Bayesian Vision for Shape Recovery

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 pieceviise linear height field, textured by a piecewise linear irradiance field, and we assume Gaussian Markovian priors for both shape vertices and irradiance variables. The observation process, also known as 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 (e.g. camera pose and noise variance) are calibrated beforehand. The major novelty of the proposed method consists of marginalizing out all the nuisance parameters (such as the irradiance field and the prior model hyperparameters), which is achieved by Laplace approximations. This reduces the inference to minimizizg an ener,q)lthat 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 not only an estimate of the mean geometry, but also of the uncertainty, which enables us to build a recursive algorithm to easily incorporate new data into the system. W-e illustrate the effectiveness of the general method described here by shape reconstruction results in a 2D case. A 3D version iising the emct s ~ z e appmach is currently under development and aims at recovering a surface from stereo pairs or multiple images, directly reconstructing the topography by marginalizing out both albedo and shading effects.