Image Segmentation via the Continuous Max-Flow Method Based on Chan-Vese Model

The Chan-Vese model using variational level set method (VSLM) has been widely used in image segmentation, but its efficiency is a challenge problem due to high computation costs of curvature as well as the Eiknal equation constraint. In this paper, we propose a continuous Max-Flow (CMF) method based on discrete graph cut approach to solve the VSLM for image segmentation. Firstly, we recast the original Chan-Vese model to a continuous max-flow problem via the primal-dual method and solve it using the alternating direction method of multipliers (ADMM). Then, we use the projection method to recover the continuous level set function for image segmentation expressed as a signed distance function. Finally, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

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

[2]  Xue-Cheng Tai,et al.  Global Binary Optimization on Graphs for Classification of High-Dimensional Data , 2015, Journal of Mathematical Imaging and Vision.

[3]  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.

[4]  Ekaterina Merkurjev,et al.  Convex Variational Methods on Graphs for Multiclass Segmentation of High-Dimensional Data and Point Clouds , 2016, Journal of Mathematical Imaging and Vision.

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

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

[7]  Gilbert Strang,et al.  Maximum flows and minimum cuts in the plane , 2010, J. Glob. Optim..

[8]  Richard G. Baraniuk,et al.  Fast Alternating Direction Optimization Methods , 2014, SIAM J. Imaging Sci..

[9]  Xue-Cheng Tai,et al.  Primal-dual method for continuous max-flow approaches , 2015 .

[10]  Guodong Wang,et al.  Some fast projection methods based on Chan-Vese model for image segmentation , 2014, EURASIP Journal on Image and Video Processing.

[11]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[12]  Xue-Cheng Tai,et al.  A study on continuous max-flow and min-cut approaches , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[14]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Xue-Cheng Tai,et al.  Maximizing Flows with Message-Passing: Computing Spatially Continuous Min-Cuts , 2015, EMMCVPR.

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

[17]  Xue-Cheng Tai,et al.  A spatially continuous max-flow and min-cut framework for binary labeling problems , 2014, Numerische Mathematik.

[18]  Qiang Chen,et al.  Integrating clustering with level set method for piecewise constant Mumford-Shah model , 2014, EURASIP J. Image Video Process..

[19]  T. Chan,et al.  A Variational Level Set Approach to Multiphase Motion , 1996 .

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