A Grau

A Sanfeliu

R Munguía

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Matching Images Features in a Wide Base Line with ICA Descriptors 
R. Munguía, A. Grau and A. Sanfeliu 
Department of Automatic Control, UPC, 
c/ Pau Gargallo, 5  E-08028 Barcelona, Spain 
{rodrigo.munguia,antoni.grau}@upc.edu
Abstract 
     In this paper we present a method to recognize 
images features with a wide base line between learning 
and recognition phases. The method is based in feature 
descriptors derived from independent component 
analysis (ICA). This technique is inspired by the 
problems of mobile robot mapping and localization 
using single camera. In the learning phase the 
descriptors are created to capture the variations in the 
appearance of each feature across a small base line 
tracking and stored in a database. The recognition 
phase proceeds to match descriptors created from the 
incoming video (with a wide base line respect to the 
learning phase) in the database. The implementation 
shows good computational performance. 
1. Introduction. 
Many vision applications can involve the 
challenging problem of determining and matching 
features between images with a wide base line. In 
applications like structure from motion or robot 
localization a video stream is available making possible 
to track the features across a small base line, several 
trackers [4, 5] can be used for this. A small base line 
tracking is useful for capture the variations in the 
appearance of each feature. Then the key is to obtain a 
descriptor that represents the feature and their variations 
in a compact way respect the original data without lose 
of its statistical meaning and can be as possible as 
invariant to changes in scale, rotation, illumination or 
projection. These descriptors can be useful for the task 
of recognition of features in a wide base line. 
Recently some approaches [7, 9] have been 
presented for address the problem of image features 
representation for tracking, recognition or reconstruction 
affine invariant descriptors reconstruction, in general 
those methods searching for extrema in image scale 
space for obtain good candidates locations for detection. 
Lowe’s scale invariant feature transform (SIFT) [6] , has 
been shown to match reliably across a wide range of 
scales and orientation changes, it uses a cascade filtering 
approach in an isotropic Gaussian scale space to identify 
points of interest, then samples gradients to create an 
orientation histogram represented in a 128-element 
descriptor. In [8] an approximate version of Kernel 
Principal Component Analysis (KPCA) was used to 
estimate features descriptors for wide base line 
matching. 
In the scenario of mobile robot mapping and 
localization, we pretend to recognize at high speed 
different features along of the incoming video. In our 
method we generate a feature descriptor database able to 
capture different variations in the features, applying 
independent component analysis (ICA) [1] to a feature 
centered window of p-by-p pixels tracked across k
images with small base line. In the recognition phase the 
system matches features descriptors obtained from the 
incoming video (with a wide base line) with the 
descriptors in the database using k-nearest neighbor 
algorithm.  
2. PCA and ICA. 
Principal Component Analysis (PCA) is a standard 
statistical tool used to find the orthogonal directions 
corresponding to the highest variance. It is equivalent to 
a decorrelation of the data using second-order 
information. The basic idea in PCA is to find the 
components y1, y2, …, yn that explain the maximum 
amount of variance, by n linearly transformed 
components. Then, the principal components are given 
by Xwy Tii = , where X = [x1, …, xm]
T, xi is an observed 
data vector, and wi is a basis vector (an eigenvector of 
the sample covariance matrix E{XXT}). It can be 
written, in matrix form, as: 
Y = WX    (1) 
where Y = [y1, …, yn]T and yi is a principal 
component vector.  
The ICA attempts to go one step further than PCA, 
by finding the orthogonal matrix V which transforms the 
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data Y into Z having Z1,Z2,…Zm statistically 
independent. The ICA is thus more general than PCA in 
trying not only to decorrelate the data, but also to find 
decomposition, transforming the input into independent 
components. 
The simplest ICA model, the noise-free linear ICA 
model, seems to be sufficient for most applications. This 
model is as follows: ICA of observed random data X
consists of estimating the generative model: 
X = AS    (2) 
where X = [x1, …, xn]T xi is an observed random vector, 
S = [s1, …, sn]T si is a latent component, and A is the 
constant mixing matrix. The transform we seek is B = 
VW, then 
Z = BX = BAS = CS   (3) 
If an orthogonal matrix V that transforms the mixed 
signals X into Z with independent components could be 
found, and assuming that at least one independent 
source sk is normally distributed, then Z=CS with C
being a non-mixing matrix. The ICA algorithms attempt 
to find the matrix B which ensures that Z is independent. 
Many ICA algorithms are available. A 
