Image lines projected from parallel 3D lines intersect at a common point called the vanishing point (VP). Manhattan world holds for the scenes with three orthogonal VPs. In Manhattan world, given several lines in a calibrated image, we aim to cluster them by three unknown-but-sought VPs. The VP estimation can be reformulated as computing the rotation between the Manhattan frame and camera frame. To estimate three degrees of freedom (DOF) of this rotation, state-of-the-art methods are based on either data sampling or parameter search. However, they fail to guarantee high accuracy and efficiency simultaneously. In contrast, we propose a set of approaches that hybridize these two strategies. We first constrain two or one DOF of the rotation by two or one sampled image line. Then we search for the remaining one or two DOF based on branch and bound. Our sampling accelerates our search by reducing the search space and simplifying the bound computation. Our search achieves quasi-global optimality. Specifically, it guarantees to retrieve the maximum number of inliers on the condition that two or one DOF is constrained. Our hybridization of two-line sampling and one-DOF search can estimate VPs in real time. Our hybridization of one-line sampling and two-DOF search can estimate VPs in near real time. Experiments on both synthetic and real-world datasets demonstrated that our approaches outperform state-of-the-art methods in terms of accuracy and/or efficiency.

中文翻译：

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曼哈顿世界的准全局最优和近/真实时消失点估计

从平行 3D 线投影的图像线在称为消失点 (VP) 的公共点相交。曼哈顿世界适用于具有三个正交 VP 的场景。在曼哈顿世界中，给定校准图像中的几条线，我们的目标是通过三个未知但寻求的 VP 对它们进行聚类。VP 估计可以重新表述为计算曼哈顿框架和相机框架之间的旋转。为了估计这种旋转的三个自由度 (DOF)，最先进的方法是基于数据采样或参数搜索。但是，它们不能同时保证高精度和高效率。相比之下，我们提出了一组混合这两种策略的方法。我们首先通过两条或一条采样图像线来约束旋转的两个或一个自由度。然后我们根据分支定界搜索剩余的一两个自由度。我们的采样通过减少搜索空间和简化边界计算来加速我们的搜索。我们的搜索实现了准全局最优。具体来说，它保证在两个或一个自由度受到约束的情况下检索最大数量的内点。我们的两线采样和单自由度搜索的混合可以实时估计 VP。我们的单线采样和双自由度搜索的混合可以近乎实时地估计 VP。对合成数据集和真实世界数据集的实验表明，我们的方法在准确性和/或效率方面优于最先进的方法。它保证在两个或一个自由度受到约束的情况下检索最大数量的内点。我们的两线采样和单自由度搜索的混合可以实时估计 VP。我们的单线采样和双自由度搜索的混合可以近乎实时地估计 VP。对合成数据集和真实世界数据集的实验表明，我们的方法在准确性和/或效率方面优于最先进的方法。它保证在两个或一个自由度受到约束的情况下检索最大数量的内点。我们的两线采样和单自由度搜索的混合可以实时估计 VP。我们的单线采样和双自由度搜索的混合可以近乎实时地估计 VP。对合成数据集和真实世界数据集的实验表明，我们的方法在准确性和/或效率方面优于最先进的方法。