Journal of Mathematical Imaging and Vision

, Volume 16, Issue 1, pp 57–68

Non-Rigid Shape Comparison of Plane Curves in Images

  • Hemant D. Tagare
  • Donal O'Shea
  • David Groisser

DOI: 10.1023/A:1013938519103

Cite this article as:
Tagare, H.D., O'Shea, D. & Groisser, D. Journal of Mathematical Imaging and Vision (2002) 16: 57. doi:10.1023/A:1013938519103


A mathematical theory for establishing correspondences between curves and for non-rigid shape comparison is developed in this paper. The proposed correspondences, called bimorphisms, are more general than those obtained from one-to-one functions. Their topology is investigated in detail.

A new criterion for non-rigid shape comparison using bimorphisms is also proposed. The criterion avoids many of the mathematical problems of previous approaches by comparing shapes non-rigidly from the bimorphism.

Geometric invariants are calculated for curves whose shapes can be exactly matched with a bimorphism. The invariants are related to the concave and convex segments of a curve and provide justification for parsing the curve into such segments.

shape analysis non-rigid correspondence plane curves 

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Hemant D. Tagare
    • 1
  • Donal O'Shea
    • 2
  • David Groisser
    • 3
  1. 1.Department of Diagnostic Radiology, Department of Electrical EngineeringYale UniversityNew HavenUSA
  2. 2.Department of MathematicsMount Holyoke CollegeSouth HadleyUSA
  3. 3.Department of MathematicsUniversity of FloridaGainsvilleUSA

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