weak dependence on thenumber of employed prototypes. When comparing the use of L1- vs. Euclideandistances in LVQ1, we find the latter to be superior and restrict the furtheranalysis to this case. While the heuristic LVQ1 yields relatively low test error,here, the cost function based GLVQ is clearly inferior. Better performance isrecovered when introducing adaptive relevance factors in the frame of GRLVQ.The training of relevance factors reveals insight into what features the clas-sification is based on. We find that a test error of about 0.20 can be achievedby comparing a small characteristic region of the grey-scale data. The lattercorresponds to a pronounced low density region in images of normal spermheads. While acrosome density is believed to carry relevant information, theyare essentially disregarded here. In forthcoming investigations we will aim atfurther optimization of the training process and LVQ architectures. For now, itremains an open question if the data in its current form is sufficient to achievesignificantly better classification schemes.Finally, we would like to point out that the goal in semen quality assessmentis not necessarily a low error rate with respect to single image classification.The aim is to estimate with high precision the fraction of non-normal heads ina sample of unknown composition [8]. The design of a classifier appropriate forthis purpose will be aimed at in a forthcoming project.References[1] Bibliography on the Self-Organizing Map (SOM) and Learning Vector Quantization(LVQ), Neural Networks Research Centre, Helsinki University of Technology, 2002.[2] A.S. Sato and K. Yamada, Generalized learning vector quantization. In: G. Tesauro,D. Touretzky, and T. Leen, eds., Advances in Neural Information Processing Systems 7(MIT Press, 1995)[3] B. Hammer and T. Villmann, Generalized relevance learning vector quantization, NeuralNetworks 15: 1059-1068, 2002.[4] T. Kohonen, Self-organizing maps, Springer, Berlin, 1995.[5] L. Thurston, W. Holt, and P. Watson. Post-thaw functional status of boar spermatozoacryopreserved using three rate freezers: a comparison. Theriogenology, 60:101–113, 2003.[6] M. Hirai et, A. Boersma, A. Hoeflich, E. Wolf, J. Foll, T.R. Aumuller, and J. Braun.Objectively measured sperm motility and sperm head morphometry in boars (Sus scrofa):relation to fertility and seminal plasma growth factors. J. Androl, 22:104–110, 2001.[7] L. Sánchez, N. Petkov, and E. Alegre. Statistical Approach to Boar Semen Head Classi-fication Based on Intracellular Intensity Distribution. In A. Gagalowicz and W. Philips,editors, Proceedings of 11th International Conference, CAIP 2005, Lecture Notes inComputer Science, Vol. 3691, pages 88–95. Springer-Verlag, 2005.[8] L. Sánchez, N. Petkov, and E. Alegre. Classification of boar spermatozoid head imagesusing a model intracellular density distribution. In M. Lazo and A. Sanfeliu, edi-tors, Progress in Pattern Recognition, Image Analysis and Applications: Proc. 10thIberoamerican Congress on Pattern Recognition, CIARP 2005, pages 154-160. Springer-Verlag, 2005.

