We present a new Bayesian vision technique that aims at recovering a shape from two or more noisy observations taken under similar lighting conditions. The shape is parametrized by a piecewise linear height field, textured by a piecewise linear irradiance field, and we assume Gaussian Markovian priors for both shape vertices and irradiance variables. The modeled observation process, equivalent to rendering, is modeled by a non‐affine projection (e.g. perspective projection) followed by a convolution with a piecewise linear point spread function, and contamination by additive Gaussian noise. We assume that the observation parameters are calibrated beforehand.
The major novelty of the proposed method consists of marginalizing out the irradiances considered as nuisance parameters, which is achieved by a hierarchy of approximations. This reduces the inference to minimizing an energy that only depends on the shape vertices, and therefore allows an efficient Iterated Conditional Mode (ICM) optimization scheme to be implemented. A Gaussian approximation of the posterior shape density is computed, thus providing estimates of both the geometry and its uncertainty. We illustrate the effectiveness of the new method by shape reconstruction results in a 2D case. A 3D version is currently under development and aims at recovering a surface from multiple images, reconstructing the topography by marginalizing out both albedo and shading.
