Hierarchies of partitions and morphological segmentation

Abstract

Segmenting an image amounts to producing a partition, in which each tile represents an object of the image. Given an image, how to segment it into a predetermined number of regions ? How to select the objects to represent or discard when the number of regions varies ? Producing a series of nested partitions, or hierarchy is an answer to this question but is also central to practically all morphological segmentation approaches. In the present paper, we define, study, construct and show how to use for various segmention or filtering tasks such hierarchies.