   University of GroningenClassification of Boar Sperm Head Images using Learning Vector QuantizationBiehl, Michael; Pasma, Piter; Pijl, Marten; Sánchez, Lidia; Petkov, NicolaiPublished in:Proc. European Symposium on Artificial Neural NetworksIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2006Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Biehl, M., Pasma, P., Pijl, M., Sánchez, L., & Petkov, N. (2006). Classification of Boar Sperm Head Imagesusing Learning Vector Quantization. In M. Verleysen (Ed.), Proc. European Symposium on Artificial NeuralNetworks: ESANN 2006 d-side publishing.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 28-10-2022Classification of Boar Sperm Head Images usingLearning Vector QuantizationMichael Biehl1, Piter Pasma1, Marten Pijl1, Lidia Sánchez2 and Nicolai Petkov11- Rijksuniversiteit Groningen - Mathematics and Computing ScienceP.O. Box 800, NL-9700 AV Groningen - The Netherlands2- University of León - Department of Electrical and Electronics EngineeringCampus de Vegazana s/n, 24071 León - SpainAbstract. We apply Learning Vector Quantization (LVQ) in automatedboar semen quality assessment. The classification of single boar spermheads into healthy (normal) and non-normal ones is based on grey-scalemicroscopic images only. Sample data was classified by veterinary expertsand is used for training a system with a number of prototypes for eachclass. We apply as training schemes Kohonen’s LVQ1 and the variantsGeneralized LVQ (GLVQ) and Generalized Relevance LVQ (GRLVQ).We compare their performance and study the influence of the employedmetric.1 IntroductionSemen quality assessment constitutes an important problem in fertility studies.Existing, relatively costly methods rely on staining or motility measurements.Mostly they have originally been developed for the analysis of human semen andclinical purposes. Here, the aim is a fast and relatively cheap reliable methodfor the inspection of boar semen samples on the basis of microscopic images.We apply methods of prototype based clustering and classification. Learningvector quantization (LVQ) as originally proposed by Kohonen is widely used ina variety of areas due to its flexibility and conceptual simplicity [1, 4]. LVQprovides a particularly intuitive and clear approach: the classification of datais based on a set of so-called prototype vectors and a feature vector is assignedto the class represented by the closest prototype.Frequently, distances are evaluated in terms of simple Euclidean metrics, butalternative measures can easily be incorporated into the standard LVQ schemes.The choice of an appropriate distance measure can indeed be crucial in practicalproblems. Recent variations of LVQ have been suggested in which an adaptivemetric is modified in the course of learning.One of the most attractive features of LVQ learning is that the parameter-ization in terms of prototype vectors allows for an immediate interpretation ofthe classifier. Prototypes are defined in the same space as the data; they are, forinstance, images themselves and provide direct information about the achievedclustering and the features that it is based on. This is in contrast to othermethods, including feed-forward neural networks and the support vector ma-chine which in general cannot be interpreted as easily. The paper is organizedas follows: in the next section we outline the problem and summarize how thedata has been acquired and pre-processed. In section 3, we describe the LVQclassifier and training algorithms. The results are presented and discussed insection 4 and we conclude with a brief summary in 5.2 Classification problem and data acquisitionComputer assisted analysis of semen fertility has been used to save costs and im-prove quality in artificial insemination. Sperm analysis is a complex task whichallows to identify the males with the best reproductive features and control thefertility of the samples. Some approaches have used image analysis techniquesto detect shape abnormalities in sperm heads [6] or classify subpopulations in asample. However, only very few methods use the information of the acrosomeintegrity or the intracellular distribution to evaluate the sperm quality [7, 8].Several commercial systems have been developed, which were designed specif-ically for human sperm cells and have been adapted to other species later. Theydo not consider the intracellular