Browsing ImageA : Applicable Mathematics in Image Engineering by Title
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A fast algorithm to compute cohomology group generators of orientable 2manifolds [Article]
(Universidad de Sevilla, 2010)In this paper a fast algorithm to compute cohomology group generators of cellular decomposition of any orientable closed 2manifold is presented. The presented algorithm is a dual version of algorithm to compute homology ...

A Linear Time Algorithm for Drawing a Graph in 3 Pages within its Isotopy Class in 3Space [Article]
(Universidad de Sevilla, 2015)We consider undirected graphs up to an ambient isotopy in 3space. 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 3space. We ...

Algebraic tools in geometrical modeling with topological control [Article]
(Universidad de Sevilla, 2011)In this paper we show a method to create a lookup table with all the possible bricks which can made up an object. Moreover, we generate a procedure to recreate any object starting from this table. More concretely, the ...

Algorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generators [Article]
(Universidad de Sevilla, 2010)An algorithm to compute a minimal length basis of representative cocycles of cohomology generators for 2D images is proposed. We based the computations on combinatorial pyramids foreseeing its future extension to 3D objects. ...

An application for gait recognition using persistent homology [Article]
(Universidad de Sevilla, 2013)This Demo presents an application for gait recognition using persistent homology. Using a background subtraction approach, a silhouette sequence is obtained from a camera in a controlled environment. A border simplicial ...

Bioinspired parallel 2D or 3D skeletonization [Article]
(Universidad de Sevilla, 2013)Algebraic Topology has been proved to be an useful tool to be used in image processing. In this case we will borrow some elements from Algebraic Topology in order to show a parallel algorithm for thinning a binary 3D image ...

Calibration in optical graph recognition [Article]
(Universidad de Sevilla, 2013)Graph drawing is the process of transforming the topological structure of a graph into a graphical representation. Primarily, it maps vertices to points and displays them by icons, and it maps edges to Jordan curves ...

CAPD::RedHom  Reduction heuristics for homology algorithms [Article]
(Universidad de Sevilla, 2015)We 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 ...

Characterizing Configurations of critical points through LBP Extended Abstract [Article]
(Universidad de Sevilla, 2015)In 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 ...

Combining regular decimation and dual graph contraction for hierarchical image segmentation [Article]
(Universidad de Sevilla, 2010)The Bounded Irregular Pyramid (BIP) is a hierarchical structure for image representation whose aim is to combine concepts from regular and irregular pyramids. The data structure is a combination of the simplest regular and ...

Computational Algebraic Topology and Its Applications. Foreword [Article]
(2011) 
Computing Fundamental Group via Forman’s Discrete Morse Theory Extended abstract [Article]
(Universidad de Sevilla, 2015)We 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. ...

Computing The Cubical Cohomology Ring (Extended Abstract) [Article]
(Universidad de Sevilla, 2010)The goal of this work is to establish a new algorithm for computing the cohomology ring of cubical complexes. The cubical structure enables an explicit recurrence formula for the cup product. We derive this formula and, ...

Counting excellent discrete Morse functions on compact orientable surfaces [Article]
(Universidad de Sevilla, 2010)We obtain the number of nonhomologically equivalent excellent discrete Morse functions defined on compact orientable surfaces. This work is a continuation of the study which has been done in [2, 4] for graphs.

Distributed boundary tracking using alpha and DelaunayCech shapes [Article]
(Universidad de Sevilla, 2013)We demonstrate real time tracking of systematic failures in sensor networks, using distributed computation of the α−shape derived from the network. More generally, our work may be applied to tracking the boundary of any ...

Gabor frames and topologybased strategies for astronomical images [Article]
(Universidad de Sevilla, 2010)The topic of this paper is the description of procedures to remove the fringes from complicated astronomical data sets, where the interference pattern is not regular, combining topological and Gaborbased analysis. A first ...

Homological Groups, Spanning Forests and Membrane Computing [Article]
(Universidad de Sevilla, 2011)In this paper we present a new way to determine the geometrical objects associated to the Homology groups of a 2Ddigital binary image. In fact, using Membrane Computing with techniques of spanning forests, we are able to ...

Human gait recognition using topological information [Article]
(Universidad de Sevilla, 2010)This paper shows an image/video application using topological invariants in human gait recognition. The 3D volume of a gait cycle is built stacking silhouettes extracted using a background substraction approach. Ideally, ...

Image Segmentation Inspired by Cellular Models using hardware programming [Article]
(Universidad de Sevilla, 2010)Several features of image segmentation make it suitable for bio–inspired techniques. It can be parallelized, locally solved and the input data can be easily encoded using representations inspired by nature. In this paper, ...