A Closed-Form Bayesian Fusion Equation Using Occupancy Probabilities

We present a new mathematical framework for multi-view surface reconstruction from a set of calibrated color and depth images. We estimate the occupancy probability of points in space along sight rays, and combine these estimates using a normalized product derived from Bayes' rule. The advantage of this approach is that the free space constraint is a natural consequence of the formulation, and not a separate logical operation. We present a single closed form implicit expression for the reconstructed surface in terms of the image data and camera projections, making analytic properties such as surface normals not only easy to compute, but exact. This expression can be efficiently evaluated on the GPU, making it ideal for high performance real-time applications, such as live human body capture for immersive telepresence.