BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-98-1604
       ENTRY:: March 19, 1998
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Theory and Applications of Steerable Functions
        TYPE:: Thesis
        TYPE:: Technical Report
      AUTHOR:: Teo, Patrick C.
        DATE:: March 1998
       PAGES:: 152
    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.
       NOTES:: [Adminitrivia V1/Prg/19980319]
         END:: STAN//CS-TR-98-1604