Recovering shape characteristics on near-flat specular surfaces

We consider the problem of capturing shape characteristics on specular (refractive and reflective) surfaces that are nearly flat. These surfaces are difficult to model using traditional methods based on reconstructing the surface positions and normals. These lower-order shape attributes provide little information to identify important surface characteristics related to distortions. In this paper, we present a framework for recovering the higher-order geometry attributes of specular surfaces. Our method models local reflections and refractions in terms of a special class of multiperspective cameras called the general linear cameras (GLCs). We then develop a new theory that correlates the higher-order differential geometry attributes with the local GLCs. Specifically, we show that Gaussian and mean curvature can be directly derived from the camera intrinsics of the local GLCs. We validate this theory on both synthetic and real-world specular surfaces. Our method places a known pattern in front of a reflective surface or beneath a refractive surface and captures a distorted image on the surface. We then compute the optimal GLC using a sparse set of correspondences and recover the curvatures from the GLC. Experiments demonstrate that our methods are robust and highly accurate.