PDE Based Shape from Specularities

When reconstructing surfaces from image data, reflections on specular surfaces are usually viewed as a nuisance that should be avoided. In this paper a different view is taken. Noting that such reflections contain information about the surface, this information could and should be used when estimating the shape of the surface. Specifically, assuming that the position of the light source and the cameras (i.e. the motion) are known, the reflection from a specular surface in a given image constrain the surface normal with respect to the corresponding camera. Here the constraints on the normals, given by the reflections, are used to formulate a partial differential equation (PDE) for the surface. A smoothness term is added to this PDE and it is solved using a level set framework, thus giving a "shape from specularity" approach. The structure of the PDE also allows other properties to be included, e.g. the constraints from PDE based stereo. The proposed PDE does not fit naturally into a level set framework. To address this issue it is proposed to couple a force field to the level set grid. To demonstrate the viability of the proposed method it has been applied successfully to synthetic data.