Hough Transform for Opaque Circles Measured from Outside and Fuzzy Voting For and Against

Geometrical limitations on the voting process in the classical Hough transform resulting from that the detected objects are opaque to the applied means of measurement are considered. It is assumed that the measurements are made from one point, like in LIDAR scanning. The detected object is a circle and the two point elementary voting set forming its chord is considered. The first type of conditions are those which can be used during the accumulation process. The side condition says that the circle lies at the opposite side of the chord than the laser source. The magnitude condition requires that points in the elementary set must not be occluded with respect to the source by any circle hypothesised in voting. The second type of conditions can be checked after after the detection. They require that points are neither inside the object nor in its shadow. Departures from this rule are admitted, so fuzzy voting between positive and negative evidence for the object is considered.