Nous proposons une méthode basée sur la connaissance a priori pour la segmentation et la reconnaissance des formes des structures internes du cerveau en IRM. Les connaissances sur les formes des structures et les distances entre elles, provenant de l'atlas de Talairach, sont modélisées par un champ flou en utilisant une analogie avec la distribution du potentiel d'électrostatique. Une sur-segmentation est d'abord effectuée sur le cerveau pour obtenir des régions homogènes. La reconnaissance des structures est ensuite obtenue par la classification des régions utilisant un algorithme génétique, suivie par un affinement au niveau du pixel. Les connaissances floues modélisées sont utilisées dans ces deux étapes. La performance de la méthode proposée est validée par référence aux résultats manuels en utilisant 4 indices de quantification

BLOYET, Daniel

MORETTI, Bruno

REVENU, Marinette

RUAN, Su

XUE, Jinhao

I-Revues

Fuzzy Knowledge-based Recognition of Internal
Structures of the Head
Su RUAN, Jinhao XUE, Bruno MORETTI, Marinette REVENU, Daniel BLOYET
GREYC CNRS UMR 6072, ISMRA
6 Bd Maréchal Juin, 14050 Caen, France
Su.Ruan@greyc.ismra.fr
Résumé - Nous proposons une méthode basée sur la connaissance a priori pour la segmentation et la reconnaissance des formes des
structures internes du cerveau en IRM. Les connaissances sur les formes des structures et les distances entre elles, provenant de l'atlas de
Talairach, sont modélisées par un champ flou en utilisant une analogie avec la distribution du potentiel d'électrostatique. Une sur-
segmentation est d'abord effectuée sur le cerveau pour obtenir des régions homogènes. La reconnaissance des structures est ensuite obtenue
par la classification des régions utilisant un algorithme génétique, suivie par un affinement au niveau du pixel. Les connaissances floues
modélisées sont utilisées dans ces deux étapes. La performance de la méthode proposée est validée par référence aux résultats manuels en
utilisant 4 indices de quantification.
Abstract – We propose a knowledge-based method for segmenting and recognizing internal brain structures viewed by MRI (Magnetic
Resonance Imaging). The knowledge about shapes of the structures and relative distances between them, derived from Talairach stereotaxic
atlas, is fuzzified by analogy with the electrostatic potential distribution. The brain is firstly over-segmented. Then the recognition of the
cerebral structures is achieved by the region-wise labeling using GAs (Genetic Algorithms), followed by a voxel-wise amendment using
parallel region growing. The fuzzy knowledge is used both to design the fitness function of GAs, and to conduct the region growing. The
performance of our proposed method has been quantitatively validated by 4 indexes with respect to manually labeled images.
1. Introduction
Automated labeling of structures is complicated, facing
difficulties due to overlapping intensities, anatomical
variability in shape, size, and orientation, partial volume
effects, as well as noise perturbations, intensity
inhomogeneities, and low contrast in images. Therefore, it is
needed to supplement domain knowledge, to achieve labeling
like what radiologists do. In recent years, many reports have
been published in this direction in terms of atlas-based (
model-based, or knowledge-based ) segmentation of
neuroanatomical structures .
One intuitive strategy to use knowledge for labeling,
named as registration-segmentation paradigm by Collins et al.
[1] , is to register and transfer labels of a pre-labeled atlas
onto the MRI images to be segmented. The performance of
this strategy over-relies on the accuracy of the registration
employed, which suffers from the limited degrees of freedom
