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Convexity prior is one of the main cue for human vision and shape completionwith important applications in image processing, computer vision. This paperfocuses on characterization methods for convex objects and applications inimage processing. We present a new method for convex objects representationsusing binary functions, that is, the convexity of a region is equivalent to asimple quadratic inequality constraint on its indicator function. Models areproposed firstly by incorporating this result for image segmentation withconvexity prior and convex hull computation of a given set with and withoutnoises. Then, these models are summarized to a general optimization problem onbinary function(s) with the quadratic inequality. Numerical algorithm isproposed based on linearization technique, where the linearized problem issolved by a proximal alternating direction method of multipliers withguaranteed convergent. Numerical experiments demonstrate the efficiency andeffectiveness of the proposed methods for image segmentation and convex hullcomputation in accuracy and computing time.

A Binary Characterization Method for Shape Convexity and Applications