On reliable curvature estimation

An empirical study of the accuracy of five different curvature estimation techniques, using synthetic range images and images obtained from three range sensors, is presented. The results obtained highlight the problems inherent in accurate estimation of curvatures, which are second-order quantities, and thus highly sensitive to noise contamination. The numerical curvature estimation methods are found to perform about as accurately as the analytic techniques, although ensemble estimates of overall surface curvature such as averages are unreliable unless trimmed estimates are used. The median proved to be the best estimator of location. As an exception, it is shown theoretically that zero curvature can be fairly reliably detected, with appropriate selection of threshold values.<>