The Selection of Critical Subsets for Signal, Image, and Scene Matching

A basic matching problem consists of locating a reference subset in a larger set of data subject to a given criterion. Variations of the problem include template matching for object recognition, matched filtering for signal detection, image registration, change detection, cartography feature location, correlation guidance, and scene matching. In the general case the data sets may be made by completely different sensors at different geometrical orientations. A data set in N dimensions can be considered as a function in N-space. The critical subset selection problem arises when one is given a function and must select some subset of the function to match with the original. In some cases uniqueness is a key feature of the best subset. Uniqueness may be measured by the number and relative magnitudes of the peaks in the cross correlation function of the original and subset functions. For a unique subset, another desirable characteristic is lack of ambiguity. This characteristic may be measured using the correlation length or 50 percent width of the main correlation peak. The smaller the correlation length, the greater the certainty one has in detecting the correct match position. In this paper a method is presented for selecting the ``best'' subset of a scene where best is defined in terms of the minimum correlation length. The best solution is shown to be a function of the entire scene, i.e., an improper subset.