of the transformations, and from anatomical inter-individual
variability (in orientation, shape, size, and position). Another
important strategy is to integrate statistical knowledge of
intensity and position into a shape model, and to locate the
structures which match the model. Staib et al. [2] used a
gradient-based parametric deformable shape model,
integrating region information and prior probability
knowledge about mean shape and variation of the structures.
Gonzalez Ballester et al. [3] guided the segmentation by
statistical shape knowledge built from data sets of pre-labeled
structures. Several researchers used ASM (Active Shape
Models) to label brain structures [4][5]. ASM are parametric
deformable models of shape and appearance of flexible
objects, which restrict the possible deformation using shape
template and intensity model, both generated through
statistics of training sets.
Besides the two strategies aforementioned, the use of the
fuzzy sets theory to represent structural information has been
introduced by I.Bloch [6][7]. From these fuzzy sets, the atlas-
based recognition using fuzzy fusion is proposed [8]. The
recognition is carried out sequentially on one structure at a
time. The information got from the atlas is updated after the
recognition of each structure in order to guide the next one.
Inversely to this method, our method use a parallel process.
The contribution of this paper is twofold. First, the
structural knowledge from the Talairach stereotaxic atlas is
modeled with fuzzy sets. The fuzzification is carried out by
analogy with the electrostatic potential distribution in the
vicinity of hollow structures with uniform surface charge
density. Second, the fuzzy sets obtained for each structure are
used to search the optimal labels from over-segmented
regions using GAs (Genetic Algorithms).
2. Fuzzification of the knowledge
The Talairach atlas is well-accepted in medical image
processing, owing to its contribution to the delineation and
labeling of numerous brain neuroanatomical structures (one
sample slice of this atlas is shown in FIG 1.a). Although it
indicates approximate shape, position and relationship of the
brain structures, it is far from the real brain (FIG 1.b).
Therefore, we use fuzzy sets to model the imprecision and the
uncertainty of the structure information.
(a)                                                   (b)
FIG. 1 (a) one sample slice of Talairach atlas: putamen (1),
ventricle (2), thalamus (3) and caudate (4), (b) one slice of
MRI brain volume.
We define the degree of fuzziness to represent the degree
of belonging to one structure.  Since our recognition process
searches for the structures in parallel, the interactions between
different structures have to be taken into account. We propose
a model which is constructed by analogy with the electrostatic
potential distribution in the vicinity of conducting objects.
The potential of any point relative to one structure is in fact
influenced by all structures.  More precisely, any structure s
( [ ]Ns ,1∈  ) is considered as an isolated conductor in the
electrical equilibrium, i.e. all the charges are distributed on its
3-D outer surface Ss. The electrostatic potential at voxel x
located outside any structure can be expressed as:
(1)
where ε
0
 is a constant of vacuum permitivity,  ζ(x’)
denotes the charge density at point x’ on Ss. If ζ(x’) is
considered as an uniform distribution, the equation (1) can be
simplified as:
(2)
where ns denotes the number of voxels vis (i=1, ...,ns) on the
surface of the structure s in the atlas TV, and d(x,vis) is a
distance from x to vis. The potential distribution of the
structure s is firstly normalized by its maximal value
 
