An efficient operator splitting method for local region Chan-Vese model

In this paper, we propose an efficient operator splitting method for local region Chan-Vese (C-V) model for image segmentation. Different from the C-V model, we employ the window function and absorb the local characteristics of the image for improving the C-V model, which we called the local C-V model. The local C-V model can deal with the problem of intensity inhomogeneity which widely exists in the real-world images. By employing a Laplacian operator, we present an operator splitting method to update the level set function. Firstly, we solve the proposed model for evolving the level set function, which drives the active contour to move toward the object boundaries. Secondly, we introduce the Laplacian operator to act on the level set function as a diffusion term, which could efficiently ensure the smoothness and stability and eliminate the complex process of re-initialization. Besides, we increase a new constraint term which avoids updating the level set function seriously. Furthermore, we present an extension for vector-valued images. Experiment results show that our method is competitive with application to synthetic and real-world images.

[1]  Anthony J. Yezzi,et al.  Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification , 2001, IEEE Trans. Image Process..

[2]  V. Caselles,et al.  A geometric model for active contours in image processing , 1993 .

[3]  Lei Zhang,et al.  Active contours driven by local image fitting energy , 2010, Pattern Recognit..

[4]  Jianhong Shen,et al.  A Stochastic-Variational Model for Soft Mumford-Shah Segmentation , 2005, Int. J. Biomed. Imaging.

[5]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[6]  Mila Nikolova,et al.  Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models , 2006, SIAM J. Appl. Math..

[7]  C. Lamberti,et al.  Maximum likelihood segmentation of ultrasound images with Rayleigh distribution , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[8]  Chunming Li,et al.  Level set evolution without re-initialization: a new variational formulation , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[9]  Allen R. Tannenbaum,et al.  Localizing Region-Based Active Contours , 2008, IEEE Transactions on Image Processing.

[10]  Chunming Li,et al.  Minimization of Region-Scalable Fitting Energy for Image Segmentation , 2008, IEEE Transactions on Image Processing.

[11]  Daniel Cremers,et al.  On the Statistical Interpretation of the Piecewise Smooth Mumford-Shah Functional , 2007, SSVM.

[12]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[13]  Roman Goldenberg,et al.  Fast Geodesic Active Contours , 1999, Scale-Space.

[14]  Abu-Bakr Al-Mehdi,et al.  Increased Depth of Cellular Imaging in the Intact Lung Using Far-Red and Near-Infrared Fluorescent Probes , 2006, Int. J. Biomed. Imaging.

[15]  Lei Zhang,et al.  Active contours with selective local or global segmentation: A new formulation and level set method , 2010, Image Vis. Comput..

[16]  Rachid Deriche,et al.  A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape , 2007, International Journal of Computer Vision.

[17]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[18]  Xue-Cheng Tai,et al.  A variant of the level set method and applications to image segmentation , 2006, Math. Comput..

[19]  Chunming Li,et al.  Distance Regularized Level Set Evolution and Its Application to Image Segmentation , 2010, IEEE Transactions on Image Processing.

[20]  Xue-Cheng Tai,et al.  A binary level set model and some applications to Mumford-Shah image segmentation , 2006, IEEE Transactions on Image Processing.

[21]  Xue-Cheng Tai,et al.  Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach , 2011, International Journal of Computer Vision.

[22]  David Zhang,et al.  Reinitialization-Free Level Set Evolution via Reaction Diffusion , 2011, IEEE Transactions on Image Processing.

[23]  Chunming Li,et al.  Active contours driven by local Gaussian distribution fitting energy , 2009, Signal Process..

[24]  Tony F. Chan,et al.  Active Contours without Edges for Vector-Valued Images , 2000, J. Vis. Commun. Image Represent..

[25]  Xianghua Xie,et al.  Active Contouring Based on Gradient Vector Interaction and Constrained Level Set Diffusion , 2010, IEEE Transactions on Image Processing.

[26]  Wenbing Tao,et al.  Multiple piecewise constant with geodesic active contours (MPC-GAC) framework for interactive image segmentation using graph cut optimization , 2011, Image Vis. Comput..

[27]  Xiaofeng Wang,et al.  An efficient local Chan-Vese model for image segmentation , 2010, Pattern Recognit..

[28]  S. Osher,et al.  A PDE-Based Fast Local Level Set Method 1 , 1998 .

[29]  Yang Xiang,et al.  An active contour model for image segmentation based on elastic interaction , 2006, J. Comput. Phys..

[30]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[31]  Olivier Faugeras,et al.  Reconciling Distance Functions and Level Sets , 2000, J. Vis. Commun. Image Represent..

[32]  Xavier Bresson,et al.  Fast Global Minimization of the Active Contour/Snake Model , 2007, Journal of Mathematical Imaging and Vision.

[33]  Guillermo Sapiro,et al.  Geodesic Active Contours , 1995, International Journal of Computer Vision.

[34]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[35]  John W. Fisher,et al.  Submitted to Ieee Transactions on Image Processing a Nonparametric Statistical Method for Image Segmentation Using Information Theory and Curve Evolution , 2022 .

[36]  James M. Keller,et al.  Snakes on the Watershed , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[38]  Amar Mitiche,et al.  Variational and Level Set Methods in Image Segmentation , 2010 .

[39]  Josiane Zerubia,et al.  A Level Set Model for Image Classification , 1999, International Journal of Computer Vision.

[40]  Mark Sussman,et al.  An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow , 1999, SIAM J. Sci. Comput..

[41]  Daniel Cremers,et al.  On Local Region Models and the Statistical Interpretation of the Piecewise Smooth Mumford-shah Functional , 2007 .

[42]  Tony F. Chan,et al.  A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model , 2002, International Journal of Computer Vision.

[43]  Martin D. Fox,et al.  Erratum: Distance regularized level set evolution and its application to image segmentation (IEEE Transactions on Image Processingvol (2010) 19:12 (3243-3254)) , 2011 .

[44]  Kaleem Siddiqi,et al.  Flux maximizing geometric flows , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[45]  Chunming Li,et al.  Implicit Active Contours Driven by Local Binary Fitting Energy , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.