Uncertainty Propagation in Stereo Matching using Copulas

This contribution presents a concrete example of uncertainty propagation in a stereo matching pipeline. It considers the problem of matching pixels between pairs of images whose radiometry is uncertain and modeled by possibility distributions. Copulas serve as dependency models between variables and are used to propagate the imprecise models. The propagation steps are detailed in the simple case of the Sum of Absolute Difference cost function for didactic purposes. The method results in an imprecise matching cost curve. To reduce computation time, a sufficient condition for conserving possibility distributions after the propagation is also presented. Finally, results are compared with Monte Carlo simulations, indicating that the method produces envelopes capable of correctly estimating the matching cost.