A New Method for Atlanta World Frame Estimation

In this paper, we propose a new Atlanta frame estimation method by considering the relationship between vertical direction and horizontal directions. Unlike previous solutions, our method does not solve all the directions at one time. On the contrary, it estimates the directions sequentially. Concretely, our method first searches the vertical direction in $\mathbb{S}^2$ globally, then estimates the horizontal directions in one-dimension. As a consequence, the dimensionality of each subproblem problem is low and it can be solved efficiently. In other words, the running time of our method will not greatly increase as the number of horizontal directions increases. The advantages of our method are validated via testing on both synthetic and real-world data.