# Quantum Multi-Model Fitting Source: [Quantum Multi-Model Fitting]() Collection index: [llms.txt]() Data updated: 2026-01-04T04:29:22.419Z Authors: Matteo Farina, Luca Magri, Willi Menapace, Elisa Ricci, Vladislav Golyanik, Federica Arrigoni Published: 2023-03-27T17:59:54.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Fundamental Matrix Estimation on AdelaideRMF single-model sequences (10% outliers)](): Fundamental Matrix Estimation; AdelaideRMF single-model sequences (10% outliers); Misclassification Error: 2.41. - [Fundamental Matrix Estimation on AdelaideRMF single-model sequences 20% outliers](): Fundamental Matrix Estimation; AdelaideRMF single-model sequences 20% outliers; Misclassification Error (%): 8.28. - [Fundamental Matrix Estimation on AdelaideRMF single-model sequences (Full)](): Fundamental Matrix Estimation; AdelaideRMF single-model sequences (Full); Misclassification Error: 10.83. - [Multi-model fitting on AdelaideRMF 15 multi-model sequences](): Multi-model fitting; AdelaideRMF 15 multi-model sequences; Mean Misclassification Error: 0.77. - [Robust Multi-Model Fitting on AdelaideRMF single-model (test)](): Robust Multi-Model Fitting; AdelaideRMF single-model (test); Mean Runtime (s): 0.99. - [Object Motion Segmentation on Hopkins Traffic2 45](): Object motion segmentation; Hopkins Traffic2 45; Mean Misclassification Error: 10. - [Vanishing point detection on York DB 15 (full)](): Vanishing Point Detection; York DB 15 (full); Mean Misclassification Error: 0.74. - [Robust Multi-Model Fitting on AdelaideRMF multi-model (test)](): Robust Multi-Model Fitting; AdelaideRMF multi-model (test); Mean Runtime (s): 0.77. - [Robust Multi-Model Fitting on Traffic2 (test)](): Robust Multi-Model Fitting; Traffic2 (test); Mean Runtime (s): 2.54. - [Robust Multi-Model Fitting on Traffic3 (test)](): Robust Multi-Model Fitting; Traffic3 (test); Mean runtime (s): 3.65. - [Robust Multi-Model Fitting on York (test)](): Robust Multi-Model Fitting; York (test); Mean Runtime (s): 1.93. - [Object Motion Segmentation on Hopkins Traffic3 45](): Object motion segmentation; Hopkins Traffic3 45; Mean Misclassification Error: 55. ## Original sources and implementation [Original paper]() [PDF]() [Implementation]()