在電腦視覺與圖形識別的應用系統中，影像分割是一個很重要的技術。許多已被提出的影像分割方法運用灰階、色彩值、梯度資訊、紋理特徵等做分割。近來一種”不使用邊的主動輪廓法 (active contours without edges) “被提出來偵測影像中的物件。這個方法使用等階集法，而且有能力去處理尖銳的端點及內凹角、並且可以自動化的改變拓撲結構。在這篇論文中，我們改進了這個方法應用於多頻譜及高雜訊的影像分割。
　　在主動輪廓法 (active contour method) 中，需要在Mumford-Shah函數裡設定參數。不同的參數設定會導致不同的分割結果。此外，如果設定的參數相差太多，分割的結果會不正確。在這篇論文中，我們分析影像的亂度，提出了一個適應性的設定參數方法做影像分割。適應性的改善對於自動化的影像分割是很有用的，特別是對於高雜訊影像。
　　由實驗的結果，我們發現我們的方案是可信賴且更有效率的，我們多花了時間在計算影像的亂度，但是對低雜訊的影像分割卻減少所需要的演化次數。在另一方面，我們改善了高雜訊影像分割時輪廓擷取的正確性。

Image segmentation is an important technique for the applications of computer vision and pattern recognition systems. Many image segmentation methods have been proposed based on gray levels, color values, gradient information, texture properties, etc. A new method called active contours without edges has been proposed to detect objects in a given image. The method employed the level set formulation and the level set method has abilities to deal with the cusps, corners, and automatic topological changes. In this study, we improve the method for multi-spectral and high-noised image segmentation.
In the active contour method, we need to set parameters in the Mumford-Shah function. Different parameters will result in different segmentation results. Moreover, the model does not perform well if the parameters are far different. In this study, we propose a method to adaptively set parameters for image segmentation. The adaptive improvement is useful for automatic image segmentation; especially for high-noised images.
From the experimental results, we can find that our scheme is reliable and more efficient. We spend time on computing entropy, but the number of iteration times of curve evolving for low-noised images is reduced. On the other hand, we improve the correctness of contour extraction for high-noised images.

[1]Canny, J. F., “A Computational approach to edge-detection,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol.8, pp.679-698, 1986.
[2]Caselles, V., R. Kimmel, and G. Sapiro, “Geodesic active contour,” Internat. J. Comput. Vision, vol.22, pp.61-69, 1997.
[3]Chan, Tony and L. A. Vese, “An efficient variational multiphase motion for the Mumford-Shah segmentation model,” in Proc. of the Thirty-Fourth Asilomar Conf. on Signals, Systems and Computers, Pacific Grove, vol.1, Nov., 2000, pp.490-494.
[4]Chan, T. and L. A. Vese, “Active contours without edges,” IEEE Trans. Image Processing, vol.10, pp.266-277, Feb. 2001.
[5]Chan, T. and L. A. Vese, “A level set algorithm for minimizing the Mumford-Shah functional in image processing,” in Proc. 1st IEEE Workshop on variational and Level Set Methods in Computer Vision, Vancouver, Canada, July 13, 2001, pp.161-168.
[6]Chang, Y. L. and X. Li, “Adaptive image region-growing,” IEEE Trans. Image Processing, vol.3, pp.868-872, 1994.
[7]Choi, W., K. Lam, and W. Siu, “An adaptive active contour model for highly irregular boundaries,” Pattern Recognition, vol.34, pp.323-331, 2001.
[8]Chopp, D., “Computing minimal surfaces via level set curvature flow,” Journal Computational Physics, vol.106, pp.77-91, May 1993.
[9]Feghali, R. and A. Mitiche, “Spatiotemporal motion boundary detection and motion boundary velocity estimation for tracking moving objects with a moving camera: a level sets PDEs approach with concurrent camera motion compensation,” IEEE Trans. on Image Processing, vol.13, pp.1473-1490, 2004.
[10]Gonzalez, C. Rafael and Richard E. Woods, Digital Image Processing, Prentice Hall, Upper Saddle River, N J, 2002.
[11]Haralick, R. M. and L. G. Shapiro, ”Survey: Image segmentation techniques,” Comput. Vis. Graph. Image Process., vol. 29, 1985, pp.100-132.
[12]Hijjatoleslami, S. A. and J. Kittler, “Region growing: A new approach,” IEEE Trans. Image Processing, vol.7, pp.1079-1084, 1998.
[13]Ji, L. and H. Yan, “An intelligent and attractable active contour model for boundary extraction,” in Proc. IEEE Int’l Conf. on Acoustic, Speech, and Signal Processing, Phoenix. Arizona, Mar., 1999, pp.3309-3312.
[14]Kass, M., A. Witikin, and D. Terzopoulos, “Snakes: Active contour models,” International Journal of Computer Vision, vol.1, no.4, pp.321-331, 1978.
[15]Kichenassamy, S., A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzy, “Gradient flows and geometric active contour models,” in Proc. Int. Conf. Computer Vision, Cambridge, MA, 1995, pp.73-78.
[16]Kim, Seongjai and Hyeona Lim, “A hibrid level set approach for efficient and reliable image segmentation,” submitted to IEEE International Conf. on Image Processing, 2005.
[17]Lam, K. M. and H. Yan, “Fast greedy algorithm for active contours,” Electronics Letters, vol.30, no.1, pp.21-22, 1994.
[18]Mansouri, A. R., “Region tracking via level set PDEs without motion computation,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol.24, pp.947-961, July 2002.
[19]Merriman, B., Bence, J., and Osher, S., “Motion of Multiple Junctions: A Level Set Approach,” Journal Computational Physics, Vol.112, pp.334-363, 1994.
[20]Mumford, D. and J. Shah, “Optimal approximation by piecewise smooth functions and associated variational problems,” Commun. Pure Appl. Math, vol.42, pp.577-685, 1989.
[21]Osher, S. and J. A. Sethian, “Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation,” Journal of Computational Physics, vol.79, pp.12-49, 1988.
[22]Osher, S. and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer-Verlag, Los Angeles, 2003.
[23]Paragios, Nikos, “A level set approach for shape-driven segmentation and tracking of the left ventricle,” IEEE Trans. Medical Imaging, vol.22, pp.773-776, June, 2003.
[24]Paragios, Nikos and R. Deriche, “A PDE-based level-set approach for detection and tracking of moving objects,” in Proc. Sixth Int. Conf. Computer Vision, Bombay, India, Jan 1998, pp.1139-1145.
[25]Paragios, Nikos and R. Deriche, “Geodesic active contours and level sets for the detection and tracking of moving objects,” IEEE Transactions on Pattern Analysis and Machine intelligence, vol.22, pp.266-280, 2000.
[26]Sethian, J. A., Level Set Methods, Cambridge University Press, California, 1996.
[27]Shannon, C. E., ” A Mathematical Theory of Communication,” Bell Sys. Tech. Journal, vol. 27, pp.379-423, 1948.
[28]Siddiqi, K., Y. B. Lauzi