Buscar
Mostrando ítems 1-9 de 9
Capítulo de Libro
Extending the notion of AT-Model for integer homology computation
(2007)
When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing (co)homology, representative (co)cycles of (co)homology generators and the cup product on cohomology of ...
Capítulo de Libro
A Graph-with-Loop Structure for a Topological Representation of 3D Objects
(2007)
Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the height function), we construct a graph G h (K) which is an extension of the Reeb graph R h (|K|). ...
Capítulo de Libro
Towards Minimal Barcodes
(2013)
In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a ...
Capítulo de Libro
Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology
(2011)
In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one for computing persistent homology [6,14,15]. We also present a decremental algorithm for computing ...
Capítulo de Libro
Reducing Computational Costs in the Basic Perturbation Lemma
(2006)
Homological Perturbation Theory [11, 13] is a well-known general method for computing homology, but its main algorithm, the Basic Perturbation Lemma, presents, in general, high computational costs. In this paper, we ...
Capítulo de Libro
Integral operators for computing homology generators at any dimension
(2008)
Starting from an nD geometrical object, a cellular subdivision of such an object provides an algebraic counterpart from which homology information can be computed. In this paper, we develop a process to drastically reduce ...
Capítulo de Libro
On the Computation of Ainfinity-Maps
(2007)
Starting from a chain contraction (a special chain homotopy equivalence) connecting a differential graded algebra A with a differential graded module M, the so-called homological perturbation technique “tensor trick” ...
Capítulo de Libro
Persistent Homology for 3D Reconstruction Evaluation
(2012)
Space or voxel carving is a non-invasive technique that is used to produce a 3D volume and can be used in particular for the reconstruction of a 3D human model from images captured from a set of cameras placed around the ...
Capítulo de Libro
Well-Composed Cell Complexes
(2011)
Well-composed 3D digital images, which are 3D binary digital images whose boundary surface is made up by 2D manifolds, enjoy important topological and geometric properties that turn out to be advantageous for some applications. ...