# MonteBoxFinder: Detecting and Filtering Primitives to Fit a Noisy Point Cloud

arXiv: https://arxiv.org/abs/2207.14268 · HTML: https://mlsanity.com/paper/2207.14268/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 28 Jul 2022.

## Builds on (most cited first, 15 of 15)

- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [PV-RCNN: Point-Voxel Feature Set Abstraction for 3D Object Detection](https://mlsanity.com/paper/1912.13192/) (2019)
- [Deep Hough Voting for 3D Object Detection in Point Clouds](https://mlsanity.com/paper/1904.09664/) (2019)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [IM2CAD](https://mlsanity.com/paper/1608.05137/) (2016)
- [Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image](https://mlsanity.com/paper/2004.01176/) (2020)
- [Holistic++ Scene Understanding: Single-view 3D Holistic Scene Parsing and Human Pose Estimation with Human-Object Interaction and Physical Commonsense](https://mlsanity.com/paper/1909.01507/) (2019)
- [Holistic 3D Scene Parsing and Reconstruction from a Single RGB Image](https://mlsanity.com/paper/1808.02201/) (2018)
- [Monte Carlo Scene Search for 3D Scene Understanding](https://mlsanity.com/paper/2103.07969/) (2021)
- [Cuboids Revisited: Learning Robust 3D Shape Fitting to Single RGB Images](https://mlsanity.com/paper/2105.02047/) (2021)

## Built on by (most cited first, 11 of 11)

- [Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives](https://mlsanity.com/paper/2307.05473/) (2023)
- [SuperDec: 3D Scene Decomposition with Superquadric Primitives](https://mlsanity.com/paper/2504.00992/) (2025)
- [AirPlanes: Accurate Plane Estimation via 3D-Consistent Embeddings](https://mlsanity.com/paper/2406.08960/) (2024)
- [Self-supervised Learning of Hybrid Part-aware 3D Representations of 2D Gaussians and Superquadrics](https://mlsanity.com/paper/2408.10789/) (2024)
- [Convex Decomposition of Indoor Scenes](https://mlsanity.com/paper/2307.04246/) (2023)
- [Learnable Earth Parser: Discovering 3D Prototypes in Aerial Scans](https://mlsanity.com/paper/2304.09704/) (2023)
- [Blocks2World: Controlling Realistic Scenes with Editable Primitives](https://mlsanity.com/paper/2307.03847/) (2023)
- [Improved Convex Decomposition with Ensembling and Negative Primitives](https://mlsanity.com/paper/2405.19569/) (2024)
- [Deep Polycuboid Fitting for Compact 3D Representation of Indoor Scenes](https://mlsanity.com/paper/2503.14912/) (2025)
- [D-Prism: Differentiable Primitives for Structured Dynamic Modeling](https://mlsanity.com/paper/2604.17082/) (2026)
- [Superquadric Primitive Decomposition of 3D point clouds via Geometric-Aware Inlier Refinement](https://mlsanity.com/paper/2609.35725/) (2026)

## Abstract (arXiv)

We present MonteBoxFinder, a method that, given a noisy input point cloud, fits cuboids to the input scene. Our primary contribution is a discrete optimization algorithm that, from a dense set of initially detected cuboids, is able to efficiently filter good boxes from the noisy ones. Inspired by recent applications of MCTS to scene understanding problems, we develop a stochastic algorithm that is, by design, more efficient for our task. Indeed, the quality of a fit for a cuboid arrangement is invariant to the order in which the cuboids are added into the scene. We develop several search baselines for our problem and demonstrate, on the ScanNet dataset, that our approach is more efficient and precise. Finally, we strongly believe that our core algorithm is very general and that it could be extended to many other problems in 3D scene understanding.