Mirror Surface Reconstruction from a Single Image

This paper tackles the problem of reconstructing the shape of a smooth mirror surface from a single image. In particular, we consider the case where the camera is observing the reflection of a static reference target in the unknown mirror. We first study the reconstruction problem given dense correspondences between 3D points on the reference target and image locations. In such conditions, our differential geometry analysis provides a theoretical proof that the shape of the mirror surface can be recovered if the pose of the reference target is known. We then relax our assumptions by considering the case where only sparse correspondences are available. In this scenario, we formulate reconstruction as an optimization problem, which can be solved using a nonlinear least-squares method. We demonstrate the effectiveness of our method on both synthetic and real images. We then provide a theoretical analysis of the potential degenerate cases with and without prior knowledge of the pose of the reference target. Finally we show that our theory can be similarly applied to the reconstruction of the surface of transparent object.