Performance Analysis of Three Likelihood Measures for Color Image Processing

1. Performance Analysis of Three Likelihood Measures for Color Image Processing

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. Mapping, Flat Ceil. Manipulated Butterworth. Fuzzy Membership

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 Reconstruction Error Euclidean Mahalonobis

16. Noise Robustness Reconstruction Error Euclidean Mahalonobis

17. Different values of p. Parameter Sensitivity Euclidean Mahalonobis Reconstruction Error

18. Homogeneity Criteria Euclidean Mahalonobis Reconstruction Error

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? ?