Joo Kyungdon, Oh Tae-Hyun, Kim Junsik, Kweon In So
IEEE Trans Pattern Anal Mach Intell. 2019 Mar;41(3):682-696. doi: 10.1109/TPAMI.2018.2799944. Epub 2018 Jan 30.
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).
大多数人造环境，如城市和室内场景，由一组平行和正交的平面结构组成。这些结构通过曼哈顿世界假设进行近似，在该假设中，概念可以表示为曼哈顿框架（MF）。给定一组输入，如表面法线或消失点，我们将MF估计问题作为一个共识集最大化问题，即在旋转搜索空间上最大化内点的数量。传统上，这个问题可以通过分支定界框架来解决，该框架在数学上保证全局最优性。然而，传统分支定界算法的计算时间与实时性相差甚远。在本文中，我们提出了一种在用于MF估计的有效测量域上的新颖的界计算方法，即扩展高斯图像（EGI）。通过放宽原始问题，我们可以以恒定的复杂度计算界，同时保持全局最优性。此外，我们定量和定性地展示了所提出方法对各种合成数据和真实世界数据的性能。我们还通过三种不同的应用展示了我们方法的通用性：扩展到多个MF估计、基于3D旋转的视频稳定和消失点估计（线聚类）。
