Abstract

Pattern recognition schemes which are invariant to rotations, translations, and dilations of a shape embedded in a scene require an image representation which is 4-D where each dimension corresponds to a transformation parameter. In this scheme each pattern transformation is converted into a shift (translation) along the approximate axes, and the matched filter theorem may be applied to determine the degree of match and the transformation states. In this case we consider two schemes for sampling this augmented pattern representation scheme which decrease the number of cross-correlations required to be computed: One, based on arrays of orientation and size specific Gabor filters, searches for economy of coding via decreasing the spectral and positional resolutions necessary to attain a satisfactory level of performance; two, based on the invariance characteristics of the target patterns, determines the minimum number of pattern templates required to attain matching performance with respect to a predetermined decision criterion. Both schemes are illustrated and compared. Our results suggest that the latter approach is more efficient than the former insofar as it utilizes properties of the signal which bear directly on the geometric invariances involved.

© 1987 Optical Society of America