Solutions for Exterior Orientation in Photogrammetry: A Review

The determination of the attitude, the position and the intrinsic geometric characteristics of the camera is recognised as the fundamental photogrammetric problem. It can be summarised as the determination of camera interior and exterior orientation parameters, as well as the determination of 3D coordinates of object points. The term "exterior orientation"of an image refers to its position and orientation related to an exterior (object space) coordinate system. Several methods can be applied to determine the parameters of the orientation of one, two or more photos. The orientation can be processed in steps (as relative and absolute orientation) but simultaneous methods (such as bundle adjustments) are now available in many software packages. Several methods have also been developed for the orientation of single images. They are based in general on geometric and topological characteristics of imaged objects.
This paper presents a survey of classical and modern methods for the determination of the exterior parameters in photogrammetry, some of which are available as software packages (with practical examples) on the Internet. The methods presented are classified in three principal groups. In the first, a selection of approximate methods for applications that do not require great accuracy is presented. Such methods are also used to calculate values required for iterative processes. In the second group, standard point–based methods derived from collinearity, coplanarity or coangularity conditions are briefly reviewed, followed by line–based approaches. The third group represents orientation methods based on constraints and on concepts of projective geometry, which are becoming of increasing interest for photogrammetrists. In the last section, the paper gives a summary of existing strategies for automatic exterior orientation in aerial photogrammetry.     

GNSS辅助摄影测量中几个问题的探讨

GNSS辅助摄影测量是在数字摄影测量基础上发展起来的一种技术手段。它使航空摄影、像片控制点布设、外方位元素的获取和空中三角测量进入了一个新时代。本文对航摄分区和补摄、区域划分以及像控点布设应注意的问题进行了探讨,同时,对应用前景进行了概述。     

射影空间中摄影测量基本几何关系式的建立

对射影空间中摄影测量的一些基本问题进行了研究,建立了射影空间中物像之间的共线条件关系式、物像之间的直接关系式以及同名像点之间的共面条件关系式。     

基于大比例尺航空影像共面约束条件的相机自检校方法

提出了基于大比例尺航空影像共面约束的相机自检校方法,该方法使用所有立体像对同名点基于共面约束对相机的内方位元素及畸变系数进行解算。首先进行航空影像同名点匹配,构建立体像对;然后基于共面约束使用直接解法和迭代优化进行相对定向,解算相机位置与姿态;最后使用最小二乘优化方法解算相机内方位元素和畸变系数。对于高分辨率大尺寸航空影像,图像中心及边缘的畸变差异较大,为了进一步提高解算精度,对图像进行网格区域划分解算畸变。使用大比例尺航空影像进行解算能真实精确反映航空摄影测量时所获取图像的相机参数和畸变系数,避免检校环境与使用环境不同解算得到的相机畸变参数不能真实反映所获取影像的畸变问题;使用所有同名点解算,避免由于选择不同特征点或控制点对检校精度的影响;通过区域网格划分,进一步提高了解算精度。对检校结果进行了分析,该方法精度较高,与基于室外检校场的精度相当,能真实精确反映航空摄影测量时所获取图像的相机参数和畸变系数,提高了三维重建的精度。     

单应性几何下的后方交会直接解法

传统的后方交会最小二乘解法需要良好的外方位元素初值。在无初值或者初值不够精确的情况下,最小二乘迭代不容易收敛。在近景摄影测量或者计算机视觉等领域,往往不提供良好的初值,无法适用传统的后方交会解法。针对上述情况,本文提出了一种基于单应性矩阵的后方交会直接解法,在不需要初值的情况下,获取外方位元素的直接解。该方法根据单应性矩阵所描述的平面几何关系,利用单应性矩阵内在的约束条件,将后方交会问题转换为一个二元二次方程组的求解问题。该方法受舍入误差影响小,在无偶然误差的情况下,解算精度能达到10–9量级,能够避免传统直接解法计算复杂的问题,为传统的平差迭代解法提供良好的初值。此外,在多个控制点共面的情况下,该方法能够直接获得外方位元素的精确解。实验结果表明:在各种不同倾角拍摄的情况下,该方法均能够获得稳定的外方位元素,为后续的后方交会最小二乘算法提供良好的初值。采用本文方法计算的初值参与平差,能够达到与人工给定初值平差一致的精度,且迭代收敛速度是人工给定初值平差的2倍以上。在控制点共面的情况下,该方法的反投影精度能够达到亚像素级,且精度优于大部分主流的直接解法。     

Direct relative orientation with four independent constraints

Relative orientation based on the coplanarity condition is one of the most important procedures in photogrammetry and computer vision. The conventional relative orientation model has five independent parameters if interior orientation parameters are known. The model of direct relative orientation contains nine unknowns to establish the linear transformation geometry, so there must be four independent constraints among the nine unknowns. To eliminate the influence of over parameterization of the conventional direct relative orientation model, a new relative orientation model with four independent constraints is proposed in this paper. The constraints are derived from the inherent orthogonal property of the rotation matrix of the right image of a stereo pair. These constraints are completely new as compared with the known literature. The proposed approach can find the optimal solution under least squares criteria. Experimental results show that the proposed approach is superior to the conventional model of direct relative orientation, especially at low altitude and close range photogrammetric applications.     

