Characterizing Images by the Gromov-Hausdorff Distances Between Derived Hierarchies

Abstract

A hierarchy is a series of nested partitions in which a coarser partition results from merging regions of finer ones. Each hierarchy derived from an image provides a particular structural description of the image content, depending upon the criteria for merging neighboring regions. Distinct hierarchies derived from a same image reflect its various facets and the distances between them nicely characterize its content. In this paper the hierarchies are constructed with the versatile stochastic watershed algorithm and their inter-distances are measured with the Gromov-Hausdorff distance. Experiments conducted on images simulated by dead leaves model illustrate the advantages of our approach in terms of learning efficiency and understandability of the results.

Deep morphological networks

“…Mathematical Morphology (MM) [3,4] applies topological operators to images to recover or filter out specific structures. It has led to important successes in many computer vision tasks, such as filtering [5,6,7] [8], segmentation [9,10,11,12][13, 14], semantic segmentation [15,16,17,18,19,20] [21,22], image fusion [23,24] [25], feature extraction [26,15,16,17,27] and edge detection [9] . With this paper, we are the first, to the best of our knowledge, to integrate exact morphological operators within a deep learning end-to-end framework.…”