Discrete Laplace Operator Estimation for Dynamic 3D Reconstruction

TL;DR

This paper introduces a graph-theoretic approach for dynamic 3D reconstruction from multiple uncontrolled image sources, jointly estimating geometry and the discrete Laplace operator to improve understanding of spatio-temporal relationships.

Contribution

It proposes a tri-convex optimization framework that models the joint estimation of 3D geometry and the Laplace operator from diverse image data, advancing the field of dynamic reconstruction.

Findings

Effective reconstruction on motion capture data

Successful application to multi-view image datasets

Enhanced geometry-based event segmentation and data association

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 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.