计算机视觉中摄像机定标及位姿和运动估计方法的研究
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摘要
计算机视觉是一个相当新且发展十分迅速的研究领域，已成为智能自动化科学的重要研究领域之一，它的研究目标是使计算机具有通过一幅或多幅图像认识周围环境信息的能力，这种能力将不仅使机器能感知环境中物体的几何信息，包括它的形状、位置、姿态和运动等，而且能对它们进行描述、存储、识别和理解。
本文首先介绍了计算机视觉中所用到的射影几何、仿射几何、度量几何和欧氏几何等各类几何学的基本概念和相关特性；概述了摄像机模型及成像原理；回顾了近年来摄像机定标方法的发展，对存在的各种摄像机定标方法进行了分析、比较和总结；最后，重点阐述了变内部参数摄像机线性自定标、平面型场景图像的透视校正、四种非线性状态估计滤波器(EKF1、EKF2、DD1和DD2)及基于单目视觉的位姿和运动估计的研究方法。
◆变内部参数摄像机线性自定标。在某些视觉系统中(例如机器人视觉系统、主动视觉系统)需要经常改变摄像机的位置或调整摄像机光学系统(如光圈与焦距)，在每次调整以后，都需要对摄像机重新定标。针对这种情况，本文提出了一种可处理畸变因子和主点已知但其它内部参数发生变化时的摄像机自定标方法，该方法先计算图像间的基本矩阵，在计算基本矩阵后得到射影重建的基础上，用线性方法恢复同形矩阵，再利用同形矩阵计算摄像机内部参数。
◆基于场景几何知识的三维度量重建。三维场景图像的度量重建一般是针对图像序列的，所使用的层次化度量重建方法都是首先得到图像序列的射影重建。如果三维物体表面都是平面(这种情况是比较常见的)，则在平面型场景图像三维度量重建的基础上，基于场景几何知识，对平面型场景图像和常规的三维场景图像的度量重建进行了回顾，然后在此基础上提出了一种不必进行射影重建且只须单幅图像的三维度量重建方法。
◆四种非线性状态估计滤波器(EKF1、EKF2、DD1和DD2)。对于某些系统不能用简单的线性模型来描述，因此必须发展非线性的滤波算法，在线性卡尔曼滤波的基础上，用一阶和二阶Taylor级数来近似非线性动态方程和测量方程，分别得到了EKF1(基于一阶Taylor近似)和EKF2(基于二阶Taylor近似)滤波器，但是使用EKF1和EKF2滤波器要求非线性动态方程和测量方程相应的一阶和二阶微分存在，在非线性动态方程和测量方程的一阶和二阶微分不存在时，用不需要计算微分的Stirling插值近似代替Taylor近似得出了另外两种新的滤波器，即DD1滤波器(基于一阶Stirling插值近似)和DD2滤波器(基于二阶Stirling插值近似)。
◆基于单目视觉的位姿和运动估计。随着计算机视觉这门新兴学科的出现，
计算机视觉中摄像机定标及位姿和运动估计方法的研究
不需要物体接触或人工干预，估计两参考坐标系之间的相对三维位姿和运动对机
器人导航、装配及测量、跟踪、目标识别和摄像机定标来说也是一个非常重要的
研究问题。利用单摄像机所获取的二维图像序列来估计两坐标系之间的相对位姿
和运动在实际应用中是可取的，其难点是从物体的三维特征投影到二维图像特征
的过程是一个非线性变换，本文研究了在运动物体尺寸和形状己知的情况下，三
维坐标变换用八元数表示，用单摄像机获取运动物体的图像，以线特征作为测量
输入，建立了位姿和运动估计系统的非线性模型，分别用IEKFI、IEKFZ、DDI
和DDZ四种滤波器进行了仿真比较，得出了位姿和运动估计结果。
关键词:变内部参数摄像机自定标;度量重建;Taylor近似;stirling插值近似;
滤波器;位姿和运动估计
Computer vision is a new research field with fast development into one of the important fields of intelligent automation. Its research object is to equip the computer with the ability to acquire information from its surrounding images or combination of images, which enables the machine not only to sense the geometrical information of the object in the environment, including its shape, position, pose and motion, etc., but to describe, store, recognize and understand them.Firstly, this dissertation introduces the basic conceptions and relevant properties of projective geometry, affine geometry, metric geometry and Euclidean geometry used in computer vision, as well as the camera model with imaging principles. Secondly, the dissertation gives review of the development of camera calibration technique in recent years. Some analysis, comparison and categorization on the existing various camera calibration techniques are discussed. Finally, the focus in my dissertation is the research on the camera self-calibration with varying intrinsic parameters, the perspective correction of plane scene image, derivations of four nonlinear state estimation filters (EKF1, EKF2, DD1 and DD2), and the estimation of pose and motion based on monocular vision. Linear camera self-calibration with varying intrinsic parameters. In some vision systems (e.g., the vision system of robot and active vision system), the camera's position and optic system (for example, the aperture and focus) require constant adjustment, and the camera must recalibration after every adjustment. Aimed at this circumstance, this paper proposes a camera self-calibration method to deal with the situation when the camera's distorted skews and principal points are already known, while the other intrinsic parameters keep varying. That is, to calculate the fundamental matrix between images to obtain projective reconstruction at first, and on which basis then, to regain the homography matrix by linear method, lastly, to obtain the camera's intrinsic parameters using homography matrix. 3D metric reconstruction based on scene geometry. The 3D metric reconstruction of scene image is often aimed to the image sequences, and the stratified metric reconstruction method is to obtain the projective reconstruction of image sequences at first. If the surfaces of 3D object are plane (This situation is familiar), then based on the perspective correction of plane scene image and the scene geometry information, we give a review of the perspective correction of plane scene
