Statistics of surface curvature estimates

摘要

Reliable curvature estimation is an important goal in image analysis to provide viewpoint independent cues for shape classification. This paper presents a model of the relationship between the variance of curvature estimates and the image noise. Agreement to within 10% is obtained for 3D range data. A perturbation error analysis is performed on the local least square surface fitting algorithm which is commonly used to obtain partial derivative estimates in the presence of noise. The theoretical results are used to implement adaptive thresholding for surface type classification. This is compared with existing constant and semi-adaptive thresholding schemes. It is concluded that any pixel-by-pixel thresholding will produce poor results. The theoretical relationships provide the basis for a probabilistic approach.