The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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According to the relationship between object points and 
corresponding points, R can be projected on the image plane, 
and the resulting curve becomes: 
a 
T 
a. 
c 
1 
((FHy') r Q(FHy 1 
c 
1 _ 
We can see that the result is a quadratic curve, whose geometric 
interpretation is a circle, hyperbola, parabola or ellipse. As a 
result, we can obtain an unbiased relationship between the 
observed centres of the ellipse and the camera model. 
The image coordinates precision is very important to calibration. 
In a word, when we extracting control points coordinate from 
image plane, it is not necessary to correct the bias for the cross 
control points, but for the circle control points. 
2.3 Photography Model 
The calibration precision is not only related to the camera lens, 
the shape of the control points, but also the photography model. 
In other words, the camera attitude, the position of the control 
points in the image and longitudinal tilt all can affect the 
precision of calibration. Next, we will introduce in detail. 
Focal length is often fixed in calibration. And the objective 
distances are similar (because it needs to take several images to 
calibrate camera at a time). In order to demarcate the focal 
length and the distortion coefficients, we should photograph in 
different objective distances so that the same object can image 
in different sizes. Because the calibration model images in the 
centre of the image, so we can solve the focal length and the 
distortion coefficients more accurately. It means that the 
relevance between the focal length and distortion coefficients 
can be eliminated in a large extent in this way. 
Lens distortion is mainly composed with the radial distortion 
and tangential distortion. Rotating camera can differentiate the 
radial distortion coefficients and tangential distortion 
coefficients. So it is a good method for calibration to rotate 
camera in photography. 
In aerial photogrammetry, it is often required that the control 
points distribute evenly in the image plane. It is as the same in 
the close range photogrammetry, in the calibration. Control 
points in the image must be even and covered the whole image. 
If the control points can’t cover the whole image plane, they 
must be around the image centre, the wilder the better. 
The longitudinal tilt of camera is an influence factor too. The 
more atilt the camera is, the more the control points crowed 
together in the direction far away from the camera. 
2.4 The scale between calibration object and measurement 
object 
The purpose of calibration is measurement. Only the calibration 
is good which contributes to the measurement accuracy. 
Therefore, we should not only consider calibration itself, but 
also the contribution that the camera calibration does to the 
measurement accuracy. 
As all know, Camera has a certain depth of field, that is, if the 
focal length is fixed, there is a clear image when the objective 
distance changes in certain range. If we use smaller plane to 
calibrate camera, when we plan to measure larger object, we 
can’t achieve high accuracy, even get wrong result at last. On 
the contrary, if we measure a smaller object with a larger plane 
to calibrate, we can not be satisfied with the accuracy, too. In 
order to assess such factor’s effect on the measurement 
accuracy, we used a series of plane with different size to 
measure the same object. So that we accessed the sensitivity of 
the measurement accuracy to the calibration plane size. 
3. EXPERIMENT 
3.1 Real data 
In experiment, we use Olympus E-500 single-lens reflex (SLR) 
camera, with the 14-45 mm lens. This camera has 800 million 
valid pixels. The CCD (Charge Coupled Device) physical size 
of 17.3 mm * 13mm. Manual focus is used in photograph and 
image resolution is set to 3264 x 2448. 
Next, the images used in the experiments are listed. They are 
photographed at the same focal length. 
Fig.l The first four images of the model plane. 
They are photographed from 4 different directions. 
Fig.2 The second four images of the model plane. 
They are photographed with the camera rotated 90 degrees anti 
clockwise.