An unconditionally stable numerical method for bimodal image segmentation

Keywords: Image segmentation Level set model Chan–Vese model Lee–Seo model Energy minimization Unconditional stability a b s t r a c t In this paper, we propose a new level set-based model and an unconditionally stable numerical method for bimodal image segmentation. Our model is based on the Lee–Seo active contour model. The numerical scheme is semi-implicit and solved by an analytical method. The unconditional stability of the proposed numerical method is proved analytically. We demonstrate performance of the proposed image segmentation algorithm on several synthetic and real images to confirm the efficiency and stability of the proposed method. Image segmentation is one of the fundamental tasks in computer vision and automatic image processing. Its goal is to divide the given image into different objects in each of which the intensity is homogeneous [1,2]. Up to now, various algorithms [3–19] have been proposed to solve the image segmentation problem. Among them, there are two widely used classical models based on the edges [3–9] or the regions [12–19]. In particular, the Chan–Vese model [13], which is a representative region-based image segmentation method, has been widely applied for various image processing applications. Their approach is based on the minimizing of the piecewise constant Mumford–Shah functional [18] by using the level set method [20]. The level set method is used to trace interfaces separating a domain into subdomains and effectively contours the image with the zero level set. Lee and Seo pointed out that the energy functional of the Chan–Vese method has no minimizer [17]. Therefore it is difficult to set a termination criterion on the algorithm. To resolve the problem, Lee and Seo proposed a new mathematical model. However, they implemented their model with an explicit finite difference scheme. In practice, a stable and robust numerical algorithm is more desirable than explicit schemes. Therefore, in this paper, we propose a new level set-based model which can be solved by an accurate and unconditionally stable semi-implicit method. This paper is organized as follows. In Section 2, a brief review of previous and our proposed models for image segmen-tation is given. We also describe our proposed numerical method and prove its unconditional stability. In Section 3, we present various image segmentation experiments on synthetic and real images using the proposed model and numerical method. Finally, conclusions are drawn in Section 4. 2. Description of the previous and the proposed models In this section, we …