  Generative reconstruction methods compute the 3D configuration (such as pose
and/or geometry) of a shape by optimizing the overlap of the projected 3D shape
model with images. Proper handling of occlusions is a big challenge, since the
visibility function that indicates if a surface point is seen from a camera can
often not be formulated in closed form, and is in general discrete and
non-differentiable at occlusion boundaries. We present a new scene
representation that enables an analytically differentiable closed-form
formulation of surface visibility. In contrast to previous methods, this yields
smooth, analytically differentiable, and efficient to optimize pose similarity
energies with rigorous occlusion handling, fewer local minima, and
experimentally verified improved convergence of numerical optimization. The
underlying idea is a new image formation model that represents opaque objects
by a translucent medium with a smooth Gaussian density distribution which turns
visibility into a smooth phenomenon. We demonstrate the advantages of our
versatile scene model in several generative pose estimation problems, namely
marker-less multi-object pose estimation, marker-less human motion capture with
few cameras, and image-based 3D geometry estimation.
