A Bayesian Generative Approach to Shape from Shading

Inferring shape from shading is a well-studied yet unresolved problem. Here, we develop a novel approach to the problem by using Bayesian inference on a generative model of shape and image formation. Using the Church probabilistic language [7], we model shape as a mixture of Gaussian perturbations to a heightfield, and we model image formation as a noisy rendering process. With this generative model, we iteratively search for the maximum a posteriori (MAP) heightfield using Markov chain Monte Carlo methods. Thus, shape is inferred through a recognition-by-synthesis loop, in which we iteratively propose candidate shapes and assess how well they match our target. This approach has the potential to overcome many of the shortcomings of previous shape-from-shading algorithms, which have suffered from sticky local minima, tackedon priors, sensitivity to noise, and limited flexibility and extensibility. Unlike most previous approaches, we are able to solve for an entire posterior distribution, thereby overstepping local minima; we recognize the problem as intrinsically probabilistic, and are thus able to incorporate priors in a principled way; we incorporate uncertainty directly into our model, and consequently our inference is robust to noise; and our generative approach is arbitrarily extensible and has potential to become automatically adaptable.