On the use of SDF-type filters for distortion invariant image location

The problem of locating a region of interest in a image subject to various distortions is a common one in many image processing tasks. The use of synthetic discriminant functions (SDFs) has enjoyed some popularity especially in SAR type problems. Since they are based on correlation operations, these SDF-type filters are very fast. However, due to the linear nature of the SDF, its performance is frequently quite poor in relation to other more sophisticated and computationally expensive techniques. In this paper, we examine how the SDF and related filters can be used to not only provide an approximate location, but also estimate the extent of the distortion. Using this information as a starting point for one of the more sophisticated methods allows a significant reduction in computational cost. In the process, we derive various sufficient conditions that the images must satisfy for this technique to work.