Residual approach on a hierarchical segmentation

Residual operators analyze the evolution of an image subject to the application of a series of transformations, for example a series of openings of increasing size. When a significant object is filtered out by a transformation corresponding to its size, an important residue is observed. Maximal residues are kept for each pixel, indicating the most significant objects present in the image. Different families of operators have been used in the literature: morphological openings or closings, attribute openings or openings by reconstruction. In this paper we propose to compute residues on a hierarchy of partitions, computing the differences between regions at different hierarchical levels based on the classical earth mover´s distance. The advantage of our approach is that it is autodual and generic as it can be applied with any hierarchical approach.