Report Number: CS-TR-98-1604
Institution: Stanford University, Department of Computer Science
Title: Theory and Applications of Steerable Functions
Author: Teo, Patrick C.
Date: March 1998
Abstract: A function is called steerable if transformed versions of the
function can be expressed using linear combinations of a
fixed set of basis functions. In this dissertation, we
propose a framework, based on Lie group theory, for studying
and constructing functions steerable under any smooth
transformation group. Existing analytical approaches to
steerability are consistently explained within the framework.
The design of a suitable set of basis functions given any
arbitrary steerable function is one of the main problems
concerning steerable functions. To this end, we have
developed two different algorithms. The first algorithm is a
symbolic method that derives the minimal set of basis
functions automatically given an arbitrary steerable
function. In practice, functions that need to be steered
might not be steerable with a finite number of basis
functions. Moreover, it is often the case that only a small
subset of transformations within the group of transformations
needs to be considered. In response to these two concerns,
the second algorithm computes the optimal set of k basis
functions to steer an arbitrary function under a subset of
the group of transformations.
Lastly, we demonstrate the usefulness of steerable functions
in a variety of applications.