Photogrammetric modeling of the relative orientation in underwater environments

Underwater photogrammetry provides an efficient means for documentation of environments which are complex and have limited accessibility. Yet the establishment of reference control networks in such settings is oftentimes difficult. In this regard, use of the coplanarity condition, which requires neither knowledge of object space coordinates nor setting a reference control network, seems to be an attractive solution. However, the coplanarity relation does not hold in such environments because of the refraction effect, and methods that have been proposed thus far for geometrical modeling of its effect require knowledge of object-space quantities. Thus, this paper proposes a geometrically-driven approach which fulfills the coplanarity condition and thereby requires no knowledge of object space data. Such an approach may prove useful not only for object space reconstruction but also as a preparatory step for application of bundle block adjustment and for outlier detection. All are key features in photogrammetric practices. Results show that no unique setup is needed for estimating the relative orientation parameters using the model and that high levels of accuracy can be achieved.     

Principle, software and experiment of GPS-supported aerotriangulation

1 IntroductionAs is now well known, the high accurate point de-termination with airborne remOe sensing data hasalways ben one of the most fundaxnental prObletns..in aerial photOgrammtry. According to the princi-ple of the geOmtry reversal in photOgramrntry,the interior and exterior orientation elements ofaerial phOtOgraphs must first be known in order toreconstnJct the measuring stereo geometric medels.For the past 60 years, however, the interior orienta-tion parameters of carnera were main…     

卫星摄影三线阵CCD影像的EEP法空中三角测量（三）

4 平差方案及模拟数据平差实验4.1 自由网+控制点空中三角测量由前方交会(2.1)式,后方交会(2.2)式以及外方位元素平滑制约条件(2.3)式,可以构成类似经典的光束法空中三角测量,但由于EFP像点坐标是推算出来的,所以控制点不宜直接参与平差过程.于是平差要分成自由网平差及利用控制点作三维线性变换两个步骤.另一方面,卫星摄影中起始角元素大约在±0.5°左右,对于经典空中三角测量,角元素起始近似值均可按零处理.但在EFP平差中,φ角起始值φ0对空中三角测量,像元素起始近似值均可按零处理.在EFP平差中,φ角起始值φ0对整条航线的几何状态影响很大,必须采用特殊的程序预先加以确定.我们采用不断步进φ角值,比较由前方交会及(1.2)式计算的Y视差的均方根值最小者,即作为φ的最佳起始值.平差框图见图4.     

航空摄影测量中立体模型的重建(英文)

This paper describes the operational issues and basic technical requirements of modern aerial photogrammetry. The accuracy of photogrammetric point determination and the y-parallax at corresponding model points is analyzed when stereo models are reconstituted by using the exterior orientation elements of aerial images. Real aerial photographs, at image scales from 1：2 500 to 1：6 0000, with DGPS/IMU data taken from various topographies in China were processed by our POS-supported bundle block adjustment program WuCAPS. The empirical results verified that the accuracy of the exterior orientation elements from bundle block adjustment meets the requirements of the specifications of topographic mapping. However, the accuracy of the exterior orientation elements determined by POS fails to meet the requirements of the specifications of topographic mapping.     

卫星摄影三线阵CCD影像的EFP法空中三角测量(一)

系统地介绍了EFP法空中三角测量的基本思想、EFP像点坐标计算、平差的数学模型和卫生摄影测量的数字模拟,并以模拟数据进行了自由网＋控制点平差、外方位元素量测值参与平差、外方位元素量测值常差的分离以及区域平差等实验计算和实验结果分析。通过研究分析得出结论：（1）三条基线的航线可以保证三线阵CCD影像光束法平差的几何强度;（2）控制点可以布设在航线首末端,二线交会区的高程精度比三线交会区仅低约1.4因子;（3）外方位元素观测值是三线阵CCD影像光束法平差不可缺少的数据,经过平差可以不同程度地提高平差的高程精度。即使外方位元素观测值达到现代的精度,光束法平差的高程精度仍比直接前方交会高,所以三线阵CCD相机比单线阵、双线阵相机在全球性无控制卫星摄影测量或外星球摄影测量方面有更大的优势。     

非量测相机获取特殊目标影像的解析模型建立

利用近景摄影测量方法对物体进行摄影,其上应布设一定数量的控制点,但在某些情况下,一些目标上不宜布设控制点。本文给出一种解决方法,即在被测目标上不布设控制点,且用普通相机摄影,其解析处理不采用直接线性变换,而采用一种平行线相对控制与空间前方交会结合的处理方法,经实验验证,在解决某些特殊物体摄影处理时是一种非常实用的方法。     

