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Using matching distance in size theory: A survey.
- Source :
- International Journal of Imaging Systems & Technology; 2006, Vol. 16 Issue 5, p154-161, 8p, 6 Diagrams
- Publication Year :
- 2006
-
Abstract
- In this survey we illustrate how the matching distance between reduced size functions can be applied for shape comparison. We assume that each shape can be thought of as a compact connected manifold with a real continuous function defined on it, that is a pair (&Mscr;,ϕ : &Mscr; → ℝ), called size pair. In some sense, the function ϕ focuses on the properties and the invariance of the problem at hand. In this context, matching two size pairs (&Mscr;, ϕ) and (&Nscr;, ψ) means looking for a homeomorphism between &Mscr; and &Nscr; that minimizes the difference of values taken by ϕ and ψ on the two manifolds. Measuring the dissimilarity between two shapes amounts to the difficult task of computing the value δ = inf<subscript>f</subscript> max<subscript>P∈&Mscr;</subscript> |ϕ(P) - ψ(f(P))|, where f varies among all the homeomorphisms from &Mscr; to &Nscr;. From another point of view, shapes can be described by reduced size functions associated with size pairs. The matching distance between reduced size functions allows for a robust to perturbations comparison of shapes. The link between reduced size functions and the dissimilarity measure δ is established by a theorem, stating that the matching distance provides an easily computable lower bound for δ. Throughout this paper we illustrate this approach to shape comparison by means of examples and experiments. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 16, 154–161, 2006 [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08999457
- Volume :
- 16
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- International Journal of Imaging Systems & Technology
- Publication Type :
- Academic Journal
- Accession number :
- 24354577
- Full Text :
- https://doi.org/10.1002/ima.20076