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

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]

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]

Segmentation Technologies Physics Based Techniques [Shafer 1985]

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

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

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

Outline a color image Compute histogram in a color space Fuzzy clustering in color Histogram domain Map initial clusters to image domain Merging neighboring clusters Stage 1: Color segmentation Stage 2: Region segmentation A set of color regions CL 1 CL 2 CL 3 ：

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

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

Two Criterions Different colors in different clusters in CL 1, next step only merge clusters CL 1 must be compact, otherwise there will be too many clusters

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

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

Object Function {C n }:set of all colors in an image H k : fuzzy membership function f(C):3D histogram P i : center of cluster i

Pseudocode M=0; f(C k )=max(f(C i )) i=1, …,N ; P M 0 =C k ; while(f(C j )V(C j )>ε∑f(C j )) { t=0; do { t=t+1; P M t+1 = ∑C i f(C i )H M / ∑f(C i )H M ; } while(|| P M t+1 - P M t ||>δ) P M t+1 = MthCenter; M=M+1; if(f(C j )V(C j )=max(f(C i )V(C i )) (i=1, …,N ) P M 0 =C j ; V(C) = ∏ k=1 M [1-G R (C-P k )] } Color histogram Center of cluster 1 Probability not belonging to any cluster Initial value of next cluster center

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

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

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

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 CL 3 ( max_num=64 ) Three methods are employed in this paper.

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

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

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

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.

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); }

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); }

Merging Method 3 Three passes: Repeatedly merge the smallest clusters 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

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)

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.

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.

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

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

Q&A

Thank you!