EU Regional School - Alliez Seminar - Part 2
Prof. Dr. Alliez - Mesh Generation and Shape Reconstruction
Inria Sophia Antipolis - Mediterranee
Shape reconstruction is concerned with recovering a digital representation of physical objects from measurement data. Shape reconstruction came to importance primarily as a result of the ability to acquire 3D point clouds: through, e.g., laser scanning, structured light and multi-view stereo. Without any prior assumption the shape reconstruction problem is inherently ill-posed, as an infinite number of shapes (curves in 2D, surfaces in 3D) pass through or near the data points. The problem must thus be regularized through several priors such as sampling density or level of noise. We will first discuss some basic methods devised in the field of Computational Geometry: these approaches, based on Voronoi diagrams and Delaunay triangulations, come with theoretical guarantees but require several assumptions that are rarely met on real-world data. We will then explore more advanced approaches based on variational formulations, that are robust to imperfect data such as noise and outliers.