Symposium on Point Based Graphics 07
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Browsing Symposium on Point Based Graphics 07 by Subject "Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling."
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Item On the use of Gromov-Hausdorff Distances for Shape Comparison(The Eurographics Association, 2007) Memoli, Facundo; M. Botsch and R. Pajarola and B. Chen and M. ZwickerIt is the purpose of this paper to propose and discuss certain modifications of the ideas concerning Gromov- Hausdorff distances in order to tackle the problems of shape matching and comparison. These reformulations render these distances more amenable to practical computations without sacrificing theoretical underpinnings. A second goal of this paper is to establish links to several other practical methods proposed in the literature for comparing/matching shapes in precise terms. Connections with the Quadratic Assignment Problem (QAP) are also established, and computational examples are presented.Item Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition(The Eurographics Association, 2007) Singh, Gurjeet; Memoli, Facundo; Carlsson, Gunnar; M. Botsch and R. Pajarola and B. Chen and M. ZwickerWe present a computational method for extracting simple descriptions of high dimensional data sets in the form of simplicial complexes. Our method, called Mapper, is based on the idea of partial clustering of the data guided by a set of functions defined on the data. The proposed method is not dependent on any particular clustering algorithm, i.e. any clustering algorithm may be used with Mapper. We implement this method and present a few sample applications in which simple descriptions of the data present important information about its structure.