A common framework for steerability, motion estimation, and invariant feature detection

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 related. In this paper, we examine the relationships between these problems and propose a theoretical framework within which they can be discussed in concert. This framework is based on constructing a 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.