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In this paper, we describe the fundamental differences between three-dimensional (range) images and two-dimensional (luminance) images. A number of problems arise which are unique to range data, including in particular a strong sensitivity to quantization effects. Although range images and luminance images are both arrays of scalars, the range image conceptually represents a surface in space and cannot be naively manipulated using the conventional image processing functions such as 3 × 3 convolution kernels. If the range data are regarded as a sampling of a surface parametrized by the focal plane coordinates, it is possible to find a representation for the surface normal and for the surface curvature in terms of familiar-looking convolution kernels.