Published February 21, 2018
| Version v1
Publication
Toward Parallel Computation of Dense Homotopy Skeletons for nD Digital Objects
Description
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 modeling and analyzing
the topology of nD digital objects and images. Let D ⊂ I be a set of
n-xels (ROI) and I be a n-dimensional digital image.We design a theoretical
parallel algorithm for constructing a topologically meaningful asymmetric
pACC HSF(D), called Homological Spanning Forest of D (HSF
of D, for short) starting from a canonical symmetric pACC associated
to I and based on the application of elementary homotopy operations
to activate the pACC processing units. From this HSF-graph representation
of D, it is possible to derive complete homology and homotopy
information of it. The preprocessing procedure of computing HSF(I) is
thoroughly discussed. In this way, a significant advance in understanding
how the efficient HSF framework for parallel topological computation of
2D digital images developed in [2] can be generalized to higher dimension
is made.
Abstract
Ministerio de Economía y Competitividad TEC2016-77785-PAbstract
Ministerio de Economía y Competitividad MTM2016-81030-PAdditional details
Identifiers
- URL
- https://idus.us.es/handle//11441/70473
- URN
- urn:oai:idus.us.es:11441/70473