Attached shadow coding: Estimating surface normals from shadows under unknown reflectance and lighting conditions

We present a novel technique, termed attached shadow coding, for estimating surface normals from shadows when the reflectance and lighting conditions are unknown. Our key idea is encoding surface points via attached shadows observed under different light source directions and then estimating surface normals on the basis of the similarity of the attached shadow codes. Because shadows do not rely on reflectance properties, our method is applicable to surfaces with various complex reflectances such as anisotropic and composite materials. Moreover, our method is robust against noise because it takes advantage of the combination of weak constraints imposed by a number of light sources. We theoretically show that the distance between the codes at two surface points is equal to the angle between the corresponding surface normals under the assumption of uniform lighting and a convex object. Our method embeds high-dimensional codes into a 3D surface normal space so that the inter-code distances are preserved. Furthermore, we extend the method in order to alleviate the effects of nonuniform lighting and cast shadows. Experimental results demonstrate the effectiveness of our method.