Image segmentation algorithm by piecewise smooth approximation
 Yan Wang,
 Chuanjiang He
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Abstract
We propose a novel image segmentation algorithm using piecewise smooth (PS) approximation to image. The proposed algorithm is inspired by four wellknown active contour models, i.e., Chan and Vese’ piecewise constant (PC)/smooth models, the regionscalable fitting model, and the local image fitting model. The four models share the same algorithm structure to find a PC/smooth approximation to the original image; the main difference is how to define the energy functional to be minimized and the PC/smooth function. In this article, pursuing the same idea we introduce different energy functional and PS function to search for the optimal PS approximation of the original image. The initial function with our model can be chosen as a constant function, which implies that the proposed algorithm is robust to initialization or even free of manual initialization. Experiments show that the proposed algorithm is very appropriate for a wider range of images, including images with intensity inhomogeneity and infrared ship images with low contrast and complex background.
 He, L, Peng, Z, Everding, B, Wang, X, Han, CY, Weiss, KL, Wee, WG (2008) A comparative study of deformable contour methods on medical image segmentation. Image Vision Comput 26: pp. 141163 CrossRef
 Papari, G, Petkov, N (2011) Edge and line oriented contour detection: state of the art. Image Vision Comput 29: pp. 79103 CrossRef
 Pal, NR, Pal, SK (1993) A review on image segmentation techniques. Pattern Recogn 26: pp. 12771294 CrossRef
 Wang, S, Siskind, JM (2003) Image segmentation with ratio cut. IEEE Trans. Pattern Anal. Mach. Intell 25: pp. 675690 CrossRef
 Nath, SK, Palaniappan, K (2009) Fast graph partitioning active contours for image segmentation using histograms. EURASIP J. Image Vide 2009: pp. 9
 Chabrier, S, Rosenberger, C, Emile, B, Laurent, H (2008) Optimizationbased image segmentation by genetic algorithms. EURASIP J. Image Vide 2008: pp. 110
 Canny, J (1986) A computational approach to edge detection. IEEE Trans. Pattern Analysis and Machine Intelligence 8: pp. 679714 CrossRef
 Kimmel, R, Bruckstein, AM (2003) On regularized Laplacian zero crossings and other optimal edge integrators. Int. J. Comput. Vis 53: pp. 225243 CrossRef
 He, L, Zheng, S, Wang, L (2010) Integrating local distribution information with level set for boundary extraction. J. Vis. Commun. Image R 21: pp. 343354 CrossRef
 Caselles, V, Catte, F, Coll, T, Dibos, F (1993) A geometric model for active contours in image processing. Numer. Math 66: pp. 131 CrossRef
 Caselles, V, Kimmel, R, Sapiro, G (1997) Geodesic active contours. Int. J. Comput. Vis 22: pp. 6179 CrossRef
 Chan, TF, Vese, LA (2001) Active contours without edges. IEEE Trans. Image Process 10: pp. 266277 CrossRef
 Li, C, Xu, C, Gui, C, Fox, MD (2005) Proceedings of IEEE conference on Computer Vision and Pattern Recognition (CVPR).
 Li, C, Kao, C, Gore, JC, Ding, Z (2008) Minimization of regionscalable fitting energy for image segmentation. IEEE Trans. Image Process 17: pp. 19401949 CrossRef
 Wang, L, Li, C, Sun, Q, Xia, D, Kao, C (2009) Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation. Comput. Med. Imaging Graph 33: pp. 520531 CrossRef
 Zhang, K, Song, H, Zhang, L (2010) Active contours driven by local image fitting energy. Pattern Recognit 43: pp. 11991206 CrossRef
 Wang, Y, He, C (2012) Adaptive level set evolution starting with a constant function. Appl. Math. Model 36: pp. 32173228 CrossRef
 Osher, S, Sethian, JA (1988) Fronts propagating with curvaturedependent speed: algorithms based on HamiltonJacobi formulations. J. Comput. Phys 79: pp. 1249 CrossRef
 Mumford, D, Shah, J (1989) Optimal approximation by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math 42: pp. 577685 CrossRef
 Wang, X, He, L, Wee, WG (2004) Deformable contour method: a constrained optimization approach. Int. J. Comput. Vis 59: pp. 87108 CrossRef
 Vese, LA, Chan, TF (2002) A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis 50: pp. 271293 CrossRef
 Tsai, A, Yezzi, A, Willsky, AS (2001) Curve evolution implementation of the Mumford–Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans. Image Process 10: pp. 11691186 CrossRef
 Lankton, S, Tannenbaum, A (2008) Localizing regionbased active contours. IEEE Trans. Image Process 17: pp. 20292039 CrossRef
 Brox, T, Cremers, D (2007) On the statistical interpretation of the piecewise smooth Mumford–Shah functional. Proceedings of the Scale Space Methods and Variational Methods (SSVM ’07), vol. 4485 of Lecture Notes in Computer Science. Ischia, Italy, pp. 203213
 Piovano, J, Rousson, M, Papadopoulo, T (2007) Efficient segmentation of piecewise smooth images. Proceedings of the Scale Space Methods and Variational Methods (SSVM ’07). Lecture Notes in Computer Science, Ischia, Italy, pp. 709720 CrossRef
 Li, C, Kao, C, Gore, J, Ding, Z (2007) Implicit active contours driven by local binary fitting energy. Proceedings of IEEE conference on Computer Vision and Pattern Recognition (CVPR). Washington, USA, pp. 17
 Gao, S, Bui, TD (2005) Image segmentation and selective smoothing by using Mumford–Shah model. IEEE Trans. Image Process 14: pp. 15371549 CrossRef
 Li, C, Xu, C, Gui, C, Fox, MD (2010) Distance regularized level set evolution and its application to image segmentation. IEEE Trans. Image Process 19: pp. 32433254 CrossRef
 Aubert, G, Kornprobst, P (2002) Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Springer, New York
 Title
 Image segmentation algorithm by piecewise smooth approximation
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

EURASIP Journal on Image and Video Processing
2012:16
 Online Date
 September 2012
 DOI
 10.1186/16875281201216
 Online ISSN
 16875281
 Publisher
 Springer International Publishing AG
 Additional Links
 Topics
 Keywords

 Image segmentation
 Active contour model
 Piecewise smooth approximation
 Level set method
 Partial differential equation
 Authors

 Yan Wang ^{(1)}
 Chuanjiang He ^{(2)}
 Author Affiliations

 1. College of Mathematics, Chongqing Normal University, Chongqing, 401331, China
 2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China