1 research outputs found
Homological Spanning Forests for Discrete Objects
Computing and representing topological information form an important
part in many applications such as image representation and compression,
classification, pattern recognition, geometric modelling, etc. The homology
of digital objects is an algebraic notion that provides a concise description
of their topology in terms of connected components, tunnels and cavities.
The purpose of this work is to develop a theoretical and practical frame-
work for efficiently extracting and exploiting useful homological information
in the context of nD digital images. To achieve this goal, we intend to
combine known techniques in algebraic topology, and image processing.
The main notion created for this purpose consists of a combinatorial
representation called Homological Spanning Forest (or HSF, for short) of a
digital object or a digital image. This new model is composed of a set of
directed forests, which can be constructed under an underlying cell complex
format of the image. HSF’s are based on the algebraic concept of chain
homotopies and they can be considered as a suitable generalization to higher
dimensional cell complexes of the topological meaning of a spanning tree of
a geometric graph.
Based on the HSF representation, we present here a 2D homology-based
framework for sequential and parallel digital image processing.Premio Extraordinario de Doctorado U