外文翻譯--基于偏微分方程的彩色圖像分割（英文）

1、 ?egmentation of Color Image Based on Partial Differential Equations Chun Yuan Division of Information Technology Graduate School at Shenzhen, Tsinghua University Shenzhen, China yuanc@sz.tsinghua.edu.cn Shangli Liang Di

2、vision of Information Technology Graduate School at Shenzhen, Tsinghua University Shenzhen, China shangliliang@gmail.comAbstract—Image segmentation is an important task in image processing. A lot of image segmentation m

3、ethods or models have been proposed. But most of these methods cannot work well with color images, which actually contain more useful information about the objects inside. In this paper, a segmentation model for colo

4、r images is proposed. The new model is based on the GAC segmentation model and extends the concept of gradient from one channel to three channels. Experiments show that the new model has better performance than the GA

5、C model, especially in the segmentation of color images. Keywords- image segmentation; image processing; PDE; GAC; I. INTRODUCTION Image segmentation is one of the most important tasks in image processing. The purpose o

6、f image segmentation is to separate the objects from the background of the image for further processing such as Object Recognition, Object Tracking and so on. A lot of segmentation methods have been proposed in the t

7、raditional image processing aspect [1] [2] [3] [4]. According to the information used, these methods can be mainly classified into three categories: method based on region/threshold, method based on edges and methods

8、based on texture. And in the recent decades, the theory of partial differential equations – PDEs has been well developed and introduced into the image processing aspect. Many new approaches of image segmentation

9、 based on PDEs have been proposed ever since. However, most of the segmentation methods mentioned above just focus on the processing of gray images and do not work well with color images. Since color images contain mu

10、ch more information about the objects than gray images, segmentation based directly on color images can achieve more accurate results. In this paper, a segmentation model of color image based on PDEs is proposed. II.

11、 RELATED WORK Image segmentation based on PDEs has been well developed in the recent years. In 1987, M. Kass, A. Witkin and D. Terzopoulos came up with the Active Contour model or Snake model which is the first image

12、segmentation model based on PDEs[5]. The key idea of the model is to translate the problem of separating the objects into minimizing an energy function of a close curve: E[C(p)] = The first two parts of the function a

13、re the inner energy of the curve which is used to shorten and smooth the curve. The last part is the energy from the image which is used to hold the curve onto the edges of the objects. But the problem of the Snake m

14、odel is that the energy function depends on not only the position and shape of the curve, but also the parameter of the curve. And the value of the energy function changes arbitrarily according to different types of t

15、he parameter. To overcome the shortness of Snake model, V. Caselles, R. Kimmel and G. Sapiro proposed the Geodesic Active Contour Model which did not contain any free parameter[6]. The GAC model is also an energy funct

16、ion of the curve which consists of the internal power of the curve and the external power from the image. Since our new segmentation model for color image mainly based of the GAC model, we will discuss more about the

17、 behavior and other details of the GAC model later. Cohen L. and Kimmel R. proposed an interactive segmentation model which can get accurate even if the background has many noises[7]. T. Chan and L. Vese proposed a se

18、gmentation model based on PDEs which can work well with images which do not contain strong edges[8]. During the evaluation of the curve, there may me topological changes. To cope with this situation, S. Osher and J. A

19、. Sethian proposed the level set segmentation method[9]. The basic idea of level set is to embed the curve into a 2D function, which is actually a 3D model. Since the curve corresponds to the zero level set of the emb

20、ed function, the evaluation of the embed function actually represents the evaluation of the curve. ?Figure 1. Level Set III. GEODESIC ACTIVE CONTOUR MODEL In the Geodesic Active Contour model, the problem of finding th

21、e best contour of the object is translated into the problem of minimizing the following energy function: 2011 Fourth International Symposium on Computational Intelligence and Design978-0-7695-4500-4/11 $26.00 © 201

22、1 IEEE DOI 10.1109/ISCID.2011.161 238(4.5) Which means the channel with larger gradient will contribute more to the total gradient of the color image. Once the gradient ?Icolor and the corresponding are obtained, the gr

23、adient descent flow 4.2 can be used to instruct the evaluation of the curve. And this color image segmentation model, or color-GAC model, can work well with color images while the traditional GAC model fails. V. CONC

24、LUSION As an important part of image processing, image segmentation is getting more and more attention. A lot of segmentation methods and models have been proposed, such as the traditional segmentation method based on

25、edges and the GAC segmentation model. But most of these methods and models only work well on gray images. Since color images have more information about the object inside, segmentation based on color images can achie

26、ve more accurate results. So in this paper, we propose a segmentation model for color images. The new color image segmentation model is actually an extension of the GAC segmentation model and is called the color-GAC

27、model. And from the experiments, we can see that the color-GAC model can work well with color images while the traditional GAC model fails. The key component of the color-GAC model is the expression of the gradient of

28、 the color images. So it is easy to be improved or extended by modifying the expression of the gradient. REFERENCE [1] Wei YingMa, B. S. Manjunath. Edge flow: a technique for boundary detection and image segmentation.

29、IEEE, IP, 2000, 9(8): 1375~1388. [2] K. R. Castlemen. Digital Image Processing. Prentice Hall, 1996. [3] J. K. Hawkins. Texture Properties for Pattern Recogintion, in Picture Processing and Psychopiclorics. New York: Aca

30、demic Press, 1980, 347~370. [4] M. Clark, A. C. Bobik, W. S. Geisler. Multi-channel texture analysis using localized spatial filter. IEEE, PAMI, 1990, 12(1): 55~73. [5] M. Kass, A. Witkin, D. Terzopoulos. Snakes: Active

31、 contour models. International journal of computer vision, 1988, 1(4):321–331. [6] V. Caselles, J. M.Morel, G. Spqiro. Geodesic active contours. Int. J. Comput. Vision, 1997, 22:61~79. [7] L. Cohen, R. Kimmel. Global min

32、imum for active contour models: a minimal path approach. Int. J. Comput. Vis., 1997. [8] T. F. Chan, L. Vese. Active contours without edges. CAM Report 98-53. UCLA. 1998. [9] S. Osher, J. Sethian. Fronts propagating with