Planar homologies as a basis for grouping and recognition

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.

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