Conference Paper
A method for recognizing the shape of a Gaussian mixture from a sparse sample set.
DOI: 10.1117/12.848604 In proceeding of: Computational Imaging VIII, part of the IS&TSPIE Electronic Imaging Symposium, San Jose, CA, USA, January 1819, 2010, Proceedings
Source: DBLP
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ABSTRACT: One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this distribution. After giving some counterexamples, we prove that this is the case for the vast majority of configurations.In the second part of the paper, the distribution of areas of subtriangles is used for characterizing point configurations. Again it turns out that most configurations are reconstructible from the distribution of areas, though there are counterexamples.Advances in Applied Mathematics. 01/2004;  01/1951;

Conference Paper: Faithful Shape Representation for 2D Gaussian Mixtures
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ABSTRACT: It has been recently discovered that a faithful representation for the shape of some simple distributions can be constructed using invariant statistics [1,2]. In this paper, we consider the more general case of a Gaussian mixture model. We show that the shape of generic Gaussian mixtures can be represented without any loss by the distribution of the distance between two points independently drawn from this mixture. In other words, we show that if their respective distributions of distances are the same, then there exists a rigid transformation mapping one Gaussian mixture onto the other. Our main motivation is the problem of recognizing the shape of an object represented by points given noisy measurements of these points which can be modeled as a Gaussian mixture.Image Processing, 2007. ICIP 2007. IEEE International Conference on; 01/2007
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