3D Watertight Mesh Generation with Uncertainties from Ubiquitous Data

In this paper, we propose a generic framework for watertight mesh generation with uncertainties that provides a confidence measure on each reconstructed mesh triangle. Its input is a set of vision-based or Lidar-based 3D measurements which are converted to a set of mass functions that characterize the level of confidence on the occupancy of the scene as occupied, empty or unknown based on Dempster-Shafer Theory. The output is a multi-label segmentation of the ambient 3D space expressing the confidence for each resulting volume element to be occupied or empty. While existing methods either sacrifice watertightness (local methods) or need to introduce a smoothness prior (global meth-ods), we derive a per-triangle confidence measure that is able to gradually characterize when the resulting surface patches are certain due to dense and coherent measurements and when these patches are more uncertain and are mainly present to ensure smoothness and/or watertightness. The surface mesh reconstruction is formulated as a global energy minimization problem efficiently optimized with the α-expansion algorithm. We claim that the resulting confidence measure is a good estimate of the local lack of sufficiently dense and coherent input measurements, which would be a valuable input for the next-best-view scheduling of a complementary acquisition. Beside the new formulation, the proposed approach achieves state-of-the-art results on surface reconstruction benchmark. It is robust to noise, manages high scale disparity and produces a watertight surface with a small Hausdorff distance in uncertainty area thanks to the multi-label formulation. By simply thresholding the result, the method shows a good reconstruction quality compared to local algorithms on high density data. This is demonstrated on a large scale reconstruction combining real-world datasets from airborne and terrestrial Lidar and on an indoor scene reconstructed from images.