computationally efficient ICA algorithm, called the 
FastICA algorithm, is chosen to be used in this work. 
See [1, 2] for more details about ICA and FastICA.  
3. ICA applied to window-based image 
features. 
The assumption of implicit Gaussian sources in 
PCA makes it inadequate when the true sources are non-
Gaussian. In particular, it has been empirically observed 
that many natural signals, like natural images are better 
described as linear combinations of sources with long 
tailed distributions. ICA provides a better probabilistic 
model of data in an n-dimensional space. It is sensitive 
to high-order statistics in the data not only to the 
covariance matrix. ICA can yield either an orthogonal or 
a non orthogonal basis, changing the relative distance 
between data points, this change in metrics may be 
useful for classification algorithms, like nearest 
neighbor, for instance that make decisions based on 
relative distances between points.  
Our goal in this work is to find descriptors to 
represent image features. If we consider a feature as a 
window of p x p pixels in a frame, we can organize each 
feature as a long vector with as many dimensions as 
number of pixels in the feature. ICA can be applied to 
this data organizing each vector into a matrix X where 
each row is the same image feature for different frames 
(Fig.1 left). In this approach, images features are 
random variables and pixels are trials (Fig.1 right), it 
makes sense to talk about independence of features or 
functions of features.  
Two features i and j are independent if when 
moving across pixels, it is not possible to predict the 
value taken by the pixel on feature j based on the value 
taken by the same pixel on feature i.
Fig.1. a) To apply ICA a matrix is formed where each 
row is a feature i tracked in frame n. b) ICA finds a weight 
vector w in the directions of statistical dependencies among the 
pixel locations. 
4. Method description. 
In the scenario of mobile robot mapping and 
localization, we pretend to recognize at high speed 
different features along a sequence of images, based in a 
two-phases algorithm: database generation (learning, 
off-line process) and recognition (matching, on-line 
process). 
In the learning phase, we employ a standard small 
base line tracker for detecting and tracking candidate 
features, in our work the Lucas Kanade Tracker (KLT) 
[4] is used, but any small base line tracker can be used. 
When the KLT locates a feature (feature i at frame f), a 
p-by-p pixels window around the feature center is stored 
as a vector ufi of length p-by-p, with a distinctive label; 
in the following frames the feature is tracked and 
repeating the above process, storing the window with 
the same label. We can choose, as a parameter, first, the 
number of frames the feature has to persist in the KLT 
in order to calculate the feature descriptor and, second 
the number of features to treat for each frame. 
Immediately vectors with the same label (same 
feature i) are regrouped in a matrix Ui = [u1i, …, uni]T
where n is the number of frames where the feature has 
been tracked. 
Then for each matrix U the FastICA is applied as it 
were shown in the previous section along with 
dimensional reduction selecting the largest eigenvalue to 
be retained. At the Output of the FastICA we obtain a 
descriptor qi whit dimension equal to the feature 
window size. The descriptors are stored in a database 
with a unique label for each feature. 
In the recognition phase features are detected but 
not tracked by the KLT for each incoming frame. Then 
for each feature detected a window is obtained in the 
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same way than the learning stage and sorted in a vector 
vi, the FastICA is directly applied to this vector without 
dimensional reduction producing a descriptor ri. A fast 
k-nearest neighbor algorithm is applied to the database 
in order to look for the 2-nearest neighbor descriptors qi1
and qi2.
Be k1 = d(ri, qi1) and k2 = d(ri, qi2) (d is the 
Euclidean distance), k1 ≤ k2, and we define α=k1 / k2;
this factor will be used by our algorithm as a threshold 
for considering a good match between the candidate 
descriptor ri and its corresponding nearest descriptors qi1
and qi2 in the database. When α tends to 0 means a great 
distance between candidates and, empirically, the results 
are better.  
4. Experiments.  
We have implemented a C++ version of our 
method that runs on a PC 2GHz Pentium IV processor, 
512MB RAM. A non-expensive USB Webcam with a 
maximum resolution of 640-by-480 pixels and 30 fps 
has been used.  
We performed a variety of experiments in order to 
examine the validity of our proposal; in this paper we 
present a few. In the learning phase, a video sequence of 
a rigid environment desktop scene was recorded moving 
the camera slowly and continuously in order to obtain a 
change of some degrees in the 3D point of view and 
rotation of the camera. Later, twenty ICA descriptors 
were created from this video sequence using windows of 
12-by-12 pixels and stored in our descriptor database as 
it has been described in the previous section, (Fig. 4 
