Most man-made environments, such as urban and indoor scenes, consist of a set of parallel and orthogonal planar structures. These structures are approximated by the Manhattan world assumption, in which notion can be represented as a Manhattan frame (MF). Given a set of inputs such as surface normals or vanishing points, we pose an MF estimation problem as a consensus set maximization that maximizes the number of inliers over the rotation search space. Conventionally, this problem can be solved by a branch-and-bound framework, which mathematically guarantees global optimality. However, the computational time of the conventional branch-and-bound algorithms is rather far from real-time. In this paper, we propose a novel bound computation method on an efficient measurement domain for MF estimation, i.e., the extended Gaussian image (EGI). By relaxing the original problem, we can compute the bound with a constant complexity, while preserving global optimality. Furthermore, we quantitatively and qualitatively demonstrate the performance of the proposed method for various synthetic and real-world data. We also show the versatility of our approach through three different applications: extension to multiple MF estimation, 3D rotation based video stabilization, and vanishing point estimation (line clustering).

中文翻译：

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近乎实时的鲁棒全局全局最优曼哈顿帧估计

大多数人造环境，例如城市和室内场景，都由一组平行和正交的平面结构组成。这些结构可以通过“曼哈顿世界”假设来近似，其中的概念可以表示为“曼哈顿框架”（MF）。给定一组输入（例如表面法线或消失点），我们提出MF估计问题，作为共识集最大化，该最大化集最大化旋转搜索空间中的内线数。按照惯例，可以通过在数学上保证全局最优的分支定界框架来解决此问题。但是，传统的分支定界算法的计算时间与实时时间相差甚远。在本文中，我们提出了一种在有效测量域上进行MF估计的新颖的边界计算方法，即扩展高斯图像（EGI）。通过放松原始问题，我们可以在保持全局最优性的同时，以恒定的复杂度来计算边界。此外，我们定量和定性地证明了所提出的方法对于各种合成和现实世界数据的性能。我们还通过三种不同的应用展示了我们方法的多功能性：扩展到多个MF估计，基于3D旋转的视频稳定以及消失点估计（线聚类）。