A recursive method to apply the Hough transform to a set of moving objects

The Hough transform is a mean to detect, from the edge-points of an image, the presence or absence of some parametric shapes the analytic formulation of which is already known, and to determine the value of the parameters vector. The principle of the method is to establish a good transform from the points in the image plane, to a curve in the parameter space, then to compute an experimental density in the parameter space, finally to find the values of parameters where the experimental density is maximum. In this paper, we show a way to get rid of the fastidious computation of density and its maximums, in the case -very common- where a priori the location of maximums is roughly known. Our method is based on the principle of a linearization of the equations of contours, with respect to the parameters, around each a priori parameter estimate. This linearization gives the opportunity to transform the problem, for each edge point, in a linear statistical estimator combined with an hypothesis-testing operator. This method can be used with high profit when a sequence of images is to be treated where the contours are slowly varying. Also, as pointed out by BALLARD, it is not necessary that the contours be simple-parametric curves as straight lines, cercles, ellipses, etc., but same results can be applied to the contours which shape is known but is moving, with rotation, translation and scaling.