Using representations of the dihedral groups in the design of early vision filters

Authors:
Reiner Lenz
Affiliations:
Dept. Electrical Engineering, Linköping University, Linköping, Sweden and Advanced Telecommunications Research Institute, Auditory and Visual Perception Laboratory, Kyoto, Japan
Venue:
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
Year:
1993

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Abstract

Most imaging devices consist of sensors that are arranged on a regular grid. Examples are the square and the hexagonal grids. The geometrical transformations that leave these grids invariant constitute the dihedral group. Many important operations in image processing are symmetrical in the sense that they are independent of these grid transformations. In this paper we will demonstrate how the theory of group representations can be used to simplify all these symmetrical operations. We will illustrate the results with some examples from the design of early vision filters.