A STUDY OF AFFINE MATCHING WITH BOUNDED SENSOR ERROR

Affine transformations of the plane have been used in a number of mode l-based recognition systems. Because the underlying mathematics are ba sed on exact data, in practice various heuristics are used to adapt th e methods to real data where there is positional uncertainty. This pap er provides a precise analysis of affine point matching under uncertai nty. We obtain an expression for the range of affine-invariant values that are consistent with a given set of four points, where each image point lies in an epsilon-disc of uncertainty. This range is shown to d epend on the actual x-y-positions of the data points. In other words, given uncertainty in the data there are no representations that are in variant with respect to the Cartesian coordinate system of the data. T his is problematic for methods, such as geometric hashing, that are ba sed on affine-invariant representations. We also analyze the effect th at uncertainty has on the probability that recognition methods using a ffine transformations will find false positive matches. We find that t here is a significant probability of false positives with even moderat e levels of sensor error, suggesting the importance of good verificati on techniques and good grouping techniques.