image and the metric reconstruction of routine 3D scene image. Then on the basis of this, this dissertation proposed a 3D metric reconstruction method of single view which don't need to obtain the projective reconstruction. Four kinds of nonlinear state estimation filters (EKFl, EKF2, DD1 and DD2). Some system can't be described by simple linear model, therefore, the development of the non-linear filter algorithm becomes a necessity. Based on Kalman filter, the first order and second order Taylor series can be adopted to approximate the non-linear dynamic equation and measurement equation, and to obtain filters of EKFl (on the basis of first order Taylor approximation) and EKF2 (on the basis of the second order Taylor approximation) respectively. Whereas, the EKFl and EKF2 filters demands the existence of corresponding the first order and the second order differentiation of non-linear dynamic equation and measurement equation. If this requirement is not satisfying, Stirling interpolation approximation which does not need differential calculus, in replacement of Taylor approximation, gives forth to another two filters, DD1 (based on the first order Stirling interpolation approximation) and DD2 (based on the second order Stirling interpolation approximation). Estimation of pose and motion based on monocular vision. With the emergence of the new-born science of computer vision, it is also very important to estimate the correlative three-dimensional pose and motion i
本文首先介绍了计算机视觉中所用到的射影几何、仿射几何、度量几何和欧氏几何等各类几何学的基本概念和相关特性；概述了摄像机模型及成像原理；回顾了近年来摄像机定标方法的发展，对存在的各种摄像机定标方法进行了分析、比较和总结；最后，重点阐述了变内部参数摄像机线性自定标、平面型场景图像的透视校正、四种非线性状态估计滤波器(EKF1、EKF2、DD1和DD2)及基于单目视觉的位姿和运动估计的研究方法。
◆变内部参数摄像机线性自定标。在某些视觉系统中(例如机器人视觉系统、主动视觉系统)需要经常改变摄像机的位置或调整摄像机光学系统(如光圈与焦距)，在每次调整以后，都需要对摄像机重新定标。针对这种情况，本文提出了一种可处理畸变因子和主点已知但其它内部参数发生变化时的摄像机自定标方法，该方法先计算图像间的基本矩阵，在计算基本矩阵后得到射影重建的基础上，用线性方法恢复同形矩阵，再利用同形矩阵计算摄像机内部参数。
◆基于场景几何知识的三维度量重建。三维场景图像的度量重建一般是针对图像序列的，所使用的层次化度量重建方法都是首先得到图像序列的射影重建。如果三维物体表面都是平面(这种情况是比较常见的)，则在平面型场景图像三维度量重建的基础上，基于场景几何知识，对平面型场景图像和常规的三维场景图像的度量重建进行了回顾，然后在此基础上提出了一种不必进行射影重建且只须单幅图像的三维度量重建方法。
◆四种非线性状态估计滤波器(EKF1、EKF2、DD1和DD2)。对于某些系统不能用简单的线性模型来描述，因此必须发展非线性的滤波算法，在线性卡尔曼滤波的基础上，用一阶和二阶Taylor级数来近似非线性动态方程和测量方程，分别得到了EKF1(基于一阶Taylor近似)和EKF2(基于二阶Taylor近似)滤波器，但是使用EKF1和EKF2滤波器要求非线性动态方程和测量方程相应的一阶和二阶微分存在，在非线性动态方程和测量方程的一阶和二阶微分不存在时，用不需要计算微分的Stirling插值近似代替Taylor近似得出了另外两种新的滤波器，即DD1滤波器(基于一阶Stirling插值近似)和DD2滤波器(基于二阶Stirling插值近似)。
◆基于单目视觉的位姿和运动估计。随着计算机视觉这门新兴学科的出现，
计算机视觉中摄像机定标及位姿和运动估计方法的研究
不需要物体接触或人工干预，估计两参考坐标系之间的相对三维位姿和运动对机
器人导航、装配及测量、跟踪、目标识别和摄像机定标来说也是一个非常重要的
研究问题。利用单摄像机所获取的二维图像序列来估计两坐标系之间的相对位姿
和运动在实际应用中是可取的，其难点是从物体的三维特征投影到二维图像特征
的过程是一个非线性变换，本文研究了在运动物体尺寸和形状己知的情况下，三
维坐标变换用八元数表示，用单摄像机获取运动物体的图像，以线特征作为测量
输入，建立了位姿和运动估计系统的非线性模型，分别用IEKFI、IEKFZ、DDI
和DDZ四种滤波器进行了仿真比较，得出了位姿和运动估计结果。
关键词:变内部参数摄像机自定标;度量重建;Taylor近似;stirling插值近似;
滤波器;位姿和运动估计
