Efficient minimal-surface regularization of perspective depth maps in variational stereo

We propose a method for dense three-dimensional surface reconstruction that leverages the strengths of shape-based approaches, by imposing regularization that respects the geometry of the surface, and the strength of depth-map-based stereo, by avoiding costly computation of surface topology. The result is a near real-time variational reconstruction algorithm free of the staircasing artifacts that affect depth-map and plane-sweeping approaches. This is made possible by exploiting the gauge ambiguity to design a novel representation of the regularizer that is linear in the parameters and hence amenable to be optimized with state-of-the-art primal-dual numerical schemes.