Transcript Multi-Valued and Universal Binary Neurons: Theory and Learning

Image recognition using analysis
of the frequency domain features
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Image Recognition

Image recognition problem is a problem
of recognition of some certain objects
that are located in an image.
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Image Recognition
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To solve any pattern
recognition/classification problem, it is
necessary to find a relevant set of those
features that can exhaustively describe an
object to be recognized.
We never will confuse recognizing where is
a tiger and where is a rabbit, but how an
automatic tool can decide who is who?
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Image Recognition:
Features Selection
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Can you propose a set of features using
which we can definitely distinguish a
tiger from a rabbit?
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Image Recognition:
Features Selection
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It is often difficult to find a proper set
of those features that would be really
exhaustive and would not be redundant
(redundancy complicates both
processes of learning and recognition).
Another problem is a formal
representation of the selected features.
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Image Recognition:
Features Selection
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PCA (Principal Component Analysis) is a
method, which is often used for obtaining
the objective features.
PCA is based on the Karhunen-Loeve
transformation of a signal (a
transformation by the eigenvectors of the
covariance matrix of the ensemble of
signals), which is computationally very
costly.
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Image Recognition:
Features Selection
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The idea behind PCA is to find a small
amount of those eigenvectors (and
spectral coefficients, respectively) that
make a major contribution to the
formation of a signal
The question: is it possible to find
another approach to obtaining the
objective features?
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Image Recognition:
Features Selection
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Oppenheim, A.V.; Lim, J.S., The
importance of phase in signals, IEEE
Proceedings, v. 69, No 5, 1981,
pp.: 529- 541
In this paper, it was shown that phase in
the Fourier spectrum of an image is much
more informative than magnitude: phase
contains the information about all shapes,
edges, orientation of all objects, etc.
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Image Recognition:
Features Selection
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Thus the Fourier Phase Spectrum can
be a very good source of the objective
features that describe all objects
located in images.
The Power Spectrum (magnitude)
describes global image properties (blur,
noise, cleanness, contrast, brightness,
etc.).
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Phase and Magnitude
Phase contains the information about an object presented by a signal
(a)
Phase (a) & Magnitude (b)
(b)
Phase (b) & Magnitude (a)
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Phase and Magnitude
Magnitude contains the information about the signal’s properties
(a)
Phase (a) & Magnitude (b)
(b)
Phase (b) & Magnitude (a)
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Phase and Magnitude
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Blur with a symmetric point-spread
function practically does not affect the
phase, while the magnitude may be
distorted significantly.
This property may be use for
recognition of blurred images using a
phase spectrum as a feature space.
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Image Recognition:
Features Selection
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Since the Fourier Transform is
computationally much simpler and more
efficient than the Karhunen-Loeve
transform (because of the existence of
a number of Fast Fourier Transform
algorithms), the use of the Fourier
phases as the features for object
recognition is very attractive.
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Image Recognition:
Decision Rule and Classifier
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The next question is: is it possible to formulate (and
formalize!) the decision rule, using which we can
classify or recognize our objects basing on the
selected features?
Can you propose the rule using which we can
definitely decide is it a tiger or a rabbit?
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Image Recognition:
Decision Rule and Classifier
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Once we know our decision rule, it is not
difficult to develop a classifier, which will
perform classification/recognition using the
selected features and the decision rule.
However, if the decision rule can not be
formulated and formalized, we should use
a classifier, which can develop the rule
from the learning process
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Image Recognition:
Decision Rule and Classifier
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In the most of recognition/classification
problems, the formalization of the decision
rule is very complicated or impossible at all.
A neural network is a tool, which can
accumulate knowledge from the learning
process.
After the learning process, a neural network
is able to approximate a function, which is
supposed to be our decision rule
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Why neural network?
f ( x1 ,..., xn )
- unknown multi-factor decision rule
Learning process using a representative learning set
( w0 , w1 ,..., wn )
fˆ ( x1 ,..., xn ) 
 P( w0  w1 x1  ...  wn xn )
- a set of weighting vectors is the
result of the learning process
- a partially defined function,
which is an approximation of the
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decision rule function
Image Recognition: Approach
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We will use the low frequency Fourier
phases as the features. They contain
the most important information about
those objects that we want to recognize
We will use a neural network as a
classifier
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Features Selection
Features are selected from the low frequency part of the
Fourier phase spectrum
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Example: Classification of Gene
Expression Patterns
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Gene expression patterns
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We have studied spatio-temporal
expression patterns of genes controlling
segmentation in the embryo of fruit fly
Drosophila.
A problem is to perform temporal
classification of the gene expression
patterns taken form the confocal electronic
microscope (8 temporal classes are
considered)
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Image of gene expression data
in Drosophila embryo
obtained by confocal
scanning microscopy
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A problem of the classification
Representatives of 8 temporal classes:
Class 1
Class 2
Class 3
Class 4
Class 5
Class 6
Class 7
Class 8
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Phases as the features
Class 1
Class 8
Phase Cl.1+
Amplitude Cl.8
Phase Cl.8 +
Amplitude Cl.1
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Learning process
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From 28 up to 32 images from each
class a priori correctly classified as
“representative” from biological view
were used for the learning
From 60 inputs up to 144 inputs (from
5 to 8 low frequency coefficients) have
been used as the features
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The Classification Results
Final classification results
Classes
1
2
3
4
5
6
7
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Number of
frequencies/
inputs
1-8/
144
1-8/
144
1-5/
144
1-5/
144
1-8/
144
1-8/
144
1-5/
144
1-5/
144
Number of
Images
48
43
68
55
78
89
66
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Recognized
46
33
53
47
56
65
48
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(95%) (76%) (77%) (85%) (71%) (73%) (72%) (69%)
Unrecognized
0
1
1
1
0
0
0
0
Misclassified
2
9
14
7
22
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18
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Recognized using
Discrimination
Analysis
(previously used
approach)
-
-
-
84%
49%
59%
61%
68%
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Problems that we will consider
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Textures classification (automatic
classification of different Gaussian and
uniform textures)
Blurred images recognition
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