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

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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?