Re-initialization Free Level Set Evolution via Reaction Diffusion

TL;DR

This paper introduces a reaction-diffusion based level set evolution method that eliminates the need for re-initialization, improving stability and simplicity in evolving active contours for image segmentation.

Contribution

The paper proposes a novel RD-LSE model with a two-step splitting method that ensures stability without re-initialization, applicable to high-dimensional problems and various level set methods.

Findings

Demonstrates improved boundary anti-leakage performance

Eliminates costly re-initialization in level set evolution

Effective on synthetic and real images

Abstract

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.