# Multidimensional Size Functions for Shape Comparison

@article{Biasotti2008MultidimensionalSF,
title={Multidimensional Size Functions for Shape Comparison},
author={Silvia Biasotti and Andrea Cerri and Patrizio Frosini and Daniela Giorgi and Claudia Landi},
journal={Journal of Mathematical Imaging and Vision},
year={2008},
volume={32},
pages={161-179}
}
• Published 1 October 2008
• Mathematics
• Journal of Mathematical Imaging and Vision
Size Theory has proven to be a useful framework for shape analysis in the context of pattern recognition. Its main tool is a shape descriptor called size function. Size Theory has been mostly developed in the 1-dimensional setting, meaning that shapes are studied with respect to functions, defined on the studied objects, with values in ℝ. The potentialities of the k-dimensional setting, that is using functions with values in ℝk, were not explored until now for lack of an efficient computational…
• Computer Science, Mathematics
• 2011
Some recent results about size functions in this multidimensional setting are surveyed, with particular reference to the localization of their discontinuities.
• Computer Science, Mathematics
• 2011
This work surveys some recent results about size functions in this multidimensional setting, with particular reference to the localization of their discontinuities.
k-dimensional Size Functions for Shape Description and Comparison
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14th International Conference on Image Analysis and Processing (ICIAP 2007)
• 2007
This paper advises the use of k-dimensional size functions for comparison and retrieval in the context of multidimensional shapes, taking into account different properties expressed by a multivalued real function defined on the shape.
Describing shapes by geometrical-topological properties of real functions
• Mathematics
CSUR
• 2008
This survey is to provide a clear vision of what has been developed so far, focusing on methods that make use of theoretical frameworks that are developed for classes of real functions rather than for a single function, even if they are applied in a restricted manner.
Robustness and Modularity of 2-Dimensional Size Functions - An Experimental Study
• Mathematics, Materials Science
CAIP
• 2011
The aim of the present paper is to validate, through some experiments on 3D-models, a computational framework recently introduced to deal with 2-dimensional Size Theory, and show that the cited framework is modular and robust with respect to noise, non-rigid and non-metric-preserving shape transformations.
A new approximation Algorithm for the Matching Distance in Multidimensional Persistence
• Computer Science
• 2011
This paper proposes a new computational framework to deal with the multidimensional matching distance, by proving some new theoretical results and using them to formulate an algorithm for computing such a distance up to an arbitrary threshold error.
Invariance properties of the multidimensional matching distance in Persistent Topology and Homology
• Mathematics
ArXiv
• 2010
This paper shows that the multidimensional matching distance is actually invariant with respect to such a choice, and formally depends on a subset of \$\R^n\times-valued filtering functions inducing a parameterization of these half-planes.
The Global-Local transformation for noise resistant shape representation
• Computer Science
Comput. Vis. Image Underst.
• 2011
Suspension models for testing shape similarity methods
• Computer Science
Comput. Vis. Image Underst.
• 2014

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