Pose estimation from reflections for specular surface recovery

This paper addresses the problem of estimating the poses of a reference plane in specular shape recovery. Unlike existing methods which require an extra mirror or an extra reference plane and camera, our proposed method recovers the poses of the reference plane directly from its reflections on the specular surface. By establishing reflection correspondences on the reference plane in three distinct poses, our method estimates the poses of the reference plane in two steps. First, by applying a colinearity constraint to the reflection correspondences, a simple closed-form solution is derived for recovering the poses of the reference plane relative to its initial pose. Second, by applying a ray incidence constraint to the incident rays formed by the reflection correspondences and the visual rays cast from the image, a closed-form solution is derived for recovering the poses of the reference plane relative to the camera. The shape of the specular surface then follows. Experimental results on both synthetic and real data are presented, which demonstrate the feasibility and accuracy of our proposed method.