# Multi-Class Model Fitting by Energy Minimization and Mode-Seeking

arXiv: https://arxiv.org/abs/1706.00827 · HTML: https://mlsanity.com/paper/1706.00827/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2017.

## Built on by (most cited first, 19 of 19)

- [Near-field Perception for Low-Speed Vehicle Automation using Surround-view Fisheye Cameras](https://mlsanity.com/paper/2103.17001/) (2021)
- [Cuboids Revisited: Learning Robust 3D Shape Fitting to Single RGB Images](https://mlsanity.com/paper/2105.02047/) (2021)
- [Quantum Motion Segmentation](https://mlsanity.com/paper/2203.13185/) (2022)
- [Quantum Multi-Model Fitting](https://mlsanity.com/paper/2303.15444/) (2023)
- [Finding Geometric Models by Clustering in the Consensus Space](https://mlsanity.com/paper/2103.13875/) (2021)
- [Multi-instance Point Cloud Registration by Efficient Correspondence Clustering](https://mlsanity.com/paper/2111.14582/) (2021)
- [PointCLM: A Contrastive Learning-based Framework for Multi-instance Point Cloud Registration](https://mlsanity.com/paper/2209.00219/) (2022)
- [PARSAC: Accelerating Robust Multi-Model Fitting with Parallel Sample Consensus](https://mlsanity.com/paper/2401.14919/) (2024)
- [Adaptive Reordering Sampler with Neurally Guided MAGSAC](https://mlsanity.com/paper/2111.14093/) (2021)
- [Learning Probabilistic Coordinate Fields for Robust Correspondences](https://mlsanity.com/paper/2306.04231/) (2023)
- [Robust Shape Fitting for 3D Scene Abstraction](https://mlsanity.com/paper/2403.10452/) (2024)
- [Instance by Instance: An Iterative Framework for Multi-instance 3D Registration](https://mlsanity.com/paper/2402.04195/) (2024)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [MultiLink: Multi-class Structure Recovery via Agglomerative Clustering and Model Selection](https://mlsanity.com/paper/2505.10874/) (2025)
- [Outlier-Robust Multi-Model Fitting on Quantum Annealers](https://mlsanity.com/paper/2504.13836/) (2025)
- [Robust and Real-time Surface Normal Estimation from Stereo Disparities using Affine Transformations](https://mlsanity.com/paper/2504.15121/) (2025)
- [Reconstructing Small 3D Objects in front of a Textured Background](https://mlsanity.com/paper/2105.11352/) (2021)
- [Robust Multi-Model Fitting through Learning Neighbor Regions](https://mlsanity.com/paper/2609.15348/) (2026)
- [Superquadric Primitive Decomposition of 3D point clouds via Geometric-Aware Inlier Refinement](https://mlsanity.com/paper/2609.35725/) (2026)

## Abstract (arXiv)

We propose a general formulation, called Multi-X, for multi-class multi-instance model fitting - the problem of interpreting the input data as a mixture of noisy observations originating from multiple instances of multiple classes. We extend the commonly used alpha-expansion-based technique with a new move in the label space. The move replaces a set of labels with the corresponding density mode in the model parameter domain, thus achieving fast and robust optimization. Key optimization parameters like the bandwidth of the mode seeking are set automatically within the algorithm. Considering that a group of outliers may form spatially coherent structures in the data, we propose a cross-validation-based technique removing statistically insignificant instances. Multi-X outperforms significantly the state-of-the-art on publicly available datasets for diverse problems: multiple plane and rigid motion detection; motion segmentation; simultaneous plane and cylinder fitting; circle and line fitting.