Iterative Linear Solution of the Perspective n-Point Problem Using Unbiased Statistics

Abstract

In this paper, we cope with the problem of pose estimation of a calibrated camera from n 3D-to-2D point correspondences (PnP). In the state of the art, there exists an efficient solution to this problem (EPnP) with linear computational complexity; nevertheless, the solution is obtained as a linear combination of four eigenvectors of a matrix and the linear coefficients are not always straightforward determined. The EPnP algorithm uses a Minimum Least Squares (MLS) solution that is biased for low signal-to-noise measurements.We propose an alternative implementation to the EPnP algorithm based on Kanatani's unbiased statistical estimators. Kanatani's approach has shown to perform better than MLS for noisy data. Our method takes into account the statistical distribution of the data and the solution is straightly computed from the null-space of a modified linear system, preserving the linear computational complexity as it is shown in the experiments.

A Wireless Visualized Sensing System with Prosthesis Pose Reconstruction for Total Knee Arthroplasty

“…An analytic and non-iterative method is then proposed to solve the coplanar perspective-4-points problem to find [ R CA , t CA ] as described in the previous subsection. There are many classical methods to solve this perspective problem, including the non-iterative method Epnp [29], the iterative linear solution using unbiased statistics [30,31], some simple methods based on P3P problem [32,33] and many linear analytic solutions [34,35,36,37,38] and so on. Compared to these classical methods, the proposed method has the advantage of low computational complexity.…”

Perspective-Three-Point (P3p) by Determining the Support Plane

“…Perspective-n-Point (PnP) is a classic problem in computer vision field and has important applications in vision based localization, object pose estimation, and metrology, etc (Fischler et al, 1981, Gao et al, 2003, Moreno-Noguer et al, 2007, Vigueras et al, 2009, Wolfe et al, 1991, Wu et al, 2006, and Zhang, et al, 2006. The task of PnP is to determine the distances between camera and a number of points (n control points), which are well known in an object coordinate space, from the image, that is taken by a calibrated camera.…”

“…Existing P3P researches can be classified into two categories. Researches in the first category try to solve P3P using different approaches, such as algebraic, geometric approaches, etc (Fischler et al, 1981, Moreno-Noguer et al, 2007, Vigueras et al, 2009, and Wolfe et al, 1991. Researches in the second one try to classify the solutions and study the distribution of multiple solutions (Fischler et al, 1981, Gao et al, 2003, Wolfe et al, 1991, Wu et al, 2006, and Zhang, et al, 2006.…”

“…Gao et al gave a complete solution set of the P3P problem (Gao et al, 2003). More work on P3P and on the general PnP problems can be found in the literatures (Moreno-Noguer et al, 2007, Vigueras et al, 2009, Wu et al, 2006, and Zhang, et al, 2006.…”