  We present a novel and effective binary representation for convex shapes. We
show the equivalence between the shape convexity and some properties of the
associated indicator function. The proposed method has two advantages. Firstly,
the representation is based on a simple inequality constraint on the binary
function rather than the definition of convex shapes, which allows us to obtain
efficient algorithms for various applications with convexity prior. Secondly,
this method is independent of the dimension of the concerned shape. In order to
show the effectiveness of the proposed representation approach, we incorporate
it with a probability based model for object segmentation with convexity prior.
Efficient algorithms are given to solve the proposed models using Lagrange
multiplier methods and linear approximations. Various experiments are given to
show the superiority of the proposed methods.
