A Simplified Active Contour Model with Free Endpoints

Abstract

The CV (Chan-Vese) model is a widely used active contour model for image segmentation and it is also known as piecewise constant active contour (PCAC) model. The minimization of the objective functional of PCAC model is non-convex even when the optimal region constants are known a priori. The piecewise smooth active contour (PSAC) model is an extension of the PCAC model and the objective functional is non-convex and harder to minimize than PCAC model. The energy functional of the active contour model with free endpoints (FEAC) is based on the PSAC model and even harder to minimize than the PSAC model. In order to find the solution of the FEAC model, a simplified active contour model with free endpoints (SFEAC) is proposed in this paper. The SFEAC model is based on the PCAC model which means that each region is represented as a constant instead of a smooth function. The level set implementation of SFEAC model is derived. A fast global minimization implementation is also proposed for SFEAC model which considers the geodesic edge term. The global optimal solution can thus be obtained. The proposed method is compared with FEAC model and superior results are obtained. The proposed method is also compared with PCAC model, PSAC model, morphological PCAC model, PCAC model incorporated with geodesic edge term (PCGAC) and fast global minimization implementation of PCAC model, experimental results show that the proposed method can get better segmentation image with higher accuracy and less running time.