Re-initialization Free Level Set Evolution via Reaction Diffusion
Kaihua Zhang, Lei Zhang , Huihui Song and David Zhang
Dept. of Computing, The Hong Kong Polytechnic University, Hong Kong, China
(a) Basic flow diagram of traditional level set evolution.
(b) Flow diagram of our proposed RD level set evolution.
Abstract ¡ª This paper presents a novel reaction-diffusion (RD) method for implicit active contours, which is completely free of the costly re-initialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in a RD-LSE equation, to which a piecewise constant solution can be derived. In order to have a stable numerical solution of the RD based LSE, we propose a two-step splitting method (TSSM) to iteratively solve the RD-LSE equation: first iterating the LSE equation, and then solving the diffusion equation. The second step regularizes the level set function obtained in the first step to ensure stability, and thus the complex and costly re-initialization procedure is completely eliminated from LSE. By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement. The proposed RD method can be generalized to solve the LSE for both variational level set method and PDE-based level set method. The RD-LSE method shows very good performance on boundary anti-leakage, and it can be readily extended to high dimensional level set method. The extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed RD-LSE approach.
1. Motion of dumbbell driven by mean curvature
(a) LSE by RD  (b) LSE without re-initialization
2. GAC model  implemented by RD method on an image with interior boundary.
(a) Level set evolution (LSE) (b) Evolution of middle slice of LSF
(c) Initial level set function (LSF) (d) Final LSF
3. LSE of PDE-based level set driven by constant force
(a) Result by RD  (b) Final LSF by RD 
(c) Result by re-initialization (d) Final LSF by re-initialization
(e) Result without re-initialization (f) Final LSF without re-initialization
 K.Zhang, L.Zhang, H.Song, and D.Zhang, ¡°Re-initialization Free Level Set Evolution via Reaction Diffusion,¡± IEEE Trans. on Image Processing, to appear.
Our former related work
 K.Zhang, L.Zhang, H.Song and W. Zhou, ¡°Active contours with selective local or global segmentation: a new formulation and level set method,¡± Image and Vision Computing, vol. 28, issue 4, pp. 668-676, April 2010.Paper Source code Website
Other related work
 C. Li, C. Xu, C. Gui, and M. D. Fox, ¡°Level set evolution without re-initialization: A new variational formulation,¡± Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 430¨C436, 2005.
 X.Xie, ¡°Active Contouring Based on Gradient Vector Interaction and Constrained Level Set Diffusion,¡± IEEE Trans. Image Processing, vol. 19, no. 1, pp. 154-164, 2010.
 V.Caselles, R.Kimmel, and G.Sapiro, ¡°Geodesic Active Contours,¡± Int. J. Comput. Vis., vol.22, no.1 pp. 61¨C79,1997.
 T. Chan and L. Vese, ¡°Active contours without edges,¡± IEEE Trans. Image Process, vol. 10, no. 2, pp. 266¨C277, Feb. 2001.
 C. Li, C. Kao, J. Gore, and Z. Ding, ¡°Implicit Active Contours Driven by Local Binary Fitting Energy,¡± Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1¨C7, 2007.
C. Li, C. Xu, C. Gui, and M. D. Fox, ¡°Distance Regularized Level Set Evolution and Its Application to Image Segmentation,¡± IEEE Trans. Image Processing, vol. 19, no. 12, pp. 154-164, Dec. 2010.