Reconstruction of a Complex Mirror Surface from a Single Image

In this work, we propose a method to recover the shape of a complex mirror surface from a single image with un-calibrated environment. A complex mirror surface reflects the same environment feature at multiple surface points. These static reflection correspondences (SRCs) can be detected with SIFT (or its variations) and provide important visual cue of the surface shape. The detected SRCs are clustered by a bipartite graph partition method so that each cluster of SRCs is within either elliptic or hyperbolic surface regions. The surface region is then further segmented by a Voronoi diagram of the SRCs. Within each Voronoi cell, the surface is approximated by a local quadric model. Assuming orthographic projection and distant environment, the SRCs of an environment feature share the same surface gradient, which provides a major constraint to the surface shape. Along with the smoothness constraints, the surface shape can be recovered with an optimization method. Synthesized and physical experiments support our proposed method.