to
guaranty ps(x) ∈ [0,1]. The fuzzy membership value related to
the structure s is than defined by:
(3)
where                                  . . The structure j has the maximal
potential value.
3. Recognition method
We propose a coarse-to-fine strategy to achieve the brain
structure recognition, based on both the fuzzy structural
knowledge from the Talairach stereotaxic atlas, and on the
information from the MRI images.
Two datasets were made available in our method. One is
the Talairach stereotaxic atlas TO ; another one is a volume of
MRI images VT, which have been registered into the
stereotaxic coordinates system using MPItool1 software
package. The volume VT is used as a registration template. To
obtain the coarse location of brain structures in a new volume
MRI VO , the AIR software package developed by Woods et
al. [9] is used to register the prepared registration template
VT  onto  VO. A matrix of mapping parameters is thus
obtained. TO is resampled using this matrix, and the
resampled result TV can be superimposed automatically onto
VO. This resampled Talairach atlas is then fuzzified by the
way described in the previous section.
3.1 Over-segmentation with fuzzy MRF
We expect the over-segmentation to fulfill the following
requirements: 1) not to result in tremendous redundant
regions like those generated by the watershed algorithm, thus
to be able to reduce the computation complexity of the
following GAs in searching optimal labeling of regions; 2) to
segment brain tissues like GM (Gray Matter ) and CSF
(Cerebro-Spinal Fluid), which contain most of the important
neuroanatomical structures; 3) to describe partial volume
effects quantitatively; and 4) to decrease the information loss
before labeling. In this context, we applied a scheme using the
combination of partial volume modeling [10] and fuzzy MRF
(Markov Random Fields) [11], which can generate regions of
pure tissues: GM, WM (White Matter),and CSF, and also
mixtures of these pure tissues. The fuzzy MRF models
simultaneously “pure” voxels using Dirac functions, and
“mixed” voxels using Lebesgue measure. Moreover, fuzzy
MRF can preserve information through fuzzy membership of
voxels belonging to a given class, as well as statistical context
information through MRF. It is justified for our requirements.
3.2 Estimation of statistical moments
The statistical mean Ms and variance σs2 of each structure
s are chosen to describe the intensity of the structure, and
estimated from a set Ωs which includes regions reliably
belonging to s. Using a fuzzy MRF segmentation, over-
segmented regions are obtained along with their fuzzy
membership values to different tissues (CSF, GM and WM).
The regions classified into Ωs should have large intersection
areas with s in the registered Talairach atlas TV, and high
values of fuzzy membership to brain tissues, e.g. high
membership to GM while regarding s as caudate, and
putamen, and membership to CSF while regarding s as
ventricle. With the help of the fuzzy model of ROI and the set
Ωs, we can estimate the mean Ms and variance σs2 with a
higher precision. The way of estimation can be written as
follows:
 (4)
                                                          
