A Novel Multi-Layer Level Set Method for Image Segmentation

In this paper, a new multi-layer level set method is proposed for multi-phase image segmentation. The proposed method is based on the conception of image layer and improved numerical solution of bimodal Chan-Vese model. One level set function is employed for curve evolution with a hierarchical form in sequential image layers. In addition, new initialization method and more efficient computational method for signed distance function are introduced. Moreover, the evolving curve can automatically stop on true boundaries in single image layer according to a termination criterion which is based on the length change of evolving curve. Specially, an adaptive improvement scheme is designed to speed up curve evolution process in a queue of sequential image layers, and the detection of background image layer is used to confirm the termination of the whole multi-layer level set evolution procedure. Finally, numerical experiments on some synthetic and real images have demonstrated the efficiency and robustness of our method. And the comparisons with multi-phase Chan-Vese method also show that our method has a less time-consuming computation and much faster convergence.

[1]  John D. Towers Two methods for discretizing a delta function supported on a level set , 2007, J. Comput. Phys..

[2]  Josef Kittler,et al.  A Performance Measure for Boundary Detection Algorithms , 1996, Comput. Vis. Image Underst..

[3]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[4]  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.

[5]  Li Jun,et al.  A Fast Level Set Approach to Image Segmentation Based on Mumford-Shah Model , 2002 .

[6]  Dana H. Ballard,et al.  Computer Vision , 1982 .

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

[8]  Sang Uk Lee,et al.  On the color image segmentation algorithm based on the thresholding and the fuzzy c-means techniques , 1990, Pattern Recognit..

[9]  Roderick Urquhart,et al.  Graph theoretical clustering based on limited neighbourhood sets , 1982, Pattern Recognit..

[10]  Witold Pedrycz,et al.  Unsupervised hierarchical image segmentation with level set and additive operator splitting , 2005, Pattern Recognit. Lett..

[11]  Andrew Blake,et al.  Initialisation and Termination of Active Contour Level-Set Evolutions , 2003 .

[12]  Milan Sonka,et al.  Image Processing, Analysis and Machine Vision , 1993, Springer US.

[13]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Y. Tsai Rapid and accurate computation of the distance function using grids , 2002 .

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

[16]  Azriel Rosenfeld,et al.  Computer Vision , 1988, Adv. Comput..

[17]  S. Osher,et al.  Total variation and level set methods in image science , 2005, Acta Numerica.

[18]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[19]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[20]  Josef Kittler,et al.  Region growing: a new approach , 1998, IEEE Trans. Image Process..

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

[22]  B. Engquist,et al.  Discretization of Dirac delta functions in level set methods , 2005 .

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

[24]  G. Allaire,et al.  A level-set method for vibration and multiple loads structural optimization , 2005 .

[25]  K. R. Ramakrishnan,et al.  Stability and convergence of the level set method in computer vision , 2007, Pattern Recognit. Lett..

[26]  Suk Ho Lee,et al.  Level set-based bimodal segmentation with stationary global minimum , 2006, IEEE Transactions on Image Processing.

[27]  Junaed Sattar Snakes , Shapes and Gradient Vector Flow , 2022 .

[28]  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..

[29]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  Xiaobo Li,et al.  Adaptive image region-growing , 1994, IEEE Trans. Image Process..