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Image and Vision Computing
Volume 16, Issue 1, 30 January 1998, Pages 21-26
Geometric Modeling and Invariants for Computing Vision
 
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doi:10.1016/S0262-8856(97)00046-2    How to Cite or Link Using DOI (Opens New Window)
Copyright © 1998 Published by Elsevier Science B.V.

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Planar homologies as a basis for grouping and recognition

Luc Van Goola, Corresponding Author Contact Information, Marc Proesmansa and Andrew Zissermanb

a ESAT/MI2, Kath. Univ. Leuven, Kard. Mercierlaan 94, 3001, Leuven, Belgium b Robotics Research Group, Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK

Received 31 January 1996; 
revised 24 March 1997; 
accepted 12 May 1997. ;
Available online 19 June 1998.

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Abstract

This article discusses a specific class of planar projective transformations, planar homologies, and illustrates their importance for geometry based grouping operations. Indeed, planar homologies keep to pop up in several areas of computer vision. Two examples are given in the article: the analysis of planar shapes and their shadows and the detection of extruded shapes. The parameters that are needed to specify homologies are given, as well as their invariants. Since only 5 parameters are required, these invariants are simpler than general projective invariants. The work therefore further corroborates the existence of grouping-specific invariants.

Author Keywords: Planar homologies; Grouping; Invariants; Projective geometry; Shadows; Extruded shapes

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Image and Vision Computing
Volume 16, Issue 1, 30 January 1998, Pages 21-26
Geometric Modeling and Invariants for Computing Vision
 
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