Random perturbation models for boundary extraction sequence

Computer vision algorithms are composed of different sub-algorithms often applied in sequence. Determination of the performance of a total computer vision algorithm is possible if the performance of each of the sub-algorithm constituents is given. The performance characterization of an algorithm has to do with establishing the correspondence between the random variations and imperfections in the output data and the random variations and imperfections in the input data. In this paper we illustrate how random perturbation models can be set up for a vision algorithm sequence involving edge finding, edge linking, and gap filling. By starting with an appropriate noise model for the input data we derive random perturbation models for the output data at each stage of our example sequence. By utilizing the perturbation model for edge detector output derived, we illustrate how pixel noise can be successively propagated to derive an error model for the boundary extraction output. It is shown that the fragmentation of an ideal boundary can be described by an alternating renewal process and that the parameters of the renewal process are related to the probability of correct detection and grouping at the edge linking step. It is also shown that the characteristics of random segments generated due to gray-level noise are functions of the probability of false alarm of the edge detector. Theoretical results are validated through systematic experiments.