r 
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RESEARCH ON CLOSE-RANGE PHOTOGRAMMETRY WITH BIG ROTATION 
ANGLE 
Lu Jue a 
a The Department of Surveying and Geo-informatics Engineering, Tongji University, Shanghai, 200092. - 
lujue 1985@ 126.com 
KEY WORDS: Big Rotation Angle; Colinearity Equation; Coplanarity Equation; Exterior Orientation 
ABSTRACT: 
This paper studies the influence of big rotation angles on the classical solution of analytical process. Close-range photogrammetry 
differs from traditional aerial photogrammetry, for the former usually adopts oblique photography or convergent photography, while 
the latter is similar to take vertical photos wherein the orientation elements are very small. In this paper, an exploration of the 
algorithm in every step of the analytical process from dependent relative orientation to absolute orientation is described. In order to 
emphasize the differences, contrasts will be made between the solution of the classical aerial photography and the algorithm of the 
close-range photogrammetry. A practical close-range photogrammetry experiment is presented to demonstrate this new algorithm. 
Through the example, it is pointed that with this new algorithm, the coordinates of the ground points and the exterior orientation can 
be accurately calculated. The results indicate that the algorithm deduced in this paper is applicable in the close-range 
photogrammetry with big rotation angle. 
1. INTRODUCTION 
Close-range photogrammetry determines the shape, size, and 
geometric position of close targets with photogrammetric 
technology [1] . Close-range photogrammetry differs from 
traditional aerial photogrammetry in several ways. For example, 
the former usually takes oblique or convergent photographs, so 
the rotation angles in the exterior orientation elements are often 
very big and the discrepancies between the adjacent camera 
stations’ three-dimensional coordinates will also be quite large, 
while the latter is similar to taking vertical photos wherein the 
orientation elements are very small. So in the field of close- 
range photogrammetry, performance of every step of the 
analytical process, such as dependent relative orientation, space 
intersection, strip formation process, absolute orientation and 
space resection, etc, a simplified model with small angles or a 
simple mathematical model can not be continued to use to 
calculate the parameters or coordinates that we need. 
In this paper, an exploration of the algorithm in every step of 
the analytical process in close-range photogrammetry is 
described. Special emphasis is placed on the contrasts between 
the solution of the classic aerial photography and the close- 
range photogrammetry. And corresponding examples will be 
presented to explain and verify the algorithm. 
matrix R. So the collinearity equations can be expressed as 
follow: 
x-x 0 =-f 
y-y 0 = -f 
a,{X-X s ) + b x {Y-Y s ) + c,(Z-Z s ) 
a 3 (X - X s ) +b 3 (Y -Y s ) +c 3 (Z - Z s ) 
a 2 (X-X s ) + b 2 (Y-Y s ) + c 2 (Z-Z s ) 
a 3 (X-X s ) + b 3 (Y-Y s ) + c 3 (Z-Z s ) 
°\ a 2 a i 
R= b, b 2 b 3 
c, c, c. 
(1) 
(2) 
Where (x 0 ,y 0 ,f) are the interior orientations. (X,Y,Z) and 
(X ,Y,Z ) are the object space coordinates of the ground 
points and the perspective centres, ai> a 2 > a^ bj> b^ b 3 ^ 
Ci > c 2 n c 3 are the 9 elements of the rotation matrix. In 
resection, once the interior parameters are known, the 
collinearity equations can be employed to determine 6 exterior 
orientation parameters. With more than 3 control points, to 
estimate better results, we linearize the collinearity equations 
and introduce the Least Square method [3] . However, good 
initial values are required for the LS estimation process to 
converge to appropriate values [2] . 
2. BASIC PRINCIPLE OF SPACE RESECTION AND 
TLS 
Collinearity condition equations are essential in analytical 
photogrammetry. The fundamental theory of the collinearity 
equations is that the perspective center, the image point, and the 
corresponding object point all lie on a line. Based on these 
equations, image and object coordinate systems will be related 
by three position parameters and three orientation parameters, 
called exterior orientations [2]. No matter what format of the 
three orientation parameters are present, they will be implicitly 
expressed in the nine elements of a 3^3 orthogonal rotation 
In traditional aerial photogrammetry, the initial values of three 
orientation parameters can be set at zeros, for its vertical 
manner [4 l But in close-range photogrammetry with big rotation 
angles, if they are still zeros, the process may not converge to 
proper results. So we need to determine the exterior orientations 
without the knowledge of their approximate values. 
In this paper, the collinearity solution based on the orthogonal 
matrix is applied. In this method, the nine elements of the 
matrix are used instead of the three angles, with three position 
parameters to take the roles of the unknown. The linear 
observation equations can then be made along with six