A bayesian approach to 3-d shape estimation for robotic vision
Basilis Gidas, Jose Ricardo De Almeida Torreao · 1990
We consider the problem of 3-D shape reconstruction for Computer Vision applications. Our treatment is based on the Bayesian statistical approach, and we use an analogy between images and Statistical Mechanics systems to encode our expectations about the 3-D scene attributes and the image formation process in terms of Hamiltonians, from which prior probability distributions of Gibbs form are constructed. Simulated Annealing for constrained and unconstrained global optimization is employed for the attributes estimation. Our shape reconstruction protocol includes surface orientation estimation, edge detection and depth-map reconstruction. We reformulate in Bayesian terms the Shape-from-Shading problem of orientation-map estimation from one undegraded input image, considering different Reflectance Map forms and various schemes for the incorporation of boundary conditions. We also treat the situation in which only partial information about the Reflectance Map is available. We consider also the reconstruction of the orientation map from two degraded input images in the Photometric-Stereo framework, i.e., for images obtained from the same viewing position with different illumination directions. Degradation by additive and multiplicative Gaussian noise and nonlinear transformations are considered. Both here and in Shape-from-Shading, we parameterize surface orientation in terms of a normal-vector field. For edge detection, we introduce two new approaches: the detection of boundaries from the orientation-field input, and the use of multiple images for edge detection in a photometric-stereo framework. The first scheme can be coupled with our surface-orientation reconstruction algorithms, and is particularly useful for the photometric-stereo reconstruction, since degraded input can then be treated for which the direct detection of edges is particularly hard. The proposed multiple-image set-up for edge detection is useful in the elimination of spurious edge elements, such as those arising from cast shadows. In the subject of depth estimation, we consider the use of shading information for the direct recovery of depth from two input images, again in the photometric-stereo set-up. We also treat the estimation of spatial orientation from texture data for images represented by a class of Gibbs distributions recently introduced.