Abstract

The perspective n-point problem (PnP), or a three-point photogrammetric resection in space, consists of the problem of finding the position and the orientation of the model of the camera of the central projection by the assigned spatial coordinates of the given points and by the corresponding coordinates of their projections on the image. Due to the available applications in robotics and machine vision, direct noniterative methods for solving such a problem are of interest. The well known general method of the direct noniterative solution of the PnP problem in the case of four control points (n = 4) uses double linearization and seems to be rather cumbersome. This paper presents an alternative simpler solution for the considered problem in the case of n = 4. The proposed method reduces the computing requirements for solving this problem. In the case of more control points, the solution obtained for four points can be used as the initial approximation for the Gauss–Newton iterations or in the RANSAC calculation scheme.

中文翻译：

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四个控制点估计中央投影相机位置的直接解决方案

摘要

透视n点问题 (PnP)，或空间中的三点摄影测量切除，包括通过给定点的指定空间坐标找到中心投影的相机模型的位置和方向的问题并通过它们在图像上的投影的相应坐标。由于机器人技术和机器视觉中的可用应用，解决此类问题的直接非迭代方法很有趣。在四个控制点 ( n = 4)的情况下，PnP 问题的直接非迭代求解的众所周知的通用方法使用双线性化，并且似乎相当麻烦。本文针对n的情况下所考虑的问题提出了另一种更简单的解决方案= 4. 所提出的方法降低了解决这个问题的计算要求。在更多控制点的情况下，四个点获得的解可以用作高斯-牛顿迭代或 RANSAC 计算方案的初始近似值。