Superpixel Clustering

Abstract

This paper offers the simplest understanding of superpixels as maximal pixel clusters providing error-free obtaining of a limited sequence of accessible optimal piecewise constant image approximations with the minimum achievable approximation error (total squared error) E for each number of pixel clusters. The superpixel hierarchy is generated by the intersection of optimal image partitions into an increasing number of clusters g. It is irregular and differs markedly from the non-hierarchical sequence of optimal approximations, since described by a non-convex dependence of the approximation error E on the cluster number g. Therefore, the task of hierarchical superpixel clustering is posed and solved, which is briefly described in the paper.