Image-A : Applicable Mathematics in Image Engineering - 2015 - Vol. IV, Nº 7
URI permanente para esta colecciónhttps://hdl.handle.net/11441/26548
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Artículo Methods of computational topology for Solar Activity forecasting (Extended abstract)(Universidad de Sevilla, 2015) Knyazeva, Irina; Makarenko, Nikolay; Malkova, DariaSolar activity is a space-time complex of events which produced by the Sun magnetic fields. One of the results of this activity is a huge plasma ejection which called solar flares. The solar flares occurs mainly in the areas with an especially strong magnetic fields called Active Regions (AR). Observation phenomenology indicates that significant change in the magnetic field topology precede the strong flares. We investigated changes in topology by the methods of computational topology. For this purpose the high frequency temporal sequence of AR magnetograms containing flares has been analyzed. Such data are available from the space observatory SDO. We seek distinctive patterns that could be associated with the flares through the tracking evolution of Euler characteristics and Betti numbers. These characteristics of course do not pretend on the comprehensive description of topological complexity but there are simple in construction and intuitive clear. We found that the large variations of the Betti numbers and Euler characteristics are preceded or accompanied by a large flares. These results give us hope that the approach based on computational topology could be useful in the task of monitoring of magnetic field evolution and should be developed in future.Artículo Computing Fundamental Group via Forman’s Discrete Morse Theory Extended abstract(Universidad de Sevilla, 2015) Brendel, Piotr; Dlotko, Pawel; Ellis, Graham; Juda, Mateusz; Mrozek, MarianWe present research in progress on the algorithmic computation of the fundamental group of a CW complex. We use the algorithm to compute certain algebraic invariants of the fundamental group of the complement of a knot. We show that the invariants classify the prime knots up to 13 crossings. The long term goal is an automated classification of knots in 3D images, in particular images of proteins.Artículo Characterizing Configurations of critical points through LBP Extended Abstract(Universidad de Sevilla, 2015) González Díaz, Rocío; Kropatsch, Walter G.; Cerman, Martin; Lamar León, Javier; Universidad de Sevilla. Departamento de Matemática Aplicada IIn this abstract we extend ideas and results submitted to [3] in which a new codification of Local Binary Patterns (LBP) is given using combinatorial maps and a method for obtaining a representative LBP image is developed based on merging regions and Minimum Contrast Algorithm. The LBP code characterizes the topological category (max, min, slope, saddle) of the 2D gray level landscape around the center region. We extend the result studying how to merge non-singular slopes with one of its neighbors and how to extend the results to nonwell formed images/maps. Some ideas related to robust LBP and isolines are also given in last section.Artículo CAPD::RedHom - Reduction heuristics for homology algorithms(Universidad de Sevilla, 2015) Juda, Mateusz; Mrozek, MarianWe present an efficient software package for computing homology of sets, maps and filtrations represented as cubical, simplicial and regular CW complexes. The core homology computation is based on classical Smith diagonalization, but the efficiency of our approach comes from applying several geometric and algebraic reduction techniques combined with smart implementation.Artículo The algorithm for going through a labyrinth by an autonomous(Universidad de Sevilla, 2015) Raduca, Eugen; Adiran, Paun; Raduca, Mihaela; Draghici, Silviu; Anghel Drugarin, CoThe paper presents an algorithm for going through a path type labyrinth by an autonomous vehicle. The detection of the path and the maintaining of the motion direction have been addressed as well as going through the labyrinth on road segments and the categories of crossings in the said labyrinth. The algorithm has been implemented in C++ and validated in an experimental model that has totally confirmed its correctness.Artículo A Linear Time Algorithm for Drawing a Graph in 3 Pages within its Isotopy Class in 3-Space(Universidad de Sevilla, 2015) Kurlin, VitaliyWe consider undirected graphs up to an ambient isotopy in 3-space. Such a graph can be represented by a plane diagram or a Gauss code. We recognize in linear time if a Gauss code represents an actual graph in 3-space. We also design a linear time algorithm for drawing a topological 3-page embedding of a graph isotopic to a given graph.