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.

翻译：几何模型拟合是一个具有挑战性的但非常基础的计算机视觉问题。最近，量子优化已经证明可以增强单一模型的鲁棒拟合，但是多模型拟合仍然是一个未解决的问题。为了应对这一挑战，本文展示了后者情况可以从量子硬件中受益，并提出了第一个针对多模型拟合的量子方法 (MMF)。我们将MMF定义为一个问题，可以通过现代绝热量子计算机有效地采样，而不需要松弛目标函数。我们还提出了一个迭代和分解版本的方法，支持真实世界尺寸的问题。实验评估证明了该方法在各种数据集上具有良好的效果。源代码可在以下网址中找到：https://github.com/FarinaMatteo/qmmf。