A Convex Clustering-based Regularizer for Image Segmentation

In this paper we present a novel way of combining the process of k-means clustering with image segmentation by introducing a convex regularizer for segmentation-based optimization problems. Instead of separating the clustering process from the core image segmentation algorithm, this regularizer allows the direct incorporation of clustering information in many segmentation algorithms. Besides introducing the model of the regularizer, we present a numerical algorithm to efficiently solve the occurring optimization problem while maintaining complete compatibility with any other gradient descent based optimization method. As a side-product, this algorithm also introduces a new way to solve the rather elaborate relaxed k-means clustering problem, which has been established as a convex alternative to the non-convex k-means problem.