Abstract

A group-theoretically motivated investigation of feature extraction is described. A feature extraction unit is defined as a complex-valued function on a signal space. It is assumed that the signal space possesses a group-theoretically defined regularity that we introduce. First the concept of a symmetrical signal space is derived. Feature mappings then are introduced on signal spaces and some properties of feature mappings on symmetrical signal spaces are investigated. Next the investigation is restricted to linear features, and an overview of all possible linear features is given. Also it is shown how a set of linear features can be used to construct a nonlinear feature that has the same value for all patterns in a class of similar patterns. These results are used to construct filter functions that can be used to detect patterns in two- and three-dimensional images independent of the orientation of the pattern in the image. Finally it is sketched briefly how the theory developed here can be applied to solve other, symmetrical problems in image processing.

© 1989 Optical Society of America

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