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March 1977 (vol. 26 no. 3)
pp. 314-317
H. Dirilten, Department of Electrical Engineering, University of British Columbia
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.
Index Terms:
Affine group, compact support, density, invariant, moment tensor, orthogonal transformation, pattern recognition, relative invariant.
Citation:
H. Dirilten, T.G. Newman, "Pattern Matching Under Affine Transformations," IEEE Transactions on Computers, vol. 26, no. 3, pp. 314-317, March 1977, doi:10.1109/TC.1977.1674832
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