Performance Analysis of Three Likelihood Measures for Color Image Processing
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.
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.
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.
Fuzzy Membership • Likelihood Measure: Rank Better Members with Smaller Numbers. • Mapping is needed: • Gaussian is used Generally.
What have we done? • Comparing the Euclidean, Mahalonobis and Reconstruction Error, in terms of: • Image Fuzzyfication (Likelihood Measures). • Homogeneity Decision.
Likelihood Measures • Distances • Euclidean. • Mahalonobis. • Reconstruction Error. • Normalization.
Mapping, Flat Ceil. Manipulated Butterworth. Fuzzy Membership
PCA Everywhere • Although not mentioned, Euclidean and Mahalanobis are PCA-Based. • Euclidean: • Mahalonibus:clear. • Reconstruction Error (RE):
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.
Experimental Results • Matlab 6.5, Image Processing Toolbox. • 42 Samples Images: • RGB. • Low-compressed, JPEG.
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.
Fuzzyfication Reconstruction Error Euclidean Mahalonobis
Noise Robustness Reconstruction Error Euclidean Mahalonobis
Different values of p. Parameter Sensitivity Euclidean Mahalonobis Reconstruction Error
Homogeneity Criteria Euclidean Mahalonobis Reconstruction Error
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.