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.

A fast low-cost programmable optical-digital scanner-processor designed mainly for the purposes of edge and curve detection and on-line processing is presented. The main components of this system are a minicomputer, a linear photodiode array with driver and conversion interface, and a digital flatbed plotter.

A nonlinear picture-to-picture transformation is introduced and compared with a straightforward linear transformation. The criterion for comparison is based on the desire to smooth noisy or textured regions while retaining edge definition. Selected examples from a large number of simulations are presented. The transformation presented is believed to be superior to many techniques presently being employed.