On estimating the uncertainty in the location of image points in 3D recognition from match sets of different sizes

Efficient and robust model-based recognition systems need to be able to estimate reliably and quickly the possible locations of other model features in the image when a match of several model points to image points is given. Errors in the sensed data lead to uncertainty in the computed pose of the object, which in turn lead to uncertainty in these positions. We present an efficient and accurate method for estimating these uncertainty regions. Our basic method deals with an initial match of three points. With a small additional computational cost it can be used to compute the uncertainty regions of the projections of many model points using the same match triplet. The basic method is then extended employing statistical methods to estimate uncertainty regions when given initial matches of any size. This is the major practical contribution of the paper because when the number of points in the match increases, the size of the uncertainty region decreases dramatically, which helps to discriminate much better between correct and incorrect matches in model-based recognition algorithms.