Image recognition using analysis of the frequency domain features

1
Image recognition using analysis of the frequency
domain features
2
Image Recognition

• Image recognition problem is a problem of
  recognition of some certain objects that are
  located in an image.

3
Image Recognition

• 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?

4
Image Recognition Features Selection

• Can you propose a set of features using which we
  can definitely distinguish a tiger from a rabbit?

5
Image Recognition Features Selection

• 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.

6
Image Recognition Features Selection

• 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.

7
Image Recognition Features Selection

• 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?

8
Image Recognition Features Selection

• 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.

9
Image Recognition Features Selection

• 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.).

10
Phase and Magnitude
Phase contains the information about an object
presented by a signal
(a) (b)
Phase (a) Magnitude (b) Phase (b)
Magnitude (a)
11
Phase and Magnitude
Magnitude contains the information about the
signals properties
(a) (b)
Phase (a) Magnitude (b) Phase (b)
Magnitude (a)
12
Phase and Magnitude

• 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.

13
Image Recognition Features Selection

• 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.

14
Image Recognition Decision Rule and Classifier

• 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?

15
Image Recognition Decision Rule and Classifier

• 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

16
Image Recognition Decision Rule and Classifier

• 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

17
Why neural network?
- unknown multi-factor decision rule
Learning process using a representative learning
set
- a set of weighting vectors is the result of the
learning process
- a partially defined function, which is an
approximation of the decision rule function
18
Image Recognition Approach

• 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

19
Features Selection
Features are selected from the low frequency part
of the Fourier phase spectrum
20
Example Classification of Gene Expression
Patterns
21
Gene expression patterns

• 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)

22
Image of gene expression data in Drosophila
embryoobtained by confocalscanning microscopy
23
A problem of the classification
Representatives of 8 temporal classes
24
Phases as the features
Class 1 Class 8
Phase Cl.1 Amplitude Cl.8
Phase Cl.8 Amplitude Cl.1
25
Learning process

• 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

26
The Classification Results
27
Problems that we will consider

• Textures classification (automatic classification
  of different Gaussian and uniform textures)
• Blurred images recognition