# MRFMap: Online Probabilistic 3D Mapping using Forward Ray Sensor Models

arXiv: https://arxiv.org/abs/2006.03512 · HTML: https://mlsanity.com/paper/2006.03512/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Approximate Differentiable Rendering with Algebraic Surfaces](https://mlsanity.com/paper/2207.10606/) (2022)
- [Flexible Techniques for Differentiable Rendering with 3D Gaussians](https://mlsanity.com/paper/2308.14737/) (2023)
- [Online Learning of a Probabilistic and Adaptive Scene Representation](https://mlsanity.com/paper/2103.16832/) (2021)
- [Belief-Aware Multi-Agent Path Finding under Map Uncertainty](https://mlsanity.com/paper/2609.40269/) (2026)

## Abstract (arXiv)

Traditional dense volumetric representations for robotic mapping make simplifying assumptions about sensor noise characteristics due to computational constraints. We present a framework that, unlike conventional occupancy grid maps, explicitly models the sensor ray formation for a depth sensor via a Markov Random Field and performs loopy belief propagation to infer the marginal probability of occupancy at each voxel in a map. By explicitly reasoning about occlusions our approach models the correlations between adjacent voxels in the map. Further, by incorporating learnt sensor noise characteristics we perform accurate inference even with noisy sensor data without ad-hoc definitions of sensor uncertainty. We propose a new metric for evaluating probabilistic volumetric maps and demonstrate the higher fidelity of our approach on simulated as well as real-world datasets.