We develop a framework for extracting a concise representation of the shape information available from diffuse shading in a small image patch. This produces a mid-level scene descriptor, comprised of local shape distributions that are inferred separately at every image patch across multiple scales. The framework is based on a quadratic representation of local shape that, in the absence of noise, has guarantees on recovering accurate local shape and lighting. And when noise is present, the inferred local shape distributions provide useful shape information without over-committing to any particular image explanation. These local shape distributions naturally encode the fact that some smooth diffuse regions are more informative than others, and they enable efficient and robust reconstruction of object-scale shape. Experimental results show that this approach to surface reconstruction compares well against the state-of-art on both synthetic images and captured photographs.
Many algorithms have been suggested for the shape-from-shading problem, and some years have passed since the publication of the survey paper by [R. Zhang, P.-S. Tsai, J.E. Cryer, M. Shah, Shape from shading: a survey, IEEE Transactions on Pattern Analysis and Machine Intelligence 21 (8) (1999) 690-706]. In this new survey paper, we try to update their presentation including some recent methods which seem to be particularly representative of three classes of methods: methods based on partial differential equations, methods using optimization and methods approximating the image irradiance equation. One of the goals of this paper is to set the comparison of these methods on a firm basis. To this end, we provide a brief description of each method, highlighting its basic assumptions and mathematical properties. Moreover, we propose some numerical benchmarks in order to compare the methods in terms of their efficiency and accuracy in the reconstruction of surfaces corresponding to synthetic, as well as to real images. Resolving local ambiguities is an important issue for shape from shading (SFS). Pixel ambiguities of SFS can be eliminated by propagation approaches. However, patch ambiguities still exist. Therefore, we formulate the global disambiguation problem to resolve these ambiguities. Intuitively, it can be interpreted as flipping patches and adjusting heights such that the result surface has no kinks. The problem is intractable because exponentially many possible configurations need to be checked. Alternatively, we solve the integrability testing problems closely related to the original one. It can be viewed as finding a surface which satisfies the global integrability constraint. To encode the constraints, we introduce a graph formulation called configuration graph. Searching the solution on this graph can be reduced to a Max-cut problem and its solution is computuble using semidefinite programming (SDP) relaxation. Tests carried out on synthetic and real images show that the global disambiguation works well for complex shapes. The traditional shape-from-shading problem, with a single light source and Lambertian reflectance, is challenging since the constraints implied by the illumination are not sufficient to specify local orientation. Photometric stereo algorithms, a variant of shape-from-shading, simplify the problem by controlling the illumination to obtain additional constraints. In this paper, we demonstrate that many natural lighting environments already have sufficient variability to constrain local shape. We describe a novel optimization scheme that exploits this variability to estimate surface normals from a single image of a diffuse object in natural illumination. We demonstrate the effectiveness of our method on both simulated and real images. We examine the shape from shading problem without boundary conditions as a polynomial system. This view allows, in generic cases, a complete solution for ideal polyhedral objects. For the general case we propose a semidefinite programming relaxation procedure, and an exact line search iterative procedure with a new smoothness term that favors folds at edges. We use this numerical technique to inspect shading ambiguities.