A global method for reducing multidimensional size graphs

Authors:
Andrea Cerri;Patrizio Frosini;Walter G. Kropatsch;Claudia Landi
Affiliations:
Vienna University of Technology, Faculty of Informatics, Pattern Recognition and Image Processing Group, Austria;Università di Bologna, ARCES and Dipartimento di Matematica, Italy;Vienna University of Technology, Faculty of Informatics, Pattern Recognition and Image Processing Group, Austria;Università di Modena e Reggio Emilia, Dipartimento di Scienze e Metodi dell'Ingegneria, Italy
Venue:
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
Year:
2011

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Abstract

This paper introduces the concept of discrete multidimensional size function, a mathematical tool studying the so-called size graphs. These graphs constitutes an ingredient of Size Theory, a geometrical/ topological approach to shape analysis and comparison. A global method for reducing size graphs is presented, together with a theorem stating that size graphs reduced in such a way preserve all the information in terms of multidimensional size functions. This approach can lead to simplify the effective computation of discrete multidimensional size functions, as shown by examples.