Level set image segmentation with Bayesian analysis

Classical level set methods easily suffer from deficiency in the presence of noise and other significant edges adjacent to the real boundary. This problem has not been effectively solved in the research community. In this paper, we propose an improved energy function to tackle this problem by continuously rectifying the deviation of the level set function according to the signed distance function. This is achieved using an expectation-maximisation algorithm. Experimental work shows the proposed framework outperforms the classical level set algorithms in accuracy and efficiency of image segmentation.

[1]  Anthony J. Yezzi,et al.  A Fully Global Approach to Image Segmentation via Coupled Curve Evolution Equations , 2002, J. Vis. Commun. Image Represent..

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

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

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

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

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

[7]  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).

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

[9]  Carlos Vázquez,et al.  Multiregion competition: A level set extension of region competition to multiple region image partitioning , 2006, Comput. Vis. Image Underst..

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

[11]  L. Evans Measure theory and fine properties of functions , 1992 .

[12]  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.

[13]  Anthony J. Yezzi,et al.  Gradient flows and geometric active contour models , 1995, Proceedings of IEEE International Conference on Computer Vision.

[14]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

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

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