1MPItool, version 2.58, Advanced Tomo Vision GmbH.
http://www.atv-gmbh.de/mpitoolh/
dS
xx
x
xp
sS
s ∫
−
=
’
)’(
4
1)(
0
ζ
piε
∑= s
n
s
i
s
vxd
xp
1 ),(
1)(
( )


≠
=
=
 sj if        )(/)()(
 s if                                 )()(
max
max
xpxpxp
jxp
x
jss
j
s
µ
))((sup)(
],1[
max xpxp i
Ni
j
∈
=
2
4
3
1
∑
Ω∈
=
sx
ss
xfx
Z
xM )()(1)( µ
(5)
where                         , and f(x) is the intensity of the voxel
x.
1.3 Region-wise recognition using Gas
GAs are stochastic search methods which use analogy with
some mechanisms of evolution in nature. They are used
widely in optimization, artificial intelligence, involving brain
structures labeling, conducted by an objective function which
is referred as fitness function in GAs related references
[12][13]. The most application-dependent component of GAs
is the fitness function, which affects significantly the
performance and computation complexity of GAs.
Our fitness function has been designed as the
multiplication of two items, based on the fuzzy model of ROI
and the statistical mean estimated above. The first item relates
to intersected shapes with the same label between the atlas  TV
and images  Vo , as :
 (6)
where r
s
µ  is the membership value corresponding to the
structure  s in the region r.                  is a normalization
coefficient, where nr represents the amount of voxels in the
region  r .
The second item measures the correlation of intensity
between regions and the corresponding structures, as:
(7)
where  mr  is the  mean of region  r , and  Ms
r denotes the
mean of the structure s in the region r, which are estimated in
equations (5). Imax ( Imin ) is the maximum (minimum)
intensity of the images.
1.4 Voxel-wise amendment conducted by
knowledge
The only use of region-wise labeling is no doubt coarse
and insufficient to achieve an accurate labeling of
neuroanatomical structures, because the over-segmentation
suffers significantly from the overlap of intensity ranges
among different structures like caudate, thalamus and
putamen.
However, after the region-wise labeling, the majority of
voxels has been correctly labeled, and can be considered as
seeds for refinement. In this context, we choose a parallel
region growing algorithm to achieve voxel-wise amendment,
conducted by the structural and statistical knowledge formerly
obtained. In this procedure, we make the different structures
grow simultaneously, to avoid one structure to grow into
another one located in its proximity and whose intensity is
overlapping.
Some of the knowledge applied are derived from the atlas
Tv, such as shape, spatial position, and distance information
represented by the fuzzy sets. Some others are derived from
the MRI images VO and its over-segmented version, such as
the statistical moments
4. Results and quantitative validation
In this study, the subjects were scanned with a GE Signa
1.5 Tesla scanner, employing a T1-weighted SPGR pulse
sequence. The parameters of the SPGR sequence were
TR=30ms, TE=7ms, flip angle=40°, image size=
256x256x124 voxels, and voxel size =0.94x0.94x1.2 mm3.
The performance of the method is demonstrated by
labeling four important neuroanatomical structures: caudate,
thalamus, ventricle and putamen. These four structures are
clearly visible close to the center of the axial Talairach atlas
(see FIG 1.a). The fuzzification of the Talairach atlas is
carried out by the method described in section 2. The slice of
index 67 is shown in FIG 2 to illustrate the four obtained
fuzzy sets corresponding to the four main structures. The
over-segmentation applied to the MRI dataset generates 2878
regions in the slice shown in FIG 1 (b). The result of this
sample image is shown in FIG 3 (a). The volume rendering
result is shown in FIG 3 (b). The results are visually satisfied.
(a)                                                    (b)
(c)                                                   (d)
FIG. 2 Fuzzy sets derived from the Talaraich atlas
(corresponding to FIG 1(a)): (a) ventricle; (b) putamen; (c)
caudate; (d) thalamus.
The quantitative validation is carried out by comparing the
results obtained by our method denoted as La, with the
“ground truth” obtained manually denoted as Lg. Seven
images were chosen randomly for the comparison. Two
indices of quantitative measures were calculated from the
statistical moments of distance histogram [14]. In fact, we
calculated the distance of any contour voxel xs of the structure
s  in  La  to the corresponding contour of  s  in  Lg: the
distance histogram, revealing the spatial distribution of
recognition errors, is built from the superimposition of La
onto the distance map of Lg, from which some characteristics
are extracted, such as mean, standard deviation (SD). The
])(1[
2
minmax
2 II
Mm
Fit
r
sr
−
−
−=
∑
=
=
rn
x
r
s
x
N
Fit
11
1 )(
1 µ
∑
=
=
tn
r r
nN
11
2
2 ])()[(1)(
s
sx
ss
Mxfx
Z
x −= ∑
Ω∈
µσ
∑
Ω∈
=
sx
s
xZ )(µ
two other indices measured are the false positive ratio
representing the error due to the misrecognition of the
structure s ( γ fp
s
 ) , and false negative representing the error
due to the loss of desired voxels of s (γ fn
s
 ). The results
obtained by these four indices are shown in Table 1. At first
