A fast Manhattan frame estimation method based on normal vectors

In most human made scenes, such as high-rise urban city or indoor environment, the surface normal vectors or direction vectors are concentrated in three orthogonal principal directions. The scene of such a pattern is called Manhattan World (MW), and the coordinate frame formed by the three principal directions is called Manhattan Frame (MF). MF estimation methods have been applied to many different fields, such as scene reconstruction, Visual based Simultaneous Localization And Mapping (V-SLAM) and camera calibration. In this paper, we propose a novel MF estimation method based on a set of normal vectors. A cost function of normal vectors and MF axes is introduced based on the trigonometric function. For computational purpose, the cost function is significantly simplified by making use of vector dot and cross products, and the reduced cost function only involves 14 scalar parameters that need to be computed with O(n) complexity. The experimental results show that the proposed MF estimation method has excellent real-time performance and gives high accuracy on both the virtual and real-world benchmark datasets of different sizes.