Nm. Vaidya et Kl. Boyer, Discontinuity-preserving surface reconstruction using stochastic differential equations, COMP VIS IM, 72(3), 1998, pp. 257-270
We address the problem of reconstructing a surface from irregularly spaced
sparse and noisy range data while concurrently identifying and preserving t
he significant discontinuities in depth. It is well known that, starting fr
om either the probabilistic Markov random field model or the mechanical mem
brane or thin plate model for the surface, the solution of the reconstructi
on problem can be eventually reduced to the global minimization of a certai
n "energy" function. Requiring the preservation of depth discontinuities ma
kes the energy function nonconvex and replete with multiple local minima. W
e present a new method for obtaining discontinuity-preserving reconstructio
n based on the numerical solution of an appropriate Ito vector stochastic d
ifferential equation (SDE). The reconstructed surface is found by following
the sample path of the (stochastic) diffusion process that solves the SDE
in question, Our central contribution is the demonstration of the efficacy
of the stochastic differential equation technique for solving a vision prob
lem. Through comparisions of the results of our method to those of the two
well-known existing global minimization based reconstruction techniques, we
show a significant improvement in the final reconstructions obtained. (C)
1998 Academic Press.