Fairing of Discrete Surfaces with Boundary That Preserves Size and Qualitative Shape

In this paper, we propose a new algorithm for fairing discrete surfaces resulting from stereo-based 3D reconstruction task. Such results are typically too dense, uneven and noisy, which is inconvenient for further processing. Our approach jointly optimises mesh smoothness and regularity. The definition is given on a discrete surface and the solution is found by discrete diffusion of a scalar function. Experiments on synthetic and real data demonstrate that the proposed approach is robust, stable, preserves qualitative shape and is applicable to even moderate-size real surfaces with boundary (0.8M vertices and 1.7M triangles).