Report Number: CS-TN-96-28
Institution: Stanford University, Department of Computer Science
Title: A Common Framework for Steerability, Motion Estimation and Invariant Feature Detection
Author: Hel-Or, Yacov
Author: Teo, Patrick C.
Date: January 1996
Abstract: Many problems in computer vision and pattern recognition involve groups of transformations. In particular, motion estimation, steerable filter design and invariant feature detection are often formulated with respect to a particular transformation group. Traditionally, these problems have been investigated independently. From a theoretical point of view, however, the issues they address are similar. In this paper, we examine these common issues and propose a theoretical framework within which they can be discussed in concert. This framework is based on constructing a more natural representation of the image for a given transformation group. Within this framework, many existing techniques of motion estimation, steerable filter design and invariant feature detection appear as special cases. Furthermore, several new results are direct consequences of this framework. First, a canonical decomposition of all filters that can be steered with respect to any one-parameter group and any multi-parameter Abelian group is proposed. Filters steerable under various subgroups of the affine group are also tabulated. Second, two approximation techniques are suggested to deal with filters that cannot be steered exactly. Approximating steerable filters can also be used for motion estimation. Third, within this framework, invariant features can easily be constructed using traditional techniques for computing point invariance.