Globally Optimal Inlier Set Maximization for Atlanta World Understanding

Abstract

Status: Accepted

In this work, we describe man-made structures via an appropriate structure assumption, called Atlanta world, which contains a vertical direction (typically the gravity direction) and a set of horizontal directions orthogonal to the vertical direction. Contrary to the commonly used Manhattan world assumption, the horizontal directions in Atlanta world are not necessarily orthogonal to each other. While Atlanta world permits to encompass a wider range of scenes, this makes the search space much larger and the problem more challenging. Our input data is a set of surface normals, for example acquired from RGB-D cameras or 3D laser scanners, and also lines from calibrated images. Given this input data, we propose the first globally optimal method of inlier set maximization for Atlanta direction estimation. We define a novel search space for Atlanta world, as well as its parametrization, and solve this challenging problem by a branch-and-bound (BnB) framework. To alleviate the computational bottleneck in BnB, i.e. bound computation, we present two bound computation strategies: rectangular bound and slice bound in an efficient measurement domain, i.e. the extended Gaussian image (EGI). In addition, we propose an efficient two-stage method to automatically estimate the number of horizontal directions of a scene. Experimental results with synthetic and real-world datasets have successfully confirmed the validity of our approach.