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利用灭点进行相机检校与定姿的充要条件及其不确定性分析

李畅   

  1. 华中师范大学
  • 收稿日期:2012-02-21 修回日期:2012-05-14 出版日期:2012-12-25 发布日期:2013-04-17
  • 通讯作者: 李畅

The Necessary and Sufficient Condition of Camera Calibration and Attitude Determination based on Vanishing Points with Their Uncertainty Analysis

  • Received:2012-02-21 Revised:2012-05-14 Online:2012-12-25 Published:2013-04-17

摘要:

本文探讨和论证了利用三个正交方向的灭点进行相机的内外方位元素定标与定参的不确定性问题,给出了灭点定参的充要条件,着重探讨了双正交方向灭点联合误差分布下解算第三灭点的问题,补充了相对误差椭圆估计灭点的不确定性方法,并提出了利用Monte-Carlo 方法模拟第三灭点空间分布和估算分布范围大小(面积)的算法。本文不仅丰富了利用灭点定参的基本理论与方法,而且揭示了灭点空间分布规律和不确定性,为研究灭点基础应用的普适性提供理论依据。

关键词: 灭点, 定参, 相对误差椭圆, 不确定性, Monte-Carlo方法

Abstract:

This paper discusses and demonstrates the uncertainty of camera calibration and attitude determination based on three orthogonal vanishing points. The necessary and sufficient condition of parameters determination is given out. Especially, under the condition of joint error distribution of two orthogonal directions vanishing points (VX, VY), how to solve the third vanishing point (VZ) is discussed. Assessment the uncertainties of vanishing points based on relative error ellipse is supplemented. Furthermore, the algorithms of simulating the spatial distribution of the VZ and estimating its area size are presented by Monte-Carlo method. This article is not only enriched the theory and methods of vanishing point, but also reveals the laws and the uncertainty of their spatial distributions, which provides a theoretical basis for studying the universality of vanishing point basic application.

Key words: vanishing point, parameters determination, relative error ellipse, uncertainty, Monte-Carlo method

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