# Discrete Laplace Operator Estimation for Dynamic 3D Reconstruction

arXiv: https://arxiv.org/abs/1908.11044 · HTML: https://mlsanity.com/paper/1908.11044/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2019.

## Built on by (most cited first, 3 of 3)

- [4DPV: 4D Pet from Videos by Coarse-to-Fine Non-Rigid Radiance Fields](https://mlsanity.com/paper/2411.10275/) (2024)
- [GTT-Net: Learned Generalized Trajectory Triangulation](https://mlsanity.com/paper/2109.03408/) (2021)
- [GeoSplat: A Deep Dive into Geometry-Constrained Gaussian Splatting](https://mlsanity.com/paper/2509.05075/) (2025)

## Abstract (arXiv)

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.