Report Number: CS-TN-96-33
Institution: Stanford University, Department of Computer Science
Title: A Computational Group-Theoretic Approach to Steerable
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.