# Marginalized Generalized IoU (MGIoU): A Unified Objective Function for Optimizing Any Convex Parametric Shapes

arXiv: https://arxiv.org/abs/2504.16443 · HTML: https://mlsanity.com/paper/2504.16443/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 29 of 29)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [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)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [Hypersim: A Photorealistic Synthetic Dataset for Holistic Indoor Scene Understanding](https://mlsanity.com/paper/2011.02523/) (2020)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [ARKitScenes: A Diverse Real-World Dataset For 3D Indoor Scene Understanding Using Mobile RGB-D Data](https://mlsanity.com/paper/2111.08897/) (2021)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [TrafficSim: Learning to Simulate Realistic Multi-Agent Behaviors](https://mlsanity.com/paper/2101.06557/) (2021)
- [Omni3D: A Large Benchmark and Model for 3D Object Detection in the Wild](https://mlsanity.com/paper/2207.10660/) (2022)
- [Rethinking Rotated Object Detection with Gaussian Wasserstein Distance Loss](https://mlsanity.com/paper/2101.11952/) (2021)
- [Objectron: A Large Scale Dataset of Object-Centric Videos in the Wild with Pose Annotations](https://mlsanity.com/paper/2012.09988/) (2020)
- [MTR++: Multi-Agent Motion Prediction with Symmetric Scene Modeling and Guided Intention Querying](https://mlsanity.com/paper/2306.17770/) (2023)
- [IoU Loss for 2D/3D Object Detection](https://mlsanity.com/paper/1908.03851/) (2019)
- [TextBoxes++: A Single-Shot Oriented Scene Text Detector](https://mlsanity.com/paper/1801.02765/) (2018)
- [MMRotate: A Rotated Object Detection Benchmark using PyTorch](https://mlsanity.com/paper/2204.13317/) (2022)
- [Enhancing Geometric Factors in Model Learning and Inference for Object Detection and Instance Segmentation](https://mlsanity.com/paper/2005.03572/) (2020)
- [Learning Modulated Loss for Rotated Object Detection](https://mlsanity.com/paper/1911.08299/) (2019)
- [The KFIoU Loss for Rotated Object Detection](https://mlsanity.com/paper/2201.12558/) (2022)
- [YOLO-Pose: Enhancing YOLO for Multi Person Pose Estimation Using Object Keypoint Similarity Loss](https://mlsanity.com/paper/2204.06806/) (2022)
- [Deep Matching Prior Network: Toward Tighter Multi-oriented Text Detection](https://mlsanity.com/paper/1703.01425/) (2017)
- [TrajGen: Generating Realistic and Diverse Trajectories with Reactive and Feasible Agent Behaviors for Autonomous Driving](https://mlsanity.com/paper/2203.16792/) (2022)
- [Diverse Multiple Trajectory Prediction Using a Two-stage Prediction Network Trained with Lane Loss](https://mlsanity.com/paper/2206.08641/) (2022)

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

- [LeAD-M3D: Leveraging Asymmetric Distillation for Real-Time Monocular 3D Detection](https://mlsanity.com/paper/2512.05663/) (2025)
- [PGL-3D: Towards Progressive Geometric Learning for 3D Visual Query Localization](https://mlsanity.com/paper/2609.33558/) (2026)

## Abstract (arXiv)

Optimizing the similarity between parametric shapes is crucial for numerous computer vision tasks, where Intersection over Union (IoU) stands as the canonical measure. However, existing optimization methods exhibit significant shortcomings: regression-based losses like L1/L2 lack correlation with IoU, IoU-based losses are unstable and limited to simple shapes, and task-specific methods are computationally intensive and not generalizable accross domains. As a result, the current landscape of parametric shape objective functions has become scattered, with each domain proposing distinct IoU approximations. To address this, we unify the parametric shape optimization objective functions by introducing Marginalized Generalized IoU (MGIoU), a novel loss function that overcomes these challenges by projecting structured convex shapes onto their unique shape Normals to compute one-dimensional normalized GIoU. MGIoU offers a simple, efficient, fully differentiable approximation strongly correlated with IoU. We then extend MGIoU to MGIoU+ that supports optimizing unstructured convex shapes. Together, MGIoU and MGIoU+ unify parametric shape optimization across diverse applications. Experiments on standard benchmarks demonstrate that MGIoU and MGIoU+ consistently outperform existing losses while reducing loss computation latency by 10-40x. Additionally, MGIoU and MGIoU+ satisfy metric properties and scale-invariance, ensuring robustness as an objective function. We further propose MGIoU- for minimizing overlaps in tasks like collision-free trajectory prediction. Code is available at https://ldtho.github.io/MGIoU