Size Theory has proven to be a useful geometrical/topological approach to shape comparison. Originally introduced by considering 1-dimensional properties of shapes, described by means of real-valued functions, it has recently been generalized to taking into account multi-dimensional properties coded by functions valued in R^k. This has led to the introduction of a shape descriptor called k-dimensional size function, and the k-dimensional matching distance to compare size functions. This paper presents new theoretical results about the 2-dimensional matching distance, leading to the formulation of an algorithm for its approximation up to an arbitrary error threshold. Experiments on 3D object comparison are shown to discuss the efficacy and effectiveness of the algorithm.

A new algorithm for computing the 2-dimensional matching distance between size functions

CERRI, ANDREA;FROSINI, PATRIZIO;
2011

Abstract

Size Theory has proven to be a useful geometrical/topological approach to shape comparison. Originally introduced by considering 1-dimensional properties of shapes, described by means of real-valued functions, it has recently been generalized to taking into account multi-dimensional properties coded by functions valued in R^k. This has led to the introduction of a shape descriptor called k-dimensional size function, and the k-dimensional matching distance to compare size functions. This paper presents new theoretical results about the 2-dimensional matching distance, leading to the formulation of an algorithm for its approximation up to an arbitrary error threshold. Experiments on 3D object comparison are shown to discuss the efficacy and effectiveness of the algorithm.
Silvia Biasotti;Andrea Cerri;Patrizio Frosini;Daniela Giorgi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/152180
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