Now showing items 1-5 of 5

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      Computational Algebraic Topology and Its Applications. Foreword  [Article]

      Berciano Alcaraz, Ainhoa; Díaz Pernil, Daniel; Sáenz de Cabezón Irigaray, Eduardo (2011)
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      Decomposing cavities in digital volumes into products of cycles  [Chapter of Book]

      Berciano Alcaraz, Ainhoa; Molina Abril, Helena; Pacheco Martínez, Ana María; Pilarczyk, Pawel; Real Jurado, Pedro (2009)
      The homology of binary 3–dimensional digital images (digital volumes) provides concise algebraic description of their topology in terms of connected components, tunnels and cavities. Homology generators corresponding to ...
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      Homological Groups, Spanning Forests and Membrane Computing  [Article]

      Berciano Alcaraz, Ainhoa; Díaz Pernil, Daniel (Universidad de Sevilla, 2011)
      In this paper we present a new way to determine the geometrical objects associated to the Homology groups of a 2D-digital binary image. In fact, using Membrane Computing with techniques of spanning forests, we are able to ...
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      Reducing Computational Costs in the Basic Perturbation Lemma  [Chapter of Book]

      Real Jurado, Pedro; Berciano Alcaraz, Ainhoa; Jiménez Rodríguez, María José (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 ...
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      Searching high order invariants in computer imagery  [Article]

      Berciano Alcaraz, Ainhoa; Molina Abril, Helena; Real Jurado, Pedro (2012)
      In this paper, we present a direct computational application of Homological Perturbation Theory (HPT, for short) to computer imagery. More precisely, the formulas of the A ∞–coalgebra maps Δ 2 and Δ 3 using the notion of ...