density distribution which provides informationabout the cell status.Veterinary experts hypothesize that there are certain patterns of cytoplasmdensity distributions which can be correlated with alive and dead sperm cells.Techniques such as fluorescence staining protocols mark sperm heads dependingon if they are alive of dead. However, these methods are expensive and requiremore work in the sample preparation. The goal of this work is to classify thesperm head images without using staining techniques in order to speed up theprocess and reduce the costs.The 1360 images used in this project are obtained from boar semen samplesby use of a phase-contrast microscope. The first processing and segmentationsteps provide aligned images of isolated sperm heads as grey-level distributionson a black (empty) background. For details of acquisition and pre-processingsee [7].Sperm heads typically display an oval shape which we approximate by anellipse. We determine its principal axes and align all images. Using nearest-neighbor interpolation, we re-scale all head images to the same aspect ratio of19 x 35 pixels. Finally, we consider an array of grey-levels which lie inside theellipse with main axes 19 and 35 pixels.Intracellular intensities in heads which were labelled as normal by veterinaryexperts display three areas: a darker region corresponding to the post nucleuscap where the tail develops from, an intermediate light area and the acrosomewhich is covering the nucleus region, see Fig. 1 for example images. As the illu-mination of the samples under the microscope is controlled manually, brightnessand contrast can vary significantly across different images. To cope with thisproblem, we perform a linear transformation which results in the same mean,µ = 100, and standard deviation, σ = 8, of the grey-levels in all images.We represent example images as vectors ξµ ∈ IRN where the N = 35 ×19 = 665 components correspond to a rectangle. All pixels outside the abovementioned ellipsoidal regions are the same in every ξµ and will play no role inthe LVQ training and classification performance. Due to variations in shape,also the ellipses can contain pixels or entire regions which do not correspondFig. 1: Examples of sperm heads which were labelled as normal (left panel)or non-normal (right panel), respectively. For clarity, background pixels aredisplayed black while for the classification they are set to the overall mean valueof all non-background pixels, see the discussion in section 2.to intracellular densities but are part of the black background in Fig. 1. In[7], such pixels were explicitly excluded when comparing different heads, whichessentially disregards differences in shape. Here, we have chosen to replacethem by a constant value, i.e. the total mean of non-background grey-scalesover all example images. Thus, we are taking into account deformations butavoid artificially large differences between corresponding pixels. By choice ofthe constant one could vary the emphasis that is put on shape, the effect of thiswill be studied in a forthcoming project.3 LVQ system and training algorithmsTraining is based on the repeated random sequential presentation of exampleimages drawn from a given (sub-) set of data ID = {ξµ, SµT }Pµ=1. Here the classmembership label as provided by the veterinary experts isSµT = +1 if ξµ is marked as normal and SµT = −1 else. (1)In the set of M prototypes{w1,w2, . . . ,wM}a vector wk is supposed to repre-sent data from class Sk ∈ {−1, +1}. Upon presentation of the pair (ξµ, SµT ) attime step t, we evaluate the distance of ξµ from the current prototypes wj(t).In the following we will use three different distance measures d(j, µ):a) (squared) Euclidean: d2(j, µ) =(ξµ − wj(t))2=∑Ni=1(ξµi − wji (t))2b) generalized (squared) Euclidean: d2,λ(j, µ) =∑Ni=1 λi(ξµi − wji (t))2with the positive and normalized relevances λi > 0,∑i λ2i = 1c) L1 metric: d1(j, µ) =∑Ni=1∣∣∣ξµi − wji (t)∣∣∣.In any case we identify the minimal distances d(j, µ) among prototypes withclass labels SjT = +1 and SjT = −1 separately and use the notation{wJ(t) (correct winner) with d(J, µ) = mink{d(k, µ)|Sk = +SµT}wK(t) (wrong winner) with d(K, µ) = mink{d(k, µ)|Sk = −SµT}.