Color Image Segmentation

1. Color Image Segmentation Speaker: Deng Huipeng 25th Oct，2007

2. Segmentation Technologies • Feature-Space Based Techniques • Clustering • K-means algorithm • Fuzzy k-means algorithm [Wu et al. 1994] • Histogram thresholding [Celenk et al.1998 ] [Park et al.1998]

3. Segmentation Technologies • Image-Domain Based Techniques • Split-and-merge techniques [Liu et al.1994] • Region growing techniques [Kanai 1998 ] • Neural-network based classification techniques [Okii et al. 1994]

4. Segmentation Technologies • Physics Based Techniques [Shafer 1985]

5. Color image segmentation-an innovative approach Tie Qi Chen , Yi Lu Pattern Recognition 35(2002)

6. About the Author:TIE-QI CHEN • Member of IEEE and ACM • Senior Software Engineer at Automotive Technologies International, Inc • Ph.D in Optics from Fudan University

7. About the Author: YI LU • Associate Professor at the University of Michigan-Dearborn • Senior member of IEEE Computer Society and associate editor of Pattern Recognition • Research interests: Computer Vision, neural networks and fuzzy logic

8. Outline a color image Compute histogram in a color space Fuzzy clustering in color Histogram domain Map initial clusters to image domain CL2 Merging neighboring clusters CL1 CL3： A set of color regions Stage 2: Region segmentation Stage 1: Color segmentation

9. Illustration • 3D Color Histogram • Provide the color distribution of the image • Fuzzy Clustering • Generate a decomposition of the 3D histogram • Output a set of non-overlapping color clusters

10. LUV Color Space CIE XYZ->CIE Luv RGB->CIE XYZ

11. Two Criterions • Different colors in different clusters in CL1, next step only merge clusters • CL1 must be compact, otherwise there will be too many clusters

12. Fuzzy clustering Algorithm How to classify similar colors into clusters? • Fuzzy membership function The likeness of a data element belonging to a color cluster • Color distance function Difference between two clusters • Distance function Difference between a color and a color cluster

13. Label Image Pixels Fuzzy membership function: where Pi is the center of the cluster P : the center of the cluster, R : the radius of the cluster.

14. Object Function {Cn}:set of all colors in an image Hk: fuzzy membership function f(C):3D histogram Pi : center of cluster i

15. Pseudocode Center of cluster 1 Color histogram M=0; f(Ck)=max(f(Ci)) i=1,…,N ; PM0=Ck; while(f(Cj)V(Cj)>ε∑f(Cj)) { t=0; do { t=t+1; PMt+1 = ∑Cif(Ci)HM/ ∑f(Ci)HM; } while(|| PMt+1-PMt||>δ) PMt+1 = MthCenter; M=M+1; if(f(Cj)V(Cj)=max(f(Ci)V(Ci)) (i=1,…,N ) PM0=Cj; V(C) = ∏k=1M[1-GR(C-Pk)] } Probability not belonging to any cluster Initial value of next cluster center

16. Discussion of Radius • The value of radius is determined by user • Larger radius: images have coarse features • Smaller radius: images with fine detailed features

17. Example: Fewer Details (a) original image, (b) R=64, (c) R=32, (d) R=16 , (e) R=8

18. Example: More Details (a) original image, (b) R=64, (c) R=32, (d) R=16, (e) R=8

19. Region segmentation An agglomerative process, three parameters used: • The color distances among neighboring clusters in the spatial domain (two versions) • Cluster sizes • The maximum number of clusters in CL3(max_num=64) Three methods are employed in this paper.

20. Color Distance Function 1 • A and B are neighboring clusters, Function 1 is defined below: Dist(A,B) = |Ave_B(A)-Ave_B(B)|, where

21. Illustration of Border Border(A,B) ={(x,y)|x_min≤x≤x_max, y_min≤y≤y_max;(x,y)∈A }

22. Color Distance Function 2 • A and B are neighboring clusters, Function 2 is defined below: Dist(A,B) = |C(A)-C(B)|, where |A|: the size of A L(p):3D color vector of p in Luv space

23. Comparison • Function 1: Work well on regions whose borders have more distinct color. • Function 2:Give a global measure of color distance between two clusters.

24. Merging Method 1 Merge the adjacent clusters having similar colors: Cl_diff_th : Color difference threshold. clu_num : Total number of clusters Pseudocode: for every cluter belonging to CL2 if(Dist(A,B)< Cl_diff_th ) MergeClusters(A,B); Update(center, clu_num , neighbours, CL2); while(clu_num>max_num) { for every cluter belonging to CL2 if(Dist(A,B) = minDistOfneighbours) MergeClusters(A,B); Update(center, clu_num , neighbours, CL2); }

25. Merging Method 2 clu_num : Total number of clusters Pseudocode: while(clu_num>max_num) { for every cluter belonging to CL2 if(Dist(A,B) = minDistOfneighbours) MergeClusters(A,B); Update(center, clu_num , neighbours, CL2); }

26. Merging Method 3 Three passes: • Repeatedly merge the smallestclusters until the number is reduced to a reasonable number • Merge two neighboring clusters who has the smallest diatances until covering majority of the pixels • Merge the smallest clusters with its neighbor until the number of clusters is no more than max_num

27. Results (a)shows an egg nebula image, (b) shows the clusters generated by the fuzzy clustering algorithm with R=16, (c), (d) and (e) show the clustering result generated by method 1, 2 and 3, respectively, from (b)

28. More Results (a) shows the input image, (b) shows the color histogram illustrated in 3D space. (c) illustrates the 4 clusters generated by the fuzzy clustering algorithm, (d) shows the 4 clusters generated by the segmentation algorithm in image domain.

29. More Results (a) The original image. (b) The image contains 12 color clusters generated by the fuzzy color clustering algorithm and 598 spatial clusters in the image domain. (c) The segmentation result.

30. More Results Radius parameter to R=8, 16, 32 and 64 respectively.

31. Conclusion • Effective & Efficient • Only one parameter cluster radius R should be specified. • Apply to variety of applications.

32. Q&A

33. Thank you!