NameMedrano Garfia, Belén
DepartmentMatemática Aplicada I
Knowledge areaMatemática Aplicada
Professional categoryProfesora Contratada Doctora
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  • No. publications

    19

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Article
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Making Sullivan Algebras Minimal Through Chain Contractions

Garvin, Antonio; González Díaz, Rocío; Marco, Miguel Ángel; Medrano Garfia, Belén (Springer, 2021)
In this note, we provide an algorithm that, starting with a Sullivan algebra gives us its minimal model. More concretely, ...
Article
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An algorithm to compute minimal Sullivan algebras

Garvín, Antonio; González Díaz, Rocío; Medrano Garfia, Belén (Cornell University, 2019)
In this note, we give an algorithm that starting with a Sullivan algebra gives us its minimal model. This algorithm is a ...
Article
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Topological tracking of connected components in image sequences

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (Elsevier, 2018)
Persistent homology provides information about the lifetime of homology classes along a filtration of cell complexes. ...
Article
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Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (Springer, 2017)
A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted ...
Presentation
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Designing a Topological Algorithm for 3D Activity Recognition

Jiménez Rodríguez, María José; Medrano Garfia, Belén; Monaghan, David S.; O'Connor, Noel E. (Springer, 2016)
Voxel carving is a non-invasive and low-cost technique that is used for the reconstruction of a 3D volume from images ...
Presentation
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Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (Springer, 2016)
We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) ...
Presentation
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Spatiotemporal Barcodes for Image Sequence Analysis

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (Springer, 2015)
Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a ...
Article
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3D well-composed polyhedral complexes

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (2015)
A binary three-dimensional (3D) image II is well-composed if the boundary surface of its continuous analog is a 2D manifold. ...
Article
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A tool for integer homology computation: lambda-AT- model

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro (2011)
In this paper, we formalize the notion of lambda-AT-model (where λ is a non-null integer) for a given chain complex, which ...
Article
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Chain Homotopies for Object Topological Representations

Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro; González Díaz, Rocío (2011)
This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable ...
Chapter of Book
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Well-Composed Cell Complexes

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (2011)
Well-composed 3D digital images, which are 3D binary digital images whose boundary surface is made up by 2D manifolds, ...
Article
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Cubical cohomology ring of 3D photographs

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén (2011)
Cohomology groups and the cohomology ring of three-dimensional (3D) objects are topological invariants that characterize ...
Chapter of Book
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Integral operators for computing homology generators at any dimension

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro; Molina Abril, Helena (2008)
Starting from an nD geometrical object, a cellular subdivision of such an object provides an algebraic counterpart from ...
Chapter of Book
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Extending the notion of AT-Model for integer homology computation

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro (2007)
When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing ...
Chapter of Book
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A Graph-with-Loop Structure for a Topological Representation of 3D Objects

González Díaz, Rocío; Jiménez Rodríguez, María José; Medrano Garfia, Belén; Real Jurado, Pedro (2007)
Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the ...
PhD Thesis
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Modelo álgebro-topológico de representación de imágenes digitales en nD

Medrano Garfia, Belén; González Díaz, Rocío; Real Jurado, Pedro (2007)
Para introducir este trabajo es necesario hablar de TOPOLOG´IA. La topología es la rama de las matemáticas que estudia las ...
Chapter of Book
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Reusing integer homology information of binary digital images

González Díaz, Rocío; Medrano Garfia, Belén; Sánchez Peláez, Javier; Real Jurado, Pedro (2006)
In this paper, algorithms for computing integer (co)homology of a simplicial complex of any dimension are designed, extending ...
Chapter of Book
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Simplicial perturbation techniques and effective homology

González Díaz, Rocío; Medrano Garfia, Belén; Sánchez Peláez, Javier; Real Jurado, Pedro (2006)
In this paper, we deal with the problem of the computation of the homology of a finite simplicial complex after an “elementary ...
Chapter of Book
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Algebraic topological analysis of time-sequence of digital images

González Díaz, Rocío; Medrano Garfia, Belén; Real Jurado, Pedro; Sáchez Peláez, Javier (2005)
This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary–valued images, ...