sight, it appears that the mean discrepancy between Lg and  La
is always less than 1 voxel, which is quite satisfactory. The
low SD indicates that the labeling errors are peakwise, which
entails a concentration of labeling errors around 1 voxel. We
can also deduce that almost all the false ratios are less than
10% (except  γ fp
s
  for caudate due to its smaller size).
(a)                                                  (b)
FIG. 3  Recognition results. (a) The four obtained
structures superimposed to the original MRI image (FIG
1(a)). (b) Volume rendering of the 4 recognized structures .
TAB. 1: Quantitative validation results with statistical
moments of distance histogram and with false positive and
false negative ratios.
Means SD γ fp
s γ fn
s
Ventricule -0.890 0.482 0.07. 0.018
Thalamus -0.801 0.908 0.090 0.063
Putamen -0.819 0.651 0.083 0.049
Caudate -0.598 1.422 0.112 0.086
5. Conclusion
An automatic, knowledge-based method to segment and
recognize brain neuroanatomical structures (ventricle,
caudate, thalamus and putamen) from MRI images has been
developed. The structural knowledge derived from Talairach
stereotaxic atlas is fuzzified to represent the impression and
uncertain information for guiding the recognition process.
Quantitative validation has also been performed to
demonstrate the performance of the proposed method, with
manually labeled images considered as “ground truth” using 4
quantitative indices. The results show that this method is
promising for quantitative analysis of brain neuroanatomical
structures. The direction of knowledge integration is certainly
worthy of further investigation in image segmentation and
recognition.
References
[1] D. Collins, C. Holmes, T. Peters, and A. Evans, Automatic 3D
model-based neuroanatomical segmentation, Human Brain
Mapping 3(3), pp. 190–208, 1995.
[2] L. Staib, A. Chakraborty, and J. Duncan, An integrated
approach for locating neuroanatomical structure from MRI,
International Journal of Pattern Recognition and Artificial
Intelligence 11(8), pp. 1247–1269, 1997.
[3] M. Gonzalez Ballester, A. Zisserman, and J. Brady,
Combined statistical and geometrical 3D segmentation
and measurement of brain structures, Proc. IEEE
Workshop on Biomedical Image Analysis, pp. 14–23,
1998.
[4] T. Cootes, A. Hill, C. Taylor, and J. Haslam, The use of
active shape models for locating structures in medical
images, Image and Vision Computing 12(6), pp. 355–
366, 1994.
[5] N. Duta and M. Sonka, Segmentation and interpretation
of MR brain images: an improved active shape model,
IEEE Transactions on Medical Imaging 17(6),
pp. 1049–1062, 1998.
[6] I.Bloch, On fuzzy distances and their use in image
processing under imprecision, Pattern Recognition, 32,
pp.1873-1895, 1999.
[7] I.Bloch, Fuzzy relative position between objets in image
processing: a morphological approach, IEEE. PAMI,
Vol.21(7), July 1999.
[8] T. Géraud, I. Bloch, and H. Matre, Atlas-guided
recognition of cerebral structures in MRI using fusion of
fuzzy structural information, in CIMAF’99 Symposium
on Artificial Intelligence, pp. 99–106, 1999.
[9] R. Woods, J. Mazziotta, and S. Cherry, MRI-PET
registration with automated algorithm, Journal of
Computer Assisted Tomography 17(4), pp. 536–546,
1993.
[10] S. Ruan, C. Jaggi, J.Xue, J.Fadili, D. Bloyet, Brain
tissue classification of magnetic resonance Images using
partial volume modeling, IEEE Medical Imaging,
Vol.19(12), pp.1179-1187, December, 2000.
[11] F. Salzenstein and W. Pieczynski, Parameter estimation
in hidden fuzzy Markov random fields and image
segmentation, Graphical Models and Image Processing
59(4), pp. 205–220, 1997.
[12] D. Goldberg, Genetic Algorithms in Search,
Optimization and Machine Learning, Addison-Wesley,
Reading, MA, 1989.
[13] M.Sonka, S.K.Tadikonda, S.M.Collins, Knowledge -based
interpretation of MR brain images, IEEE Medical Imaging,
Vol 15(4), pp.443-452, August 1996.
[14] B. Moretti, J. Fadili, S. Ruan, D. Bloyet, and B.
Mazoyer, Phantom-based performance evaluation:
application to the brain segmentation from magnetic
resonance images, Medical Image Analysis, 4. pp.303-
316, 2000.


Fuzzy knowledge-based recognition of internal structures of the head

National audienceNous proposons une méthode basée sur la connaissance a priori pour la segmentation et la reconnaissance des formes des structures internes du cerveau en IRM. Les connaissances sur les formes des structures et les distances entre elles, provenant de l'atlas de Talairach, sont modélisées par un champ flou en utilisant une analogie avec la distribution du potentiel d'électrostatique. Une sursegmentation est d'abord effectuée sur le cerveau pour obtenir des régions homogènes. La reconnaissance des structures est ensuite obtenue par la classification des régions utilisant un algorithme génétique, suivie par un affinement au niveau du pixel. Les connaissances floues modélisées sont utilisées dans ces deux étapes. La performance de la méthode proposée est validée par référence aux résultats manuels en utilisant 4 indices de quantification

Fuzzy knowledge-based recognition of internal structures of the head

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