On reliable curvature estimation

Surface curvature properties have been successfully employed for surface classification and 3D object recognition. A number of methods have been proposed in the computer vision literature for the estimation of curvature; some are based on the analytic computation of derivatives from a local surface fit, and others estimate derivatives or curvature directly from the range data. In this paper, we conduct an empirical study of the accuracy of five different curvature estimation techniques, employing synthetic range images and images obtained from three range sensors. The results obtained highlight the problems inherent in accurate estimation of curvatures, which are second-order quantities, and thus highly sensitive to noise contamination. We conclude with some general recommendations about the utility of surface curvature estimation in range image analysis.