Binocular projection of a random scene

Current approaches to large-scale visual reconstruction would benefit from a statistical model of multiple-view projection. In particular, global constraints based on sceneclutter and occlusion are required. This work presents a new statistical model, starting from the simplest example of a random scene, viewed by two cameras. It has previously been shown that, if the scene is modelled as a Poisson process of identical objects, then the distance to a visible object follows an exponential distribution. But this is not qualitatively realistic, because the mode of the exponential is at zero, implying that the optical centre is fully amid the clutter. Real range-data, in contrast, follows a two-tailed distribution along each ray. A more realistic visibility density is proposed, in which the optical centre is displaced from the Poisson scene by a Gaussian shift. This means that the distance to an un-occluded object is now distributed according to the convolution of the exponential and Gaussian distributions, which has a variable mode. This distribution is re-parameterized along the corresponding epipolar line in another view, via the appropriate Jacobian. The resulting correspondence density gives the prior probability of a binocular match. The parameters of the density are estimated from a data-set of outdoor laser range-scans. This makes it possible to generate full 3D Poisson models that are statistically consistent with the real data. These synthetic scenes are used to further investigate the correspondence density, by Monte Carlo simulation.