  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.
