Abstract :
In the following we consider the action of the group of affine transformations on a class of patterns representable by continuous functions with compact support. It is first shown how to accomplish a reduction of the action of the affine group to that of the orthogonal group. In the two-dimensional case, it is shown how to find the particular orthogonal transformation necessary to complete a pattern match. Finally invariants under the orthogonal group are presented. Examples are given which present typical results obtained by implementing the techniques via a digital-optical scanner and minicomputer software.
Keywords :
Affine group, compact support, density, invariant, moment tensor, orthogonal transformation, pattern recognition, relative invariant.; Covariance matrix; Equations; Mathematics; Microcomputers; Packaging; Pattern matching; Pattern recognition; Probability density function; Tensile stress; Affine group, compact support, density, invariant, moment tensor, orthogonal transformation, pattern recognition, relative invariant.;