(2)Further, the total winner is denoted as wL(t) ={wJ (t) if d(J, µ) < d(K, µ)wK(t) else.We consider the following training schemes:Fig. 2: Left panel: The upper (lower) row displays prototypes in LVQ1 fornormal (non-normal) heads, respectively. Right panel: Relevances as obtainedby GRLVQ: the classification is based on very few components with considerableλi, corresponding to the dark region in the figure.a) LVQ1At each learning step, only the total winner wL(t) is updated:wL(t + 1) = wL(t) + η(t)[SµT SL](ξµ − wL(t))(3)The update is towards (away from) the input ξµ if the class label of thewinning prototype and that of the example agree (disagree). In LVQ1 wehave considered the use of the distance measures d2(j, µ) and d1(j, µ).b) GLVQIn this learning scheme we restrict our implementation to the Euclideandistance measure d(j, µ) = d2(j, µ). Both winning prototypes, wJ andwK , are modified. Defining zµ = (d(J, µ) − d(K, µ))/ (d(J, µ) + d(K, µ))the update of wJ can be written aswJ(t + 1) = wJ (t) + η(t)[SµT SJ ]f ′ (zµ)d(K, µ)(d(J, µ) + d(K, µ))2(ξµ − wJ (t))(4)and that of wK is of the same form with indices K and J exchanged.This corresponds to a step in the direction of the negative gradient ofthe function f(zµ) w.r.t. wK and wL. The function f has been set tof(x) = (1 + e−x)−1 in [2, 3]. For the limited range of possible arguments−1 ≤ zµ ≤ 1 the sigmoidal is very close to linear, however, and we replaceit by the simpler f(x) = x, f ′(x) = 1 in the following.c) GRLVQIn GRLVQ as suggested in [3], the distance measure d(j, µ) = d2,λ(j, µ) isused and the cost function f(zµ) = zµ of GLVQ is re-defined accordingly.Both prototypes wJ (t), wK(t) and also the relevances λi are updated inthe direction of the respective negative gradient, see [3] for details.In all considered algorithms the learning rate should gradually decrease in thecourse of learning. We have implemented a schedule of the formη(t) = ηo for τ < τo and η(t) = ηo/[1 + b(τ − τo)] for τ ≥ τo.Here, τ counts the number of randomly shuffled sweeps through the actualtraining set. In each training process we have performed 80 such sweeps andused the values τo = 10, ηo = 0.1, and b = 0.3.4 ResultsIn order to evaluate the quality of the obtained classification we have performedten-fold cross-validation: We split the set of 1360 available data into ten disjointsubsets IDi of equal size. For a given number of prototypes each of ten identi-cally designed LVQ systems (n = 1, 2, . . . 10) was trained from ∪i6=nIDi, whileIDn served as a test set. The following table summarizes some of our results:# of prototypes: 3 / 3 (normal/non-normal) 1 / 7LVQ1 (L1 measure) εtest = 0.232 (σ = 0.037) εtest = 0.215 (σ = 0.058)LVQ1 (Euclidean) εtest = 0.186 (σ = 0.040) εtest = 0.184 (σ = 0.045)GLVQ (Euclidean) εtest = 0.244 (σ = 0.041) εtest = 0.236 (σ = 0.038)GRLVQ (Euclidean) εtest = 0.185 (σ = 0.035) εtest = 0.183 (σ = 0.037)Here εtest is the mean test error and σ denotes its standard deviation over theten (statistically dependent) training sets. Note that a training error of 0.20comparable with the above test error was achieved for the same data set using asingle normal cell prototype and a distance threshold [7, 8]. We are not aware ofother published results for boar sperm head classification based on microscopicimages only.As a first result we note that the performance depends only weakly on thenumber of prototypes. Relatively low test errors can be achieved by using asingle prototype for the class of normal heads while the non-normal spermsare represented by several prototypes. We observe only weak variations and noindication of significant over–fitting in the considered range of 1−10 normal and3−16 non-normal prototypes. We have studied the performance of LVQ1 usingthe squared Euclidean distance as well as the L1-metric. In all considered caseswe have found a lower classification error when using the Euclidean measureand, hence, we restrict our comparison of different algorithms to this case.An important observation is that the performance of GLVQ is inferior to thatof LVQ1 (with Euclidean distances). One attractive feature of GLVQ is that itcan be interpreted as a gradient descent with respect to a plausible cost function.However, the relation of the latter with the goal of good generalization is notobvious. Indeed, we observe that, here, training and test error typically increasein the course of GLVQ training while the associated cost function decreases.By introducing adaptive relevances, the good performance of LVQ1 is recov-ered in GRLVQ. It is interesting to note that only very few relevances