Computer vision is a new research field with fast development into one of the important fields of intelligent automation. Its research object is to equip the computer with the ability to acquire information from its surrounding images or combination of images, which enables the machine not only to sense the geometrical information of the object in the environment, including its shape, position, pose and motion, etc., but to describe, store, recognize and understand them.Firstly, this dissertation introduces the basic conceptions and relevant properties of projective geometry, affine geometry, metric geometry and Euclidean geometry used in computer vision, as well as the camera model with imaging principles. Secondly, the dissertation gives review of the development of camera calibration technique in recent years. Some analysis, comparison and categorization on the existing various camera calibration techniques are discussed. Finally, the focus in my dissertation is the research on the camera self-calibration with varying intrinsic parameters, the perspective correction of plane scene image, derivations of four nonlinear state estimation filters (EKF1, EKF2, DD1 and DD2), and the estimation of pose and motion based on monocular vision. Linear camera self-calibration with varying intrinsic parameters. In some vision systems (e.g., the vision system of robot and active vision system), the camera's position and optic system (for example, the aperture and focus) require constant adjustment, and the camera must recalibration after every adjustment. Aimed at this circumstance, this paper proposes a camera self-calibration method to deal with the situation when the camera's distorted skews and principal points are already known, while the other intrinsic parameters keep varying. That is, to calculate the fundamental matrix between images to obtain projective reconstruction at first, and on which basis then, to regain the homography matrix by linear method, lastly, to obtain the camera's intrinsic parameters using homography matrix. 3D metric reconstruction based on scene geometry. The 3D metric reconstruction of scene image is often aimed to the image sequences, and the stratified metric reconstruction method is to obtain the projective reconstruction of image sequences at first. If the surfaces of 3D object are plane (This situation is familiar), then based on the perspective correction of plane scene image and the scene geometry information, we give a review of the perspective correction of plane scene
image and the metric reconstruction of routine 3D scene image. Then on the basis of this, this dissertation proposed a 3D metric reconstruction method of single view which don't need to obtain the projective reconstruction. Four kinds of nonlinear state estimation filters (EKFl, EKF2, DD1 and DD2). Some system can't be described by simple linear model, therefore, the development of the non-linear filter algorithm becomes a necessity. Based on Kalman filter, the first order and second order Taylor series can be adopted to approximate the non-linear dynamic equation and measurement equation, and to obtain filters of EKFl (on the basis of first order Taylor approximation) and EKF2 (on the basis of the second order Taylor approximation) respectively. Whereas, the EKFl and EKF2 filters demands the existence of corresponding the first order and the second order differentiation of non-linear dynamic equation and measurement equation. If this requirement is not satisfying, Stirling interpolation approximation which does not need differential calculus, in replacement of Taylor approximation, gives forth to another two filters, DD1 (based on the first order Stirling interpolation approximation) and DD2 (based on the second order Stirling interpolation approximation). Estimation of pose and motion based on monocular vision. With the emergence of the new-born science of computer vision, it is also very important to estimate the correlative three-dimensional pose and motion i
引文
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