Image-A : Applicable Mathematics in Image Engineering - 2010 - Vol. I, Nº 1
URI permanente para esta colecciónhttps://hdl.handle.net/11441/2590
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Artículo Tracking features in image sequences using discrete Morse functions(Universidad de Sevilla, 2010) Jerse, Gregor; Mramor Kosta, NezaThe goal of this contribution is to present an application of discrete Morse theory to tracking features in image sequences. The proposed algorithm can be used for tracking moving figures in a filmed scene, for tracking moving particles, as well as for detecting canals in a CT scan of the head, or similar features in other types of data. The underlying idea which is used is the parametric discrete Morse theory presented in [13], where an algorithm for constructing the bifurcation diagram of a discrete family of discrete Morse functions was given. The original algorithm is improved here for the specific purpose of tracking features in images and other types of data, in order to produce more realistic results and eliminate irregularities which appear as a result of noise and excess details in the data.Artículo Towards optimality in discrete Morse Theory through chain homotopies(Universidad de Sevilla, 2010) Real Jurado, Pedro; Molina Abril, Helena; Universidad de Sevilla. Departamento de Matemática Aplicada IOnce a discrete Morse function has been defined on a finite cell complex, information about its homology can be deduced from its critical elements. The main objective of this paper is to define optimal discrete gradient vector fields on general finite cell complexes, where optimality entails having the least number of critical elements. Our approach is to consider this problem as a homology computation question for chain complexes endowed with extra algebraic nilpotent operator.Artículo The efficiency of a homology algorithm based on discrete morse theory and coreductions (extended abstract)(Universidad de Sevilla, 2010) Harker, Shaun; Mischaikow, Konstantin; Mrozek, Marian; Nanda, Vidit; Wagner, Hubert; Juda, Mateusz; Dlotko, PawelTwo implementations of a homology algorithm based on the Forman’s discrete Morse theory combined with the coreduction method are presented. Their efficiency is compared with other implementations of homology algorithms.Artículo Counting excellent discrete Morse functions on compact orientable surfaces(Universidad de Sevilla, 2010) Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio; Universidad de Sevilla. Departamento de Geometría y TopologíaWe obtain the number of non-homologically 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.Artículo Perfect discrete Morse functions on 2-complexes(Universidad de Sevilla, 2010) Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio; Universidad de Sevilla. Departamento de Geometría y TopologíaThis paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the i-th Betti number of the complex. In particular, we establish conditions under which a 2-complex admits a perfect discrete Morse function and conversely, we get topological properties of a 2-complex admitting such kind of functions. This approach is more general than the known results in the literature [7], since our study is not restricted to surfaces. These results can be considered as a first step in the study of perfect discrete Morse functions on 3-manifolds.