Scale space operators on hierarchies of segmentations

Abstract

A hierarchy of segmentations(partitions) is a multiscale set representation of the image. This paper introduces a new set of scale space operators or transformations on the space of hierarchies of partitions. An ordering of hierarchies is proposed which is endowed by an ω-ordering based on a global energy over the classes of the hierarchy. A class of Matheron semigroups are shown to exists in this ordering of hierarchies. A second contribution is the saliency transformation which fuses a saliency function corresponding to a hierarchy, with an external function, rendering a new or transformed saliency function. The results are demonstrated on the Berkeley dataset. © 2013 Springer-Verlag.