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 methods), 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 \(\alpha \)-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.