Journal of Mathematical Imaging and Vision

, Volume 35, Issue 1, pp 86–102 | Cite as

Shape Metrics Based on Elastic Deformations

  • Matthias FuchsEmail author
  • Bert Jüttler
  • Otmar Scherzer
  • Huaiping Yang


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.


Shape space Shape metric Shape modeling Elastic deformation 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Matthias Fuchs
    • 1
    Email author
  • Bert Jüttler
    • 3
  • Otmar Scherzer
    • 1
    • 2
  • Huaiping Yang
    • 3
  1. 1.Dept. of MathematicsUniv. of InnsbruckInnsbruckAustria
  2. 2.RICAMAustrian Acad. of ScienceLinzAustria
  3. 3.Inst. of Applied GeometryUniv. of LinzLinzAustria

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