# PSDF Fusion: Probabilistic Signed Distance Function for On-the-fly 3D Data Fusion and Scene Reconstruction

arXiv: https://arxiv.org/abs/1807.11034 · HTML: https://mlsanity.com/paper/1807.11034/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2018.

## Built on by (most cited first, 13 of 13)

- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [Marching-Primitives: Shape Abstraction from Signed Distance Function](https://mlsanity.com/paper/2303.13190/) (2023)
- [UncLe-SLAM: Uncertainty Learning for Dense Neural SLAM](https://mlsanity.com/paper/2306.11048/) (2023)
- [ASH: A Modern Framework for Parallel Spatial Hashing in 3D Perception](https://mlsanity.com/paper/2110.00511/) (2021)
- [HRBF-Fusion: Accurate 3D reconstruction from RGB-D data using on-the-fly implicits](https://mlsanity.com/paper/2202.01829/) (2022)
- [Fast Monocular Scene Reconstruction with Global-Sparse Local-Dense Grids](https://mlsanity.com/paper/2305.13220/) (2023)
- [Learning Online Multi-Sensor Depth Fusion](https://mlsanity.com/paper/2204.03353/) (2022)
- [Online Learning of a Probabilistic and Adaptive Scene Representation](https://mlsanity.com/paper/2103.16832/) (2021)
- [A Geometric Algorithm for Blood Vessel Reconstruction from Skeletal Representation](https://mlsanity.com/paper/2402.12797/) (2024)
- [Uncertainty-aware retinal layer segmentation in OCT through probabilistic signed distance functions](https://mlsanity.com/paper/2412.04935/) (2024)
- [Rendering and Tracking the Directional TSDF: Modeling Surface Orientation for Coherent Maps](https://mlsanity.com/paper/2108.08115/) (2021)
- [PRISM: Probabilistic Real-Time Inference in Spatial World Models](https://mlsanity.com/paper/2212.02988/) (2022)
- [Rendering the Directional TSDF for Tracking and Multi-Sensor Registration with Point-To-Plane Scale ICP](https://mlsanity.com/paper/2301.12796/) (2023)

## Abstract (arXiv)

We propose a novel 3D spatial representation for data fusion and scene reconstruction. Probabilistic Signed Distance Function (Probabilistic SDF, PSDF) is proposed to depict uncertainties in the 3D space. It is modeled by a joint distribution describing SDF value and its inlier probability, reflecting input data quality and surface geometry. A hybrid data structure involving voxel, surfel, and mesh is designed to fully exploit the advantages of various prevalent 3D representations. Connected by PSDF, these components reasonably cooperate in a consistent frame- work. Given sequential depth measurements, PSDF can be incrementally refined with less ad hoc parametric Bayesian updating. Supported by PSDF and the efficient 3D data representation, high-quality surfaces can be extracted on-the-fly, and in return contribute to reliable data fu- sion using the geometry information. Experiments demonstrate that our system reconstructs scenes with higher model quality and lower redundancy, and runs faster than existing online mesh generation systems.