A Complete, Accurate and Efficient Solution for the Perspective-N-Line Problem

Abstract

This paper presents a complete, accurate, and efficient solution for the Perspective-n-Line (PnL) problem. Generally, the camera pose can be determined from N ≥ 3 2D-3D line correspondences. The minimal problem (N = 3) and the least-squares problem (N > 3) are generally solved in different ways. This paper shows that a least-squares PnL problem can be transformed into a quadratic equation system that has the same form as the minimal problem. This leads to a unified solution for the minimal and least-squares PnL problems. We adopt the Gram-Schmidt process and a novel hidden variable polynomial solver to increase the numerical stability of our algorithm. Experimental results show that our algorithm is more accurate and robust than the state-of-the-art least-squares algorithms [1]-[4] and is significantly faster. Moreover, our algorithm is more stable than previous minimal solutions [3], [5], [6] with comparable runtime.