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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.
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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