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Performance Analysis of Three Likelihood Measures for Color Image Processing
Arash Abadpour Dr. Shohreh Kasaei
Mathematics Science Department Computer Engineering Department
Sharif University of Technology, Tehran, Iran
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.2
2
1
2
1)(
x
exf
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.
Homogeneity Criteria
Fuzzy Membership
Mapping, Flat Ceil. Manipulated
Butterworth.
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.
Fuzzy Membership.
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
Noise Robustness
Parameter Sensitivity
Different values of p.
Homogeneity Criteria
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.
Any Questions?