Solving the PnL problem using the hidden variable method: an accurate and efficient solution
- PDF / 1,559,041 Bytes
- 12 Pages / 595.276 x 790.866 pts Page_size
- 106 Downloads / 189 Views
ORIGINAL ARTICLE
Solving the PnL problem using the hidden variable method: an accurate and efficient solution Ping Wang1
· Yongxin Chou2 · Aimin An1 · Guili Xu3
Accepted: 17 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper addresses the camera pose estimation problem from 3D lines and their 2D projections, known as the perspectiven-line (PnL) problem. Although many successful solutions have been presented, it is still a challenging to optimize both computational complexity and accuracy at the same time. In our work, we parameterize the rotation by using the Cayley– Gibbs–Rodriguez (CGR) parameterization and formulate the PnL problem into a polynomial system solving problem. Instead of the Gröbner basis method, which may encounter numeric problems, we seek for an efficient and stability technique— the hidden variable method—to solve the polynomial system and polish the solution via the Gauss–Newton method. The performance of our method is evaluated by using simulations and real images, and results demonstrate that our method offers accuracy and precision comparable or better than existing state-of-the-art methods, but with significantly lower computational cost. Keywords Perspective-n-line problem (PnL) · Camera pose estimation · Absolute position and orientation · Computer vision
1 Introduction Determining the orientation and position of a known object from its single image is an important problem in computer vision and photogrammetry community [3,4,10,12,16, 19,23,27,34,37]. When the correspondences between object points and image points are known, this problem becomes the well-known perspective-n-point (PnP) problem [14], and many successful methods [8,13,17,20,24,25,28,30,36,38,43, 44] have been proposed to solve this problem. Meanwhile for
B
Ping Wang [email protected]; [email protected] Yongxin Chou [email protected] Aimin An [email protected] Guili Xu [email protected]
1
College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2
School of Electrical and Automatic Engineering, Changshu Institute of Technology, Suzhou 215500, China
3
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
line features, it corresponds to the perspective-n-line problem and is still a challenging issue. The reason is that the traditional PnL solutions cannot balance the computational complexity, accuracy and scalability.
1.1 Literature review The minimal P3L (n = 3) problem has been systematically investigated over the past few decades. In one of the earliest works, Dhome et al. [11] presented an analytical method to solve the P3L problem. Their works showed that there may exist at most 8 solutions to the P3L problem. Chen [9] proposed another algebraic method to the P3L problem. However, this method offers poor accuracy in the presences of noise. Caglioti [7] addressed the P3L problem for a particular case, where three lines lie in a common plane and inter
Data Loading...
