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:
this https URL

本文提出了第一种量子方法来解决多模型拟合问题，并且经过实验验证在各种数据集上的应用效果非常有前途。

量子多模型拟合

Quantum Multi-Model Fitting

The Progressive-X algorithm, Prog-X in short, is proposed for geometric
multi-model fitting. The method interleaves sampling and consolidation of the
current data interpretation via repetitive hypothesis proposal, fast rejection,
and integration of the new hypothesis into the kept instance set by labeling
energy minimization. Due to exploring the data progressively, the method has
several beneficial properties compared with the state-of-the-art. First, a
clear criterion, adopted from RANSAC, controls the termination and stops the
algorithm when the probability of finding a new model with a reasonable number
of inliers falls below a threshold. Second, Prog-X is an any-time algorithm.
Thus, whenever is interrupted, e.g. due to a time limit, the returned instances
cover real and, likely, the most dominant ones. The method is superior to the
state-of-the-art in terms of accuracy in both synthetic experiments and on
publicly available real-world datasets for homography, two-view motion, and
motion segmentation.

本文提出了一种名为 Prog-X 的算法，通过重复的假设提出、快速拒绝和新假设的整合，探索数据的进展，实现几个有益于现有技术的性质，进而完成几个几何模型的拟合。

Progressive-X: 高效、随时可用、多模型拟合算法

Progressive-X: Efficient, Anytime, Multi-Model Fitting Algorithm

Many standard approaches for geometric model fitting are based on pre-matched
image features. Typically, such pre-matching uses only feature appearances
(e.g. SIFT) and a large number of non-unique features must be discarded in
order to control the false positive rate. In contrast, we solve feature
matching and multi-model fitting problems in a joint optimization framework.
This paper proposes several fit-&-match energy formulations based on a
generalization of the assignment problem. We developed an efficient solver
based on min-cost-max-flow algorithm that finds near optimal solutions. Our
approach significantly increases the number of detected matches. In practice,
energy-based joint fitting & matching allows to increase the distance between
view-points previously restricted by robustness of local SIFT-matching and to
improve the model fitting accuracy when compared to state-of-the-art
multi-model fitting techniques.

本文提出基于赋对问题的多模型匹配能量公式，以及基于最小费用最大流算法的高效求解器，该方法能够显著增加匹配数量，并且可以提高模型拟合精度。