center).  
Fig.2. Relationship between the sizes of the window used 
to create the ICA descriptors and the false positive.  Note the 
local minimum at p=12. 
Together with these 20 descriptors, the database 
contains another 1000 descriptors corresponding to other 
video sequences. The objective of these experiments 
consists of observing the response of our system when a 
set of descriptors coming from an online video sequence 
(close to the learning sequence, as it is explained below) 
will be matched with the descriptors database.  
The first experiment has been to observe the 
response to the change of the p-by-p window size used 
to create the descriptors in images of 320-by-240. Figure 
2 shows percentage of false positive versus different 
sizes of p.
A second experiment has been to observe the 
response of the system in front the changes in parameter 
 in the following four cases (Fig. 3):  
a) Little change in 3D point of view with respect to the 
position in the learning phase and little change in 
illumination. b) Little change in 3D point of view and 
medium change in illumination. c) Approximately a 
change of 20 degrees in the 3D point of view and 
medium change in illumination (Fig. 4 left). d) 
Approximately a change of 10 degrees in the 3D point 
of view, 5 degrees in rotation and medium change in 
illumination (Fig. 4 right). 
The response of the algorithm is expressed in terms 
of two measurements:  
1) percentage of classification as the ratio between 
the number of descriptors matched (correctly or 
incorrectly) and those that potentially can be found, we 
talk about “potentially can be found” because one of the 
objectives of our method is running fast; to achieve this 
goal, we consider only a finite number of possible 
locations in each frame to be matched. These possible 
locations are established by the feature detecting 
algorithm of the same tracker used in learning phase. 
Then it would be possible that some features to match 
actually exist in the frame but the algorithm does not 
detect them making impossible the matching process. 
The number of regions to consider in each frame can be 
selected, in our experiment we chose forty. 
2) Percentage of false positive as a quality 
measurement of detection, and it defined as the ratio 
between false positive and the number of (correctly or 
incorrectly) descriptors matched. 
In Figure 3 is relevant to show the trade-off 
between percentage of classification and percentage of 
false positive when varying α. The lower the threshold, 
the lower is the number of false positive, but 
consequently the percentage of classification is also low. 
The computational speed in the matching process, 
among the forty possible descriptors in each frame 
versus one thousand descriptors in the database, is about 
15Hz. 
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Fig.3. Response of the percentage of classification and percentage of false positives to the change of the parameter α.
Fig.4. Descriptors created in the learning phase (central image). Examples of descriptors matched in the recognition phase: (left
image) case c: a change of 20 degrees in the 3D point of view and medium change in illumination; (right image) case d: a change of 10 
degrees in the 3D point of view, 5 degrees in rotation and medium change in illumination.  
5. Conclusions. 
 We have presented a method for matching image 
features in a wide based line based ICA descriptors. In 
general the method shows good results, especially in 
terms of computational performance. The descriptors 
showed to be a little sensitive respect to some changes. 
Our next step is to work in a preprocessing stage for 
making ICA descriptors more robust. The method can 
be applied in a variety of applications where a video 
stream is available. 
6. References. 
[1] P. Comon, “Independent component analysis, A new 
concept?,” Signal Processing, vol. 36, pp. 287–314, 1994.  
[2] A. Hyvarinen and E. Oja. “A fast fixed-point algorithm for 
independent component analysis.” Neural Computation,
9(7):1483–1492, 1997.  
[3] Stewart, Movellan and Sejnowski, “Face Recognition by 
Independent Component analysis” IEEE T. on Neural 
Networks, vol 13-6 2002. 
[4] J. Shi and C. Tomasi. “Good Features to Track,” IEEE 
CVPR, 1994. 
[5] C. Harris and M. Stephens. “A combined corner and edge 
detector.” Alvey Vision Conference, 1988. 
[6] D. Lowe. “Distinctive image features from scale invariant 
key points,” IJCV, June 2003. 
[7] K. Mikolajczyk, C. Schmid. “An affine invariant interest 
point detector.” Proc. ECCV, 2002. 
[8] J Meltzer, M H. Yang, R Gupta, and Stefano Soatto, 
“Multiple view feature descriptors from image sequences 
via kernel principal component analysis”, Proc. ECCV,
2004.
[9] D. Lowe. “Object recognition from local scale-invariant 
features,” Proc. ICCV, Corfu, Greece, September 1999.
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Matching Images Features in a Wide Base Line with ICA Descriptors

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Matching Images Features in a Wide Base Line with ICA Descriptors

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