A.: Specular surface reconstruction from sparse reflection correspondences

We present a practical approach for surface reconstruc-tion of smooth mirror-like objects using sparse reflection correspondences (RCs). Assuming finite object motion with a fixed camera and un-calibrated environment, we derive the relationship between RC and the surface shape. We show that by locally modeling the surface as a quadric, the relationship between the RCs and unknown surface param-eters becomes linear. We develop a simple surface recon-struction algorithm that amounts to solving either an eigen-value problem or a second order cone program (SOCP). Ours is the first method that allows for reconstruction of mirror surfaces from sparse RCs, obtained from standard algorithms such as SIFT. Our approach overcomes the practical issues in shape from specular flow (SFSF) such as the requirement of dense optical flow and undefined/infinite flow at parabolic points. We also show how to incorporate auxiliary information such as sparse surface normals into our framework. Experiments, both real and synthetic are shown that validate the theory presented. 1