We introduce algorithms for the computation of homology, cohomology, and related
operations on cubical cell complexes, using the technique based on a chain contraction …

Abstract In [14], a topologically consistent framework to support parallel topological analysis
and recognition for 2D digital objects was introduced. Based on this theoretical work, we …

In this paper we propose a mathematical framework that can be used for defining
cohomology of digital images. We state the Eilenberg-Steenrod axioms and the Universal …

Data Science aims to extract meaningful knowledge from unorganised data. Real datasets
usually come in the form of a cloud of points. It is a requirement of numerous applications to …

The paper analyzes the connectivity information (more precisely, numbers of tunnels and
their homological (co) cycle classification) of fractal polyhedra. Homology chain contractions …

Topological representations of binary digital images usually take into consideration different
adjacency types between colors. Within the cubical-voxel 3D binary image context, we …

Discrete gradient vector fields are combinatorial structures that can be used for accelerating
the homology computation of CW complexes, such as simplicial or cubical complexes, by …

An appropriate generalization of the classical notion of abstract cell complex, called primal-
dual abstract cell complex (pACC for short) is the combinatorial notion used here for …

In this paper, we propose a bio-inspired membrane computational framework for
constructing discrete Morse complexes for binary digital images. Our approach is based on …

In this paper we develop a new computational technique called boundary scale-space
theory. This technique is based on the topol 1 ogical paradigm consisting of representing a …