1. Performance Analysis of Three Likelihood Measures for Color Image Processing Arash AbadpourDr. Shohreh Kasaei Mathematics Science DepartmentComputer Engineering Department Sharif University of Technology, Tehran, Iran

2. Outline Introduction  Image Segmentation, Color Image Segmentation, Fuzzy Membership, What we have done. Method  Likelihood Measure, Homogeneity Criteria, Fuzzy Membership, PCA Everywhere, Different Color spaces. Experimental Results  Fuzzyfication, Noise Robustness, Parameter Sensitivity, Homogeneity Criteria. Conclusions.

3. Image Segmentation A Low Level Operation, before Recognition, Compression, Tracking,… Splitting to Homogenous Regions. An Spatial-Spectral Process:  Satisfying (sometimes) Contradictory Concerns. Based on A Likelihood Measure or A Homogeneity Criteria.

4. Color Image Segmentation The Easy Way: A Color image is a Combination of Grayscale Images.  Using a Min/Max method. The Better way:  Euclidean: Only depends on the central point. Generally used in the literature. Known as an applicable measure.  Mahalonobis: Depending on the central point and the distribution margins. Called Weighted Euclidean, when used in color domain. Computationally expensive.

5. Fuzzy Membership Likelihood Measure: Rank Better Members with Smaller Numbers. Mapping is needed: Gaussian is used Generally.

6. What have we done? Comparing the Euclidean, Mahalonobis and Reconstruction Error, in terms of:  Image Fuzzyfication (Likelihood Measures).  Homogeneity Decision.

7. Likelihood Measures Distances  Euclidean.  Mahalonobis.  Reconstruction Error. Normalization.

8. Homogeneity Criteria

9. Fuzzy Membership Mapping, Flat Ceil. Manipulated Butterworth.

10. PCA Everywhere Although not mentioned, Euclidean and Mahalanobis are PCA-Based. Euclidean: Mahalonibus:clear. Reconstruction Error (RE):

11. Color Spaces Although RGB Used, the Same hold for Linear Reversible color spaces:  CMYK, YCbCr, YIQ, YUV, I1I2I3 Not for:  Nonlinear: HIS, HSV, CIE-XYZ, CIELab, CIE-Luv, CIE-LHC, HMMD.  Irreversible.

12. Experimental Results Matlab 6.5, Image Processing Toolbox. 42 Samples Images:  RGB.  Low-compressed, JPEG.

13. Fuzzy Membership.

14. Computational Complexity & Memory Computational Complexity:  Data Extraction: Euclidean: Mean. Mahalonobis: Mean and Complete Al PCs. RE: Mean and one PC.  Measurement: Euclidean: 7 flops. Mahalonobis 111 flops. RE: 22 flops. Memory:  Euclidean: 3.  Mahalonobis: 12.  RE: 6.

15. Fuzzyfication

16. Noise Robustness

17. Parameter Sensitivity Different values of p.

18. Homogeneity Criteria

19. Conclusions Analyzing the performance of:  Euclidean, Mahalanobis, and Reconstruction Error.  As likelihood measures and homogeneity criteria. Euclidean distance:  Used commonly, is the fastest and needs least memory.  Neither gives applicable fuzzyfication results, nor gives proper homogeneity criteria. Comparing Reconstruction error and Mahalonobis:  RE is more robust against noise, leads to promising homogeneity criteria, is fastest and needs less memory.

20. Any Questions?