Liu Yinlong, Chen Guang, Knoll Alois
IEEE Trans Pattern Anal Mach Intell. 2022 Apr;44(4):1949-1962. doi: 10.1109/TPAMI.2020.3027047. Epub 2022 Mar 4.
In man-made environments, most of the objects and structures are organized in the form of orthogonal and parallel planes. These planes can be approximated by an Atlanta world assumption, in which the normals of planes can be represented by Atlanta frames. The Atlanta world assumption has one vertical frame and multiple horizontal frames. Conventionally, given a set of inputs such as surface normals, the Atlanta frame estimation problem can be solved by a branch-and-bound (BnB) algorithm. However, the runtime of the BnB algorithm will increase greatly when the dimensionality (i.e., the number of horizontal frames) increases. In this paper, we estimate only the vertical direction, instead of all Atlanta frames at once. Accordingly, we propose a vertical direction estimation method by considering the relationship between the vertical frame and horizontal frames. Concretely, our approach employs a BnB algorithm to search the vertical direction, thereby guaranteeing global optimality without requiring prior knowledge of the number of Atlanta frames. In order to guarantee convergence, four novel bounds are investigated, by mapping a 3D hemisphere to a 2D region. We verify the feasibility of the proposed method using various challenging synthetic and real-world data.
在人造环境中，大多数物体和结构都是以正交和平行平面的形式组织的。这些平面可以通过亚特兰大世界假设来近似，其中平面的法线可以由亚特兰大框架表示。亚特兰大世界假设具有一个垂直框架和多个水平框架。传统上，给定一组输入，如表面法线，亚特兰大框架估计问题可以通过分支定界（BnB）算法来解决。然而，当维度（即水平框架的数量）增加时，BnB算法的运行时间将大大增加。在本文中，我们只估计垂直方向，而不是一次性估计所有亚特兰大框架。因此，我们通过考虑垂直框架和水平框架之间的关系，提出了一种垂直方向估计方法。具体来说，我们的方法采用BnB算法来搜索垂直方向，从而在不需要亚特兰大框架数量先验知识的情况下保证全局最优性。为了保证收敛性，通过将三维半球映射到二维区域，研究了四个新的边界。我们使用各种具有挑战性的合成数据和真实世界数据验证了所提方法的可行性。
