Discrete Laplace Operator Estimation for Dynamic 3D Reconstruction
This addresses the problem of reconstructing dynamic scenes from arbitrary temporal data for applications like event segmentation, but it appears incremental as it builds on existing graph and optimization frameworks.
The paper tackles dynamic 3D reconstruction from uncontrolled image sources by proposing a graph-theoretic method that jointly estimates 3D geometry and its discrete Laplace operator, achieving results on motion capture and multi-view datasets.
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 Euclideanshape-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.