Discrete Laplace Operator Estimation for Dynamic 3D Reconstruction

Xiangyu Xu, Enrique Dunn

Abstract: We present a general paradigm for dynamic 3D reconstruction from multiple independent and uncontrolled image sources having arbitrary temporal sampling density and distribution. Our graph-theoretic formulation models the spatio-temporal relationships among our observations in terms of the joint estimation of their 3D geometry and its discrete Laplace operator. Towards this end, we define a tri-convex optimization framework that leverages the geometric properties and dependencies found among a Euclidean shape-space and the discrete Laplace operator describing its local and global topology. We present a reconstructability analysis, experiments on motion capture data and multi-view image datasets, as well as explore applications to geometry-based event segmentation and data association.