Motion Analysis by Random Sampling and Voting Process

In computer vision, motion analysis is a fundamental problem. Applying the concepts of congruence checking in computational geometry and geometric hashing, which is a technique used for the recognition of partially occluded objects from noisy data, we present a new random sampling approach for the estimation of the motion parameters in two- and three-dimensional Euclidean spaces of both a completely measured rigid object and a partially occluded rigid object. We assume that the two- and three-dimensional positions of the vertices of the object in each image frame are determined using appropriate methods such as a range sensor or stereo techniques. We also analyze the relationships between the quantization errors and the errors in the estimation of the motion parameters by random sampling, and we show that the solutions obtained using our algorithm converge to the true solutions if the resolution of the digitalization is increased.