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.