Image-A : Applicable Mathematics in Image Engineering - 2010 - Vol. I, NÂș 3https://hdl.handle.net/11441/25922018-10-22T15:58:01Z2018-10-22T15:58:01ZHuman gait recognition using topological informationhttps://hdl.handle.net/11441/262202016-11-30T10:12:56Z2010-01-01T00:00:00ZHuman gait recognition using topological information
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, the border cell complex is obtained from the 3D volume with one connected component and one cavity. Then, it is necessary to apply a topological enrichment strategy in order to obtain a robust and discriminative representation for person recognition. Using a sliding cutter plane normal to some direction of view it is possible to divide the border cell complex in different parts. The incremental algorithm is used to compute the homology on each part. A vectorial representation is built ordering the number of connected components and tunnels obtained for each cut. In order to evaluate the robustness of this representation the silhouettes were diminished to a quarter of the original size. At the same time, this is considered a simulation of a human gait captured at long distance. Even, under these difficult conditions it was possible to get a 74% of correct classification rates on CASIA-B database.
2010-01-01T00:00:00ZAlgorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generatorshttps://hdl.handle.net/11441/262152018-02-02T09:51:13Z2010-01-01T00:00:00ZAlgorithm to Compute a Minimal Length Basis of Representative Cocycles of Cohomology Generators
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. In our research we are looking for a more refined topological description of deformable 2D and 3D shapes, than they are the often used Betti numbers. We define contractions on the object edges toward the inner of the object until the boundaries touch each other, building an irregular pyramid with this purpose. We show the possible use of the algorithm seeking the minimal cocycles that connect the convex deficiencies on a human silhouette. We used minimality in the number of cocycle edges in the basis, which is a robust description to rotations and noise.
2010-01-01T00:00:00ZA fast algorithm to compute cohomology group generators of orientable 2-manifoldshttps://hdl.handle.net/11441/262132016-11-30T10:12:56Z2010-01-01T00:00:00ZA fast algorithm to compute cohomology group generators of orientable 2-manifolds
In this paper a fast algorithm to compute cohomology group generators of cellular decomposition of any orientable closed 2-manifold is presented. The presented algorithm is a dual version of algorithm to compute homology generators presented by David Eppstein [12] and developed by Jeff Erickson and Kim Whittlesey [13].
2010-01-01T00:00:00ZComputing The Cubical Cohomology Ring (Extended Abstract)https://hdl.handle.net/11441/262112016-11-30T10:12:56Z2010-01-01T00:00:00ZComputing The Cubical Cohomology Ring (Extended Abstract)
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, next, show how to extend the Mrozek and Batko [7] homology coreduction algorithm to the cohomology ring structure. The implementation of the algorithm is a work in progress. This research is aimed at applications in electromagnetism and in image processing, among other fields.
2010-01-01T00:00:00Z