# Bounding Box Disparity: 3D Metrics for Object Detection With Full Degree of Freedom

arXiv: https://arxiv.org/abs/2207.03720 · HTML: https://mlsanity.com/paper/2207.03720/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 18 references that are in the map.
- First posted on arXiv 8 Jul 2022.

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

- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Habitat-Matterport 3D Dataset (HM3D): 1000 Large-scale 3D Environments for Embodied AI](https://mlsanity.com/paper/2109.08238/) (2021)
- [ARKitScenes: A Diverse Real-World Dataset For 3D Indoor Scene Understanding Using Mobile RGB-D Data](https://mlsanity.com/paper/2111.08897/) (2021)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [Learning joint reconstruction of hands and manipulated objects](https://mlsanity.com/paper/1904.05767/) (2019)
- [STD: Sparse-to-Dense 3D Object Detector for Point Cloud](https://mlsanity.com/paper/1907.10471/) (2019)
- [3D Bounding Box Estimation Using Deep Learning and Geometry](https://mlsanity.com/paper/1612.00496/) (2016)
- [Objectron: A Large Scale Dataset of Object-Centric Videos in the Wild with Pose Annotations](https://mlsanity.com/paper/2012.09988/) (2020)
- [FCAF3D: Fully Convolutional Anchor-Free 3D Object Detection](https://mlsanity.com/paper/2112.00322/) (2021)
- [A Review on Object Pose Recovery: from 3D Bounding Box Detectors to Full 6D Pose Estimators](https://mlsanity.com/paper/2001.10609/) (2020)

## Built on by (most cited first, 2 of 2)

- [Polyra Swarms: A Shape-Based Approach to Machine Learning](https://mlsanity.com/paper/2506.13217/) (2025)
- [PGL-3D: Towards Progressive Geometric Learning for 3D Visual Query Localization](https://mlsanity.com/paper/2609.33558/) (2026)

## Abstract (arXiv)

The most popular evaluation metric for object detection in 2D images is Intersection over Union (IoU). Existing implementations of the IoU metric for 3D object detection usually neglect one or more degrees of freedom. In this paper, we first derive the analytic solution for three dimensional bounding boxes. As a second contribution, a closed-form solution of the volume-to-volume distance is derived. Finally, the Bounding Box Disparity is proposed as a combined positive continuous metric. We provide open source implementations of the three metrics as standalone python functions, as well as extensions to the Open3D library and as ROS nodes.