A Binary Characterization Method for Shape Convexity and Applications

Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image processing. We present a new method for convex objects representations using binary functions, that is, the convexity of a region is equivalent to a simple quadratic inequality constraint on its indicator function. Models are proposed firstly by incorporating this result for image segmentation with convexity prior and convex hull computation of a given set with and without noises. Then, these models are summarized to a general optimization problem on binary function(s) with the quadratic inequality. Numerical algorithm is proposed based on linearization technique, where the linearized problem is solved by a proximal alternating direction method of multipliers with guaranteed convergent. Numerical experiments demonstrate the efficiency and effectiveness of the proposed methods for image segmentation and convex hull computation in accuracy and computing time.