Convex Object(s) Characterization and Segmentation Using Level Set Function

In practice, the objects of interest have some shape priors, which would be destroyed by occlusions, distortions and noises. Therefore, the characterization of the shape priors attracts increasing attention. This paper is devoted to characterization of convexity prior and its applications in objects segmentation in two-dimensional (2D) spaces using level set function. The shape convexity can be characterized by the Laplacian nonnegativity of the associated signed distance function on the whole image domain, zero-sublevel set and zero-superlevel set. This result is extended to characterization for multiple convex objects and ring shape object with outer, inner and both convex boundaries. One of the advantages of this method is that only one signed distance function is needed to characterize a single object, multiple objects and ring shape with boundary(ies) convexity prior. The characterization methods are incorporated into image segmentation model. In addition, some labels on the foreground and background and landmarks on the boundary of the object(s) can be taken into account as constraints to improve the accuracy of segmentation. A general and efficient numerical framework is developed to solve the proposed models using alternative direction method. Experiments on various images validated the effectiveness and efficiency of the proposed models and algorithms.