Subpixel Photometric Stereo

Conventional photometric stereo recovers one normal direction per pixel of the input image. This fundamentally limits the scale of recovered geometry to the resolution of the input image, and cannot model surfaces with subpixel geometric structures. In this paper, we propose a method to recover subpixel surface geometry by studying the relationship between the subpixel geometry and the reflectance properties of a surface. We first describe a generalized physically-based reflectance model that relates the distribution of surface normals inside each pixel area to its reflectance function. The distribution of surface normals can be computed from the reflectance functions recorded in photometric stereo images. A convexity measure of subpixel geometry structure is also recovered at each pixel, through an analysis of the shadowing attenuation. Then, we use the recovered distribution of surface normals and the surface convexity to infer subpixel geometric structures on a surface of homogeneous material by spatially arranging the normals among pixels at a higher resolution than that of the input image. Finally, we optimize the arrangement of normals using a combination of belief propagation and MCMC based on a minimum description length criterion on 3D textons over the surface. The experiments demonstrate the validity of our approach and show superior geometric resolution for the recovered surfaces.