Ainhoa Berciano

Segmenting images with gradient-based edge detection using Membrane Computing

In this paper, we present a parallel implementation of a new algorithm for segmenting images with gradient-based edge detection by using techniques from Natural Computing. This bio-inspired parallel algorithm has been implemented in a novel device architecture called CUDA(TM)(Compute Unified Device Architecture). The implementation has been designed via tissue P systems on the framework of Membrane Computing. Some examples and experimental results are also presented.

Searching high order invariants in computer imagery

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 Δ2 and Δ3 using the notion of AT-model of a digital image, and the HPT technique are implemented. The method has been tested on some specific examples, showing the usefulness of this computational tool for distinguishing 3D digital images.

Parallel skeletonizing of digital images by using cellular automata

Recent developments of computer architectures together with alternative formal descriptions provide new challenges in the study of digital Images. In this paper we present a new implementation of the Guo & Hall algorithm [8] for skeletonizing images based on Cellular Automata. The implementation is performed in a real-time parallel way by using the GPU architecture. We show also some experiments of skeletonizing traffic signals which illustrates its possible use in real life problems.

Membrane parallelism for discrete Morse theory applied to digital images

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 the discrete Morse theory and we work with cubical complexes. As example, a parallel algorithm for computing homology groups of binary 3D digital images is designed.

A ∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤ p )

Abstract In this article, we study the structure maps of the A ∞ coalgebra structure for the homology H∗(K(π, n); ℤ p ) of an Eilenberg-Mac Lane space K(π, n), where π is a finitely generated abelian group, n is a positive integer and p is a prime number different to 2. Using diverse techniques of homological perturbation, we obtain that all the components of Δi vanish except for Δ i(p–2)+2 of degree i(p–2) and i ≥ 0.

Decomposing cavities in digital volumes into products of cycles

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 these features are represented by nontrivial 0- cycles, 1-cycles and 2-cycles, respectively. In the framework of cubical representation of digital volumes with the topology that corresponds to the 26-connectivity between voxels, we introduce a method for algorithmic computation of a coproduct operation that can be used to decompose 2-cycles into products of 1-cycles (possibly trivial). This coproduct provides means of classifying different kinds of cavities; in particular, it allows to distinguish certain homotopically non-equivalent spaces that have isomorphic homology. We define this coproduct at the level of a cubical complex built directly upon voxels of the digital image, and we construct it by means of the classical Alexander-Whitney map on a simplicial subdivision of faces of the voxels.

Effective homology of k-D digital objects (partially) calculated in parallel

Abstract In [18], a membrane parallel theoretical framework for computing (co)homology information of foreground or background of binary digital images is developed. Starting from this work, we progress here in two senses: (a) providing advanced topological information, such as (co)homology torsion and efficiently answering to any decision or classification problem for sum of k-xels related to be a (co)cycle or a (co)boundary; (b) optimizing the previous framework to be implemented in using GPGPU computing. Discrete Morse theory, Effective Homology Theory and parallel computing techniques are suitably combined for obtaining a homological encoding, called algebraic minimal model, of a Region-Of-Interest (seen as cubical complex) of a presegmented k-D digital image.

Searching Partially Bounded Regions with P Systems

The problem of automatically marking the interior and exterior regions of a simple curve in a digital image becomes a hard task due to the noise and the intrinsic difficulties of the media where the image is taken. In this paper, we propose a definition of the interior of a partially bounded region and present a bio-inspired algorithm for finding it in the framework of Membrane Computing.

First steps for a corner detection using membrane computing

Corner Detection is a well known problem in Digital Imagery. In this paper we present a novel approach to detect corners in digital images. In particular, in the framework of Membrane Computing, given a 2D-image, we have designed a theoretical algorithm to solve a type of the corner detection problem, using tissue-like P systems with promoters. Finally, we show some examples of how this algorithm works theoretically.

Bio-inspired parallel computing of representative geometrical objects of holes of binary 2D-images

In this paper, we present a bio-inspired parallel implementation of a solution of the problem of looking for the representative geometrical objects of the homology groups in a binary 2D image (extended-HGB2I problem), which is an extended version of a well-known problem in homology theory. In particular, given a binary 2D image, all black connected components and the representative curves of the holes of these components are obtained and labelled. To this aim, a new technique for labelling the connected components of a binary image is presented. In order to compute the solution, the formal framework uses techniques from membrane computing and the implementation has been done in a hardware architecture called compute unified device architecture (CUDA). The computational complexity of the proposed solution is O(m) with respect to the input (image) size m ∼ n². Finally, some examples and applications are also presented.