LIE GENERATORS FOR COMPUTING STEERABLE FUNCTIONS

We present a computational, group-theoretic approach to steerable func tions. The approach is group-theoretic in that the treatment involves continuous transformation groups for which elementary Lie group theory may be applied. The approach is computational in that the theory is c onstructive and leads directly to a procedural implementation. For fun ctions that are steerable with n basis functions under a k-parameter g roup, the procedure is efficient in that at most nk + 1 iterations of the procedure are needed to compute all the basis functions. Furthermo re, the procedure is guaranteed to return the minimum number of basis functions. If the function is not steerable, a numerical implementatio n of the procedure could be used to compute basis functions that appro ximately steer the function over a range of transformation parameters. Examples of both applications are described. (C) 1998 Elsevier Scienc e B.V.