Discontinuity preserving surface reconstruction through global optimization

We address the problem of reconstructing a surface from sparse and noisy depth data while concurrently identifying and preserving the significant discontinuities in depth. It is well known that, starting from either the probabilistic Markov random field model or the mechanical membrane or thin plate model for the surface, the solution of the reconstruction problem eventually reduces to the global minimization of a certain "energy" function. Requiring the preservation of depth discontinuities makes the energy function nonconvex and replete with multiple local minima. We present a new method for obtaining discontinuity-preserving reconstruction based on the numerical solution of an appropriate vector stochastic differential equation.