Estimating pose uncertainty for surface registration

Accurate registration of surfaces is a common task in computer vision. Several algorithms exist to refine an approximate value for the pose to an accurate value. They are all more or less variants of the iterative closest point (ICP) algorithm of Besl and McKay. Up to now the problem of determining the uncertainty in the pose estimate when registering surfaces has not been solved. In this paper we provide a solution applicable when registering a noisy measured surface to an accurately known surface model. We contend that it is necessary to use the normal-projection ICP of Chen and Medioni to obtain a meaningful uncertainty estimate. Knowledge of the uncertainty provides a quantitative signal for cases of near degenerate surface shape where accurate pose estimation may not be possible. We introduce a new parameter called the registration index to give a simple means of quantifying the pose errors one might expect when registering a particular shape.