立方特異単体複体による3次元物体の復元とホモロジー群の高速計算

概要

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Simplex or triangularization models have been widely used for reconstruction,coding and recognition of 3D objects. The Voronoi graph or its dual,the Delaunay teiangularization,even known as the optimal simplex model,can only be constructed for convex objects presently. Besides,the generation algorithms,like many of their approximate variations,require a large amount of computation and complicated local tests. The triangular mesh model is also not convenient to adjust the resolution. In this paper,a singular simplicial complex model of 3D objects is proposed,which is then trained by a self-organization neural network. It is known that Kohonen's map, developed for unsupervised learning of 2D probabilistic distribution,reserves only local planer topology but can not applied to 3D surface distribution. Thus,we have to extend the Kohonen's map to 3D case in order to learn a continuous map from n-cube to topological space X,which defined a cubical singular simplex. Furthermore, a pyramid structure of resolutions is derived as a natural results of the cubical singular simplicial complex model. Finally,we show a fast computation method to calculate the homology group as topological invariants using the cubical singular simplicial complex model.
社団法人電子情報通信学会の論文
1995-09-05