A fast algorithm for color image segmentation

1. A fast algorithm for color image segmentation Liju Dong1,2,3 Philip Ogunbona1 Wanqing Li1 Ge Yu3 Linan Fan2 Gang Zheng1 1 University of Wollongong, Australia 2 Shenyang University 3 Northeastern University, China Proceedings of the First International Conference on Innovative Computing, Information and Control (ICICIC'06) 2006 IEEE Speaker：鄭棕翰。

2. Outline • Introduction • The K-Means algorithm • The Proposed method • Two-layer pyramid data structure • An improved K-means with integer lookup tables • The new algorithm • Experimental results

3. Introduction-1/2 • Based on K-means and a two-layer pyramid structure, a fast algorithm is proposed for color image segmentation. • The K-means algorithm has been widely used in the segmentation of color images for many applications. • For large images, the algorithm takes a considerably large amount of computation time. • This paper proposes a fast algorithm by combining effectively a two-layer pyramid structure of an image with an improved K-means with integer look up table implementation.

4. Introduction-2/2 • The algorithm employs two strategies. • Firstly, a two-layer structure of a color image is established. • Then, an improved K-means with integer based lookup table implementation is applied to each layer. • The clustering result on the upper layer (lower resolution) is used to guide the clustering in the lower layer (higher resolution). • Experiments have shown that the proposed algorithm is significantly faster than the original K-means algorithm.

5. Outline • Introduction • The K-Means algorithm • The Proposed method • Two-layer pyramid data structure • An improved K-means with integer lookup tables • The new algorithm • Experimental results

6. The K-Means algorithm-1/4

7. The K-Meansalgorithm-2/4 • Set X be a finite data set where N is a number of data items and Rp is the p-dimensional Euclidean space. • VKN be the set of K×N matrices with K , 2 ≦K＜N , being the number of clusters. • X = all image pixel data. • K = number of clusters. • xk = pixel data xk,k=1~N

8. The K-Meansalgorithm-3/4 • A K partition of X is defined as • uik =1 denotes xkbelongs to cluster i and • ujk=0 denotes xkis not in cluster j 􀀑 • The objective function is defined as • The minimization of JK(U,V) produces an optimal K partition of X.

9. The K-Meansalgorithm-4/4

10. Outline • Introduction • The K-Means algorithm • The Proposed method • Two-layer pyramid data structure • An improved K-means with integer lookup tables • The new algorithm • Experimental results

11. The Proposed method-1/6Two-layer pyramid data structure • The algorithm employs two strategies. • Firstly, a two-layer structure of a color image is established. • Then, an improved K-means with integer based lookup table implementation is applied to each layer. • A typical size of the upper layer is 1/16 of the size of its lower layer. Therefore, the clustering in the upper layer can be completed quickly, and the approximate cluster centers can be obtained.

12. The Proposed method-2/6Two-layer pyramid data structure

13. The Proposed method-3/6An improved K-means with integer lookup tables • The conventional K-means algorithm usually has many repetitive operations in computing the distances, djk, for the pixels with the same color or RGB values. Here, we design an integer lookup table, LUT, to eliminate the repetition.

14. The Proposed method-4/6 An improved K-means with integer lookup tables • LUT is three-dimensional and defined as follows: • Establishing such a lookup table takes K×3×256 times of computation. If K=4, then K×3×256=3072, which is much less than the number of pixels in a large image. The maximum value of LUT is 100×(255-0)2=6502500.

15. The Proposed method-5/6The new algorithm

16. The Proposed method-6/6The new algorithm • In the above algorithm, steps 1-6 are performed upon the upper layer and the rest steps are performed on the lower layer. • In steps 5(a) and 9(a) the relative distances from a pixel to the cluster centers are obtained directly from the lookup tables.

17. Outline • Introduction • The K-Means algorithm • The Proposed method • Two-layer pyramid data structure • An improved K-means with integer lookup tables • The new algorithm • Experimental results

18. Experimental results-1/5 • In the experiments, over 30 large color images were used to compare the proposed algorithm and the conventional K-means algorithm. • The terminating condition ε was set to 0.1 for both algorithms. • Fig. 2(a) is a 3000×2000 color image, in which the white, blue and other regions represent cloud, water, and mountain, respectively. • Fig. 2(b) gives the identical segmentation results obtained by the two algorithms.

19. Experimental results-2/5

20. Experimental results-3/5 • M1×M2is the number of pixels of the original image, and M3is the number of the pixels classified differently by the two algorithms.

21. Experimental results-4/5 • Fig. 3(a) is the original color image of size 4000×2600. • Table 2 summarizes the results. In this example, although the rate of the same classified pixelsis not 100% (but very close to 100%).

22. Experimental results-5/5

23. Conclusion • In this paper, a fast algorithm is proposed by effectively combining a two-layer pyramid structure and an improved implementation of the K-means algorithm. • The proposed algorithm performs significantly faster without noticeable degradation of the results in comparison to conventional the K-means algorithm.