λi remainsignificantly different from zero in the training process. Fig. 2 (right panel) dis-plays a typical vector of relevances in grey-scale. GRLVQ selects mainly thosepixels which correspond to the pronounced light region in normal head images.Apparently, the achieved performance could be obtained from a comparison ofthese regions only, while the acrosome and post nucleus cap densities are essen-tially disregarded. This seems to indicate that the resolution of the obtainedimages might be insufficient to exploit the latter information.5 Summary and OutlookWe have applied several LVQ schemes in the classification of boar sperm headimages. Unlike other more sophisticated and more expensive approaches, weaim at a classification which is based on grey-scale microscopic images only. Weare aware of only two earlier publications [7, 8] which report results based onsimilar data and we find that plausible LVQ algorithms yield comparable, if notsuperior performance. It is very well feasible that a more careful fine-tuning ofthe LVQ algorithms, e.g. with respect to the learning rate schedule, will yieldan even lower classification error.Cross validation estimates of εtest display a rather weak dependence on thenumber of employed prototypes. When comparing the use of L1- vs. Euclideandistances in LVQ1, we find the latter to be superior and restrict the furtheranalysis to this case. While the heuristic LVQ1 yields relatively low test error,here, the cost function based GLVQ is clearly inferior. Better performance isrecovered when introducing adaptive relevance factors in the frame of GRLVQ.The training of relevance factors reveals insight into what features the clas-sification is based on. We find that a test error of about 0.20 can be achievedby comparing a small characteristic region of the grey-scale data. The lattercorresponds to a pronounced low density region in images of normal spermheads. While acrosome density is believed to carry relevant information, theyare essentially disregarded here. In forthcoming investigations we will aim atfurther optimization of the training process and LVQ architectures. For now, itremains an open question if the data in its current form is sufficient to achievesignificantly better classification schemes.Finally, we would like to point out that the goal in semen quality assessmentis not necessarily a low error rate with respect to single image classification.The aim is to estimate with high precision the fraction of non-normal heads ina sample of unknown composition [8]. The design of a classifier appropriate forthis purpose will be aimed at in a forthcoming project.References[1] Bibliography on the Self-Organizing Map (SOM) and Learning Vector Quantization(LVQ), Neural Networks Research Centre, Helsinki University of Technology, 2002.[2] A.S. Sato and K. Yamada, Generalized learning vector quantization. In: G. Tesauro,D. Touretzky, and T. Leen, eds., Advances in Neural Information Processing Systems 7(MIT Press, 1995)[3] B. Hammer and T. Villmann, Generalized relevance learning vector quantization, NeuralNetworks 15: 1059-1068, 2002.[4] T. Kohonen, Self-organizing maps, Springer, Berlin, 1995.[5] L. Thurston, W. Holt, and P. Watson. Post-thaw functional status of boar spermatozoacryopreserved using three rate freezers: a comparison. Theriogenology, 60:101–113, 2003.[6] M. Hirai et, A. Boersma, A. Hoeflich, E. Wolf, J. Foll, T.R. Aumuller, and J. Braun.Objectively measured sperm motility and sperm head morphometry in boars (Sus scrofa):relation to fertility and seminal plasma growth factors. J. Androl, 22:104–110, 2001.[7] L. Sánchez, N. Petkov, and E. Alegre. Statistical Approach to Boar Semen Head Classi-fication Based on Intracellular Intensity Distribution. In A. Gagalowicz and W. Philips,editors, Proceedings of 11th International Conference, CAIP 2005, Lecture Notes inComputer Science, Vol. 3691, pages 88–95. Springer-Verlag, 2005.[8] L. Sánchez, N. Petkov, and E. Alegre. Classification of boar spermatozoid head imagesusing a model intracellular density distribution. In M. Lazo and A. Sanfeliu, edi-tors, Progress in Pattern Recognition, Image Analysis and Applications: Proc. 10thIberoamerican Congress on Pattern Recognition, CIARP 2005, pages 154-160. Springer-Verlag, 2005.

Classification of Boar Sperm Head Images using Learning Vector Quantization

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