Image Segmentation with Partial Convexity Shape Prior Using Discrete Conformality Structures

Abstract

Image segmentation aims to partition an image into meaningful regions and extract important objects therein. In real applications, the given images may contain multiple overlapping objects with noisy background, creating great challenges to the segmentation task. In these cases, prior information of the target object is essential for an accurate and meaningful segmentation result. In this paper, we present a new convexity shape prior segmentation framework to guarantee the segmented region to be fully or partially convex according to the user's preference. The basic idea is to incorporate a registration-based segmentation model with a specially designed convexity constraint. The convexity constraint is based on the discrete conformality structures of the image mesh. To solve the segmentation model, we propose an iterative scheme, which smoothly deforms a template object to trace the boundary of the target object. A projection is carried out to enforce the convexity constraint. The target object is then captured by a (fully or partially) convex region. Convexity is the only prior information needed for a (fully) convex shape, whereas the location of partial convexity is needed for a partially convex shape. Experiments have been carried out on both synthetic and real images and the results demonstrate the effectiveness of our proposed framework.