GEO-REFERENCING WITHOUT GROUND CONTROL

A geo-reference is a global or regional geographical or geodetic coor-dinate system to which sensors or spatial object data are related.Hence,geo-ref-erencing is close to the well known photogrammetric concept of exterior or abso-lute orientation,the common execution of which is indirect,via the use of groundcontrol point.GPS and INS technologies have changed the situation,permittingdirect measurement of position and attitude parameters and making exterior orien-tation feasible without ground control at all,in principle.The analysis of accuracyand reliability performance discloses,however,that especially INS does not yetmeet the high demands of photogrammetry.Moreover,control of systematic er-rors,the problem of datum transformation,and reliability conditions make theuse of some ground control points still mandatory,at least for any high perfor-mance geo-referencing.     

近景摄影测量中大角度问题的探讨

应用摄影测量中的解析算法,研究倾斜摄影和交向摄影中大角度摄影情况下的解算方法对经典解析算法的影响,推导大角度摄影情况下从相对定向至绝对定向这一解析过程的算法,通过算例证明在大倾角摄影条件下利用该算法能够准确计算出地面点坐标以及反算出像片的外方位元素,从而验证本算法在大倾角近景摄影测量中的适用性。     

不同焦距的连续像对相对定向严密公式

针对现有解算相对定向元素的公式通常用于具有相同焦距的立体像对这一现状,为充分利用不同相机所拍摄的现有影像信息,以像点坐标作为观测量,给其加入改正数,借助计算机代数系统对共面方程进行严格的线性化,推导出了适用于解算不同焦距立体像对相对定向元素的严密公式;最后,通过算例验证了该方法的正确性,可在一定程度上丰富摄影测量理论。     

Relative orientation based on multi-features

In digital photogrammetry, corresponding points have been widely used as the basic source of information to determine the relative orientation parameters among adjacent images. Sometimes, though, the conventional relative orientation process cannot be precisely implemented due to the accumulation of random errors or in the case of inadequate corresponding points. A new relative orientation approach with multiple types of corresponding features, including points, straight lines, and circular curves, is proposed in this paper. The origin of the model coordinate system is set at the projection center of the first image of a strip, and all of the exterior orientation parameters, except φ and ω of the first image, are set at zero. The basic models of relative orientation with corresponding points, straight lines, and circular curves are discussed, and the general form of a least squares adjustment model for relative orientation based on multi-features is established. Our experimental results show that the proposed approach is feasible and can achieve more reliable relative orientation results than the conventional approach based on corresponding points only.     

基于普通数码相机的旋转全景摄影测量方法

普通数码相机固定在高精度旋转平台上可集成为旋转全景相机,水平旋转多位置拍摄,可获取全景影像。给出了旋转全景相机的成像几何关系模型,实现了旋转全景相机的标定,利用稀疏分布的少量控制点（最少3个）,即可解算出平台旋转中心坐标与起始方位角,及每张像片的外方位元素,再利用多站旋转拍摄的影像进行前方交会就可获得物方点坐标。实验结果表明,本文提出的方法在实际摄影测量中可少受视野和控制点数量的限制,通过较少的控制点即可解算出物方点坐标,且测量精度较好。该方法是在困难场景进行近景摄影测量的一种新的有效手段。     

GPS／INS组合系统的工作原理及其在航空遥感中的应用现状

GPS／INS组合系统应用于航空摄影测量时可以直接给出相机曝光瞬间的外方位元素，从而部分乃至全部地摆脱传统摄影测量对地面控制点的依赖。本文主要介绍GPS／INS组合系统的工作原理及特点，以及GPS／INS组合系统辅助航空摄影测量与遥感的国内外应用现状。     

一种单像外方位元素的稳健估计方法

获取影像外方位元素是摄影测量学一直要解决的问题,传统的单像空间后方交会利用测量控制点来计算外方位元素,但是很多情况下用于计算的数据是包含粗差的,粗差出现的概率约占1%~10%。本文设计了一种稳健的单像空间后方交会计算方法,把控制点坐标作为未知参数对待并线性化共线方程,最终达到了剔除粗差的目标,提高了计算结果的可靠性,可得到控制点及像点坐标的精度评价。     

三线阵CCD影像短航线空中三角测量的模拟实验研究

本文主要介绍了解决三线阵CCD影像短航线空中三角测量问题的自由外方位元素平差方法及相关数学模型,按不同的卫星摄影测量条件,分别用直接前方交会、自由外方位元素平差方法及外方位元素观测值参与平差,进行了数学模拟计算,结论是:采用自由外方位元素平差方法,可以构建精度与直接前方交会相当,但“无y视差”的短航线立体模型。