# Differentiable Mesh State Estimation via Factor Graph Inference for Deformable Object Reconstruction

arXiv: https://arxiv.org/abs/2609.16686 · HTML: https://mlsanity.com/paper/2609.16686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Learning Deformable Tetrahedral Meshes for 3D Reconstruction](https://mlsanity.com/paper/2011.01437/) (2020)
- [DiSECt: A Differentiable Simulation Engine for Autonomous Robotic Cutting](https://mlsanity.com/paper/2105.12244/) (2021)
- [From Monocular Vision to Autonomous Action: Guiding Tumor Resection via 3D Reconstruction](https://mlsanity.com/paper/2503.16263/) (2025)
- [PERSEUS: Perception with Semantic Endoscopic Understanding and SLAM](https://mlsanity.com/paper/2509.13541/) (2025)

## Abstract (arXiv)

Estimating deformable object states remains a fundamental challenge in robotics and simulation. We propose a novel factor graph-based framework for probabilistic mesh state estimation of deformable objects. The method directly updates a tetrahedral mesh, a rich and physically-grounded representation of an environment, by combining physics priors, noisy sensor measurements, and temporal smoothness constraints within a unified probabilistic formulation. The estimation problem is posed as a nonlinear least-squares optimization and solved using Levenberg-Marquardt. Ex vivo central-airway obstruction experiments and simulations on deforming cube models demonstrate reliable and accurate reconstruction under both rigid motion and deformation, highlighting the potential of this probabilistic approach for principled, measurement-driven mesh state estimation in deformable object reconstruction.