We present a single-shot system to recover surface geometry of objects with spatially-varying albedos, from images captured under a calibrated RGB photometric stereo setup---with three light directions multiplexed across different color channels in the observed RGB image. Since the problem is ill-posed point-wise, we assume that the albedo map can be modeled as piece-wise constant with a restricted number of distinct albedo values. We show that under ideal conditions, the shape of a non-degenerate local constant albedo surface patch can theoretically be recovered exactly. Moreover, we present a practical and efficient algorithm that uses this model to robustly recover shape from real images. Our method first reasons about shape locally in a dense set of patches in the observed image, producing shape distributions for every patch. These local distributions are then combined to produce a single consistent surface normal map. We demonstrate the efficacy of the approach through experiments on both synthetic renderings as well as real captured images.
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. Since the first shape-from-shading (SFS) technique was developed by Horn in the early 1970s, many different approaches have emerged. In this paper, six well-known SFS algorithms are implemented and compared. The performance of the algorithms was analyzed on synthetic images using mean and standard deviation of depth (Z) error, mean of surface gradient (p, q) error, and CPU timing. Each algorithm works well for certain images, but performs poorly for others. In general, minimization approaches are more robust, while the other approaches are faster.  A method will be described for finding the shape of a smooth opaque object from a monocular image, given a knowledge of the surface photometry, the position of the light-source and certain auxiliary information to resolve ambiguities. This method is complementary to the use of stereoscopy which relies on matching up sharp detail and will fail on smooth objects. Until now the image processing of single views has been restricted to objects which can meaningfully be considered two-dimensional or bounded by plane surfaces. It is possible to derive a first-order non-linear partial differential equation in two unknowns relating the intensity at the image points to the shape of the object. This equation can be solved by means of an equivalent set of five ordinary differential equations. A curve traced out by solving this set of equations for one set of starting values is called a characteristic strip. Starting one of these strips from each point on some initial curve will produce the whole solution surface. The initial curves can usually be constructed around so-called singular points. A number of applications of this method will be discussed including one to lunar topography and one to the scanning electron microscope. In both of these cases great simplifications occur in the equations. A note on polyhedra follows and a quantitative theory of facial make-up is touched upon. An implementation of some of these ideas on the PDP-6 computer with its attached image-dissector camera at the Artificial Intelligence Laboratory will be described, and also a nose-recognition program.