Combining Shape from Shading and Stereo: A Variational Approach for the Joint Estimation of Depth, Illumination and Albedo

Shape from shading (SfS) and stereo are two fundamentally different strategies for image-based 3-D reconstruction. While approaches for SfS infer the depth solely from pixel intensities, methods for stereo are based on a matching process that establishes correspondences across images. In this paper we propose a joint variational method that combines the advantages of both strategies. By integrating recent stereo and SfS models into a single minimisation framework, we obtain an approach that exploits shading information to improve upon the reconstruction quality of robust stereo methods. To this end, we fuse a Lambertian SfS approach with a robust stereo model and supplement the resulting energy functional with a detail-preserving anisotropic second-order smoothness term. Moreover, we extend the novel model in such a way that it jointly estimates depth, albedo and illumination. This in turn makes it applicable to objects with non-uniform albedo as well as to scenes with unknown illumination. Experiments for synthetic and real-world images show the advantages of our combined approach: While the stereo part overcomes the albedo-depth ambiguity inherent to all SfS methods, the SfS part improves the degree of details of the reconstruction compared to pure stereo methods.