Report Number: CS-TN-96-33
Institution: Stanford University, Department of Computer Science
Title: A Computational Group-Theoretic Approach to Steerable Functions
Author: Teo, Patrick C.
Author: Hel-Or, Yacov
Date: April 1996
Abstract: We present a computational, group-theoretic approach to steerable functions. 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 constructive and leads directly to a procedural implementation. For functions that are steerable with $n$ basis functions under a $k$-parameter group, the procedure is efficient in that at most $nk+1$ iterations of the procedure are needed to compute all the basis functions. Furthermore, the procedure is guaranteed to return the minimum number of basis functions. If the function is not steerable, a numerical implementation of the procedure could be used to compute basis functions that approximately steer the function over a range of parameters. Examples of both applications are described.