Morphological Filtering in Shape Spaces: Applications using Tree-Based Image Representations

TL;DR

This paper introduces a novel framework for morphological filtering in shape spaces using tree-based image representations, generalizing existing connected operators and proposing new self-dual operators called morphological shapings.

Contribution

It extends tree-based connected operators to operate on shape spaces, introducing a new class of self-dual morphological shapings for advanced image filtering.

Findings

Framework includes classical connected operators as special cases.

Introduces a new class of self-dual connected operators.

Demonstrates the effectiveness of morphological shapings in image filtering.

Abstract

Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute an attribute on each node of the tree and keep only the nodes for which the attribute is sufficiently strong. This operation can be seen as a thresholding of the tree, seen as a graph whose nodes are weighted by the attribute. Rather than being satisfied with a mere thresholding, we propose to expand on this idea, and to apply connected filters on this latest graph. Consequently, the filtering is done not in the space of the image, but on the space of shapes build from the image. Such a processing is a generalization of the existing tree-based connected operators. Indeed, the framework includes classical existing connected operators by attributes. It also allows us to propose a class of novel connected operators from the leveling family, based on shape attributes. Finally, we also propose a novel class of self-dual connected operators that we call morphological shapings.