Shape Metrics Based on Elastic Deformations

Authors:
Matthias Fuchs;Bert Jüttler;Otmar Scherzer;Huaiping Yang
Affiliations:
Dept. of Mathematics, Univ. of Innsbruck, Innsbruck, Austria;Inst. of Applied Geometry, Univ. of Linz, Linz, Austria;Dept. of Mathematics, Univ. of Innsbruck, Innsbruck, Austria and RICAM, Austrian Acad. of Science, Linz, Austria;Inst. of Applied Geometry, Univ. of Linz, Linz, Austria
Venue:
Journal of Mathematical Imaging and Vision
Year:
2009

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Abstract

Deformations of shapes and distances between shapes are an active research topic in computer vision. We propose an energy of infinitesimal deformations of continuous 1- and 2-dimensional shapes that is based on the elastic energy of deformed objects. This energy defines a shape metric which is inherently invariant with respect to Euclidean transformations and yields very natural deformations which preserve details. We compute shortest paths between planar shapes based on elastic deformations and apply our approach to the modeling of 2-dimensional shapes.