A new binary representation method for shape convexity and application to image segmentation

Abstract

We present a novel and computable characterization method for convex shapes. We prove that the shape convexity is equivalent to a quadratic constraint on the associated indicator function. Such a simple characterization method allows us to design efficient algorithms for various applications with convex shape prior. In order to show the effectiveness of the proposed approach, this method is incorporated with a probability-based model to extract an object with convexity prior. The Lagrange multiplier method is used to solve the proposed model. Numerical results on various images show the superiority of the proposed method.

A Binary Characterization Method for Shape Convexity and Applications

“…The numerical results illustrate that our proposed algorithm can maintain the convexity of objects(s) of interest, and the segmentation accuracies are improved. Comparing with the paper [26],…”

“…(ii) Proximal ADMM is employed to solve the resulting linearized minimization problems. Not only the numerical efficiency is higher than the algorithm in [26], but also the convergence of our proposed algorithm is guaranteed theoretically by selecting some proper semi-definite terms [28].…”

“…Very recently, we proposed a novel method for convex shape characterization in our short paper [26]. This method is similar to the level set function method reviewed above except a binary function is used to compute the curvature of the boundary curve.…”

“…The main purpose of this paper is to extend and improve the method in [26] in the sense that it has the ability to address multiple convex objects segmentation issue efficiently. Even more, we develop an efficient iterative algorithm based on linearization technique so that the considered model is divided into a series of convex minimization problems.…”

“…Finally, we also design an interactive technique to improve segmentation accuracies step by step according to additional subscribed labels by users. As mentioned in [26], the main computational cost lies in the convolution operations for the convex shape constraints on the objects. In our algorithm, only a few of b r 's with changed radii r's are used in the iteration procedure to reduce computation cost.…”