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：几何模型拟合是计算机视觉中具有挑战性但基础性的问题。近年来，量子优化已被证明能够增强单模型情况下的鲁棒拟合，但多模型拟合问题仍未解决。针对这一挑战，本文表明后者情况能够显著受益于量子硬件，并提出了首个用于多模型拟合（MMF）的量子方法。我们将MMF建模为一个可通过现代绝热量子计算机高效采样的问题，且无需对目标函数进行松弛。我们还提出了所提方法的迭代与分解版本，以支持实际规模的问题。实验评估在多种数据集上展示了具有前景的结果。源代码见：https://github.com/FarinaMatteo/qmmf。