A LONG RANGE PHOTOGRAMMETRIC METHOD 
WITH ORTHOGONAL PROJECTION MODEL 
Tetsu ONO*, Shin-ichi AKAMATSU*, Susumu HATTORI** 
*Graduate School of Engineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, JAPAN 
ono@jf.gee.kyoto-u.ac.jp, akamatsu@info.gee.kyoto-u.ac.jp 
**Faculty of Engineering, Fukuyama University, 1 Sanzo, Gakuen-cho, Fukuyama, 729-0292, JAPAN 
hattori@fuip.fukuyama-u.ac.jp 
KEY WORDS: photogrammetry, vision metrology, orthogonal projection, orientation model, long range observation 
ABSTRACT 
This paper describes a method appropriate for 3-D measurement from a long distance with a digital camera mounting 
a super telescopic lens. Long distance observation with telescopic lens camera is a effective method for displacement 
measurement such as small movement of top of a large cliff. However the conventional orientation method with the 
central perspective model widely used in close range photogrammetry is unstable in this case because of weak condition. 
In this study, an alternative model called the orthogonal projection model is applied. This model, which derived from 
the affine projection model with a constraint of orthogonality, is simple and better adapted to long distance observation. 
Furthermore, it is a great advantage that the orthogonal projection model does not require initial values of orientation 
parameters. In this study, the geometric characteristics of the orthogonal projection model were clarified by various 
simulations, and also the effectiveness of the method was verified by long distance field tests. Focal length of telescopic 
lens used in the field test was 400mm and distance to objects was over 100m. RMSE between the adjusted results with a 
camera and those with a totalstation was about 2.8mm. The accuracy with the proposed method is more than twice higher 
than that with the conventional method. 
1 INTRODUCTION 
In recent years digital close range photogrammetry has be- 
come applied to various objects in various fields. However 
it has not widely enough spread in fields of civil engineer- 
ing and construction. In construction work, displacements 
of cliff faces or construction materials have to be precisely 
observed for disaster prevention, but ordinarily the target 
sites range over vast areas and moreover arrangement of 
view points is restricted. For example, movement of un- 
stable rocks on top of large cliff has to be monitored to an 
accuracy of a few millimeters at ground points over 100m 
distant in some cases. 
Close range photogrammetric techniques using camera with 
wide-angle lens are not available in these situations. Ap- 
proaching the target objects is dangerous and may be im- 
possible. It is not uncommon that fixing a deal of reflective 
targets on the objects is not allowed. In many cases, there is 
no alternative but to observe the object shape without clear 
marks from a distance. By using a telescopic lens cam- 
era, optical resolution can be kept high enough in spite of 
long distance observation. As focal length increased, how- 
ever, view angle becomes smaller and geometric condition 
becomes worse. What is worse, available control points 
may be not many enough and may be ill-placed. Under 
these circumstances, the central perspective model gener- 
ally used in close range photogrammetry is hardly applica- 
ble because of ill-posed problems. 
Scaled orthographic projection models are widely used in 
computer vision to model the imaging process(Ullman 1979; 
Huang and Lee 1989; Tomasi and Kanade 1992; Shapiro et 
al 1995; Xu and Sugimoto 1999). They are mainly used for 
calculation of an approximation to perspective projection 
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model, but it should be noted that these models are stable in 
ill-conditions. Some papers in computer vision categorize 
them to the following camera models; the affine model, the 
weak perspective model and the para-perspective model. 
The authors contrived the orthogonal projection model (Ono 
2002), which belongs to the weak perspective model in the 
sense of camera model, but the basic concept is quite dif- 
ferent from that of computer vision. The main aim of 3-D 
image analysis in computer vision is efficient estimation 
of motion. The weak perspective model is not a rigorous 
model but a approximate one in the real world. On the 
other hand, the orthogonal projection model is directly de- 
rived from the central perspective model without approx- 
imation. This model can provide an accurate solution by 
itself. 
2 ORTHOGONAL PROJECTION MODEL 
2.1 Basic concept 
The conceptual diagram of orthogonal projection model is 
illustrated in Figure 1. The procedures of orthogonal pro- 
jection model consist of the weak perspective projection 
and the projection transformation from the central perspec- 
tive images. 
From another viewpoint, this can be considered as a pro- 
gressive model of the affine projection model, which Okamoto 
(1992,1998) proposed for long range observation. 
2.2 Derivation of model equations 
If the lens distortions and the shift of the principal points 
are negligible, the central perspective model is expressed 
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