Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms
This work addresses the challenge of incorporating convexity priors in image segmentation, which is incremental as it builds on existing methods by offering a more efficient representation.
The paper tackled the problem of representing convex shapes for image segmentation by introducing a novel binary representation based on inequality constraints, which led to efficient algorithms for segmentation with convexity prior, as demonstrated through various experiments showing its superiority.
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.