# Quantum Multi-Model Fitting

arXiv: https://arxiv.org/abs/2303.15444 · HTML: https://mlsanity.com/paper/2303.15444/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 59 references that are in the map.
- First posted on arXiv 27 Mar 2023.

## Builds on (most cited first, 20 of 20)

- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [Quantum Permutation Synchronization](https://mlsanity.com/paper/2101.07755/) (2021)
- [Q-Match: Iterative Shape Matching via Quantum Annealing](https://mlsanity.com/paper/2105.02878/) (2021)
- [A practical heuristic for finding graph minors](https://mlsanity.com/paper/1406.2741/) (2014)
- [A Quantum Computational Approach to Correspondence Problems on Point Sets](https://mlsanity.com/paper/1912.12296/) (2019)
- [Adiabatic Quantum Computing for Multi Object Tracking](https://mlsanity.com/paper/2202.08837/) (2022)
- [Adiabatic Quantum Graph Matching with Permutation Matrix Constraints](https://mlsanity.com/paper/2107.04032/) (2021)
- [Multi-Class Model Fitting by Energy Minimization and Mode-Seeking](https://mlsanity.com/paper/1706.00827/) (2017)
- [Quantum-soft QUBO Suppression for Accurate Object Detection](https://mlsanity.com/paper/2007.13992/) (2020)
- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [Quantum Motion Segmentation](https://mlsanity.com/paper/2203.13185/) (2022)
- [Semiconductor Defect Detection by Hybrid Classical-Quantum Deep Learning](https://mlsanity.com/paper/2208.03514/) (2022)
- [Quantum Robust Fitting](https://mlsanity.com/paper/2006.06986/) (2020)
- [Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting](https://mlsanity.com/paper/1802.01129/) (2018)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)
- [Hypergraph Optimization for Multi-structural Geometric Model Fitting](https://mlsanity.com/paper/2002.05350/) (2020)
- [Mode-Seeking on Hypergraphs for Robust Geometric Model Fitting](https://mlsanity.com/paper/1603.07807/) (2016)
- [Hypergraph Modelling for Geometric Model Fitting](https://mlsanity.com/paper/1607.02829/) (2016)
- [Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting](https://mlsanity.com/paper/1611.01408/) (2016)
- [A Bi-clustering Framework for Consensus Problems](https://mlsanity.com/paper/1405.6159/) (2014)

## Built on by (most cited first, 12 of 12)

- [Quantum Visual Fields with Neural Amplitude Encoding](https://mlsanity.com/paper/2508.10900/) (2025)
- [3D-QAE: Fully Quantum Auto-Encoding of 3D Point Clouds](https://mlsanity.com/paper/2311.05604/) (2023)
- [Robust Fitting on a Gate Quantum Computer](https://mlsanity.com/paper/2409.02006/) (2024)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing](https://mlsanity.com/paper/2310.12153/) (2023)
- [Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients](https://mlsanity.com/paper/2310.15128/) (2023)
- [Quantum Annealing for Computer Vision Minimization Problems](https://mlsanity.com/paper/2312.12848/) (2023)
- [Outlier-Robust Multi-Model Fitting on Quantum Annealers](https://mlsanity.com/paper/2504.13836/) (2025)
- [Quantum Multiple Rotation Averaging](https://mlsanity.com/paper/2602.10115/) (2026)
- [Accelerating Outlier-robust Rotation Estimation by Stereographic Projection](https://mlsanity.com/paper/2502.06337/) (2025)
- [HQC-NBV: A Hybrid Quantum-Classical View Planning Approach](https://mlsanity.com/paper/2505.05212/) (2025)
- [Robust Multi-Model Fitting through Learning Neighbor Regions](https://mlsanity.com/paper/2609.15348/) (2026)

## Abstract (arXiv)

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.