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

Blind Perspective-n-Point (PnP) is the problem of estimating the position and
orientation of a camera relative to a scene, given 2D image points and 3D scene
points, without prior knowledge of the 2D-3D correspondences. Solving for pose
and correspondences simultaneously is extremely challenging since the search
space is very large. Fortunately it is a coupled problem: the pose can be found
easily given the correspondences and vice versa. Existing approaches assume
that noisy correspondences are provided, that a good pose prior is available,
or that the problem size is small. We instead propose the first fully
end-to-end trainable network for solving the blind PnP problem efficiently and
globally, that is, without the need for pose priors. We make use of recent
results in differentiating optimization problems to incorporate geometric model
fitting into an end-to-end learning framework, including Sinkhorn, RANSAC and
PnP algorithms. Our proposed approach significantly outperforms other methods
on synthetic and real data.

该研究提出了一种基于端到端学习的盲 PnP 求解器，利用最近的优化问题微分研究结果将几何模型拟合集成到学习框架中，包括 Sinkhorn、RANSAC 和 PnP 算法，可有效地实现全局定位和三维场景点的快速估计

利用鲁棒可微几何优化端到端解决盲视角 N 点问题

Solving the Blind Perspective-n-Point Problem End-To-End With Robust  Differentiable Geometric Optimization

We present an efficient deterministic hypothesis generation algorithm for
robust fitting of multiple structures based on the maximum feasible subsystem
(MaxFS) framework. Despite its advantage, a global optimization method such as
MaxFS has two main limitations for geometric model fitting. First, its
performance is much influenced by the user-specified inlier scale. Second, it
is computationally inefficient for large data. The presented MaxFS-based
algorithm iteratively estimates model parameters and inlier scale and also
overcomes the second limitation by reducing data for the MaxFS problem. Further
it generates hypotheses only with top-n ranked subsets based on matching scores
and data fitting residuals. This reduction of data for the MaxFS problem makes
the algorithm computationally realistic. Our method, called iterative MaxFS
with inlier scale estimation and subset updating (IMaxFS-ISE-SU) in this paper,
performs hypothesis generation and fitting alternately until all of true
structures are found. The IMaxFS-ISE-SU algorithm generates substantially more
reliable hypotheses than random sampling-based methods especially as
(pseudo-)outlier ratios increase. Experimental results demonstrate that our
method can generate more reliable and consistent hypotheses than random
sampling-based methods for estimating multiple structures from data with many
outliers.

本文介绍了一种有效的确定性假设生成算法，用于基于最大可行子系统（MaxFS）框架的多结构稳健拟合。所提出的 IMaxFS-ISE-SU 算法通过降低 MaxFS 问题的数据量来克服计算效率低下的问题，并利用排名最高的子集和数据拟合残差来生成假设，从而比基于随机抽样的方法更可靠地估计具有许多离群值的数据的多个结构。

使用迭代的最大 FS 算法进行多结构确定性拟合，同时进行内点尺度估计和子集更新

Deterministic Fitting of Multiple Structures using Iterative MaxFS with  Inlier Scale Estimation and Subset Updating

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。