Vanishing Hull

Vanishing points are valuable in many vision tasks such as orientation estimation, pose recovery and 3D reconstruction from a single image. Many methods have been proposed to address the problem, however, a consistent framework to quantitatively analyze the stability and accuracy of vanishing point estimation is still absent. This paper proposes a new concept, vanishing hull, which solves the problem. Given an edge error model, the range of a true edge can be modeled using a fan region. The intersection of all these fan regions is a convex hull, which is called vanishing hull. A vanishing hull gives the region of a true vanishing point, and its distribution determines the probability of the vanishing point. The expectation of the vanishing hull is the optimal solution of the vanishing point, its variance defines the accuracy of the estimation, and its shape determines the stability of the vanishing point. Hence, we can quantitatively analyze the stability and accuracy of the vanishing point estimation using vanishing hull. Simulation results show that our method is significantly better than one state-of-the-art technique, and real data results are also promising.