# Outlier-Robust Multi-Model Fitting on Quantum Annealers

arXiv: https://arxiv.org/abs/2504.13836 · HTML: https://mlsanity.com/paper/2504.13836/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 18 Apr 2025.

## Builds on (most cited first, 21 of 21)

- [Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm](https://mlsanity.com/paper/1906.02290/) (2019)
- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (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 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)
- [Adiabatic Quantum Linear Regression](https://mlsanity.com/paper/2008.02355/) (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)
- [Quantum Robust Fitting](https://mlsanity.com/paper/2006.06986/) (2020)
- [Quantum Annealing Formulation for Binary Neural Networks](https://mlsanity.com/paper/2107.02751/) (2021)
- [Quantum Multi-Model Fitting](https://mlsanity.com/paper/2303.15444/) (2023)
- [CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes](https://mlsanity.com/paper/2303.16202/) (2023)
- [Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting](https://mlsanity.com/paper/1802.01129/) (2018)
- [Finding Geometric Models by Clustering in the Consensus Space](https://mlsanity.com/paper/2103.13875/) (2021)
- [Robust Fitting on a Gate Quantum Computer](https://mlsanity.com/paper/2409.02006/) (2024)
- [Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting](https://mlsanity.com/paper/1611.01408/) (2016)
- [Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients](https://mlsanity.com/paper/2310.15128/) (2023)

## Built on by (most cited first, 1 of 1)

- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)

## Abstract (arXiv)

Multi-model fitting (MMF) presents a significant challenge in Computer Vision, particularly due to its combinatorial nature. While recent advancements in quantum computing offer promise for addressing NP-hard problems, existing quantum-based approaches for model fitting are either limited to a single model or consider multi-model scenarios within outlier-free datasets. This paper introduces a novel approach, the robust quantum multi-model fitting (R-QuMF) algorithm, designed to handle outliers effectively. Our method leverages the intrinsic capabilities of quantum hardware to tackle combinatorial challenges inherent in MMF tasks, and it does not require prior knowledge of the exact number of models, thereby enhancing its practical applicability. By formulating the problem as a maximum set coverage task for adiabatic quantum computers (AQC), R-QuMF outperforms existing quantum techniques, demonstrating superior performance across various synthetic and real-world 3D datasets. Our findings underscore the potential of quantum computing in addressing the complexities of MMF, especially in real-world scenarios with noisy and outlier-prone data.