1. Image recognition using analysis of the frequency domain features 1

2. Image Recognition Image recognition problem is a problem of recognition of some certain objects that are located in an image. 2

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? 3

4. Image Recognition: Features Selection Can you propose a set of features using which we can definitely distinguish a tiger from a rabbit? 4

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. 5

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. 6

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? 7

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. 8

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.). 9

10. Phase and Magnitude (a) (b) Phase (a) & Magnitude (b) Phase (b) & Magnitude (a) Phase contains the information about an object presented by a signal 10

11. Phase and Magnitude (a) (b) Phase (a) & Magnitude (b) Phase (b) & Magnitude (a) Magnitude contains the information about the signal’s properties 11

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. 12

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. 13

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? 14

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 15

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 16

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 17

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 18

19. Features Selection Features are selected from the low frequency part of the Fourier phase spectrum 19

20. Example: Classification of Gene Expression Patterns 20

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) 21

22. Image of gene expression data in Drosophila embryo obtained by confocal scanning microscopy 22

23. A problem of the classification Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8 Representatives of 8 temporal classes: 23

24. Phases as the features Class 1 Class 8 Phase Cl.1+ Amplitude Cl.8 Phase Cl.8 + Amplitude Cl.1 24

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 25

26. The Classification Results Final classification results Classes12345678 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 4843685578896646 Recognized 46 (95%) 33 (76%) 53 (77%) 47 (85%) 56 (71%) 65 (73%) 48 (72%) 32 (69%) Unrecognized01110000 Misclassified2914722241814 Recognized using Discrimination Analysis (previously used approach) ---84%49%59%61%68% 26

27. Problems that we will consider Textures classification (automatic classification of different Gaussian and uniform textures) Blurred images recognition 27