changed over time in an image, the changing rule of the exterior 
geometric elements (position and attitude) during the scanning 
process is approximately expressed, and the collinear equations 
couldn’t strict in theory, so that the advantage of the collinear 
equations is not certainly remarkable comparing with the 
polynomials rectification in the dynamic scanning image. 
The polynomials rectification is a traditional method, its 
principle being quite intuitive and computation simple, and the 
process for geometric spatial imagery is avoided, because the 
registration is mathematical simulation directly to image 
distortion but to the mathematical model of sensor image 
configuration. The method considers the general distortion as 
translation, zoom, rotation, affine, leaning and bending as well 
as the integral function of the general distortion in higher levels, 
therefore, a suitable polynomial can rectifícate the coordinates 
of points before and after rectification, that is, a suitable 
polynomial is selected to approximately describe the 
relationship of the conjugate points on the images before and 
after rectification, and the coefficients in the polynomials is to 
computed by means of least square method by using the the 
image coordinates of control point and the theoretic coordinates 
on reference system, then correction by the method. It is 
universally applicable for the most kinds of rectification of 
sensors. 
3.2.1 Selection of the ground control point (GCP): GCP is 
the ground control point used in geometric accurate rectification 
and the precision of GCP directly affects the precision of 
geometric rectification. There are some rules in the selection of 
the GCP. 
1) . Ground control points must be clear and stable and can 
be found easily in the image and the geography space, 
especially which pixel is the certain GCP accurately in 
the image space; 
2) . The distribution of GCP must be uniform in the image 
space; 
3) . Measurements must be accurate, so the image space 
must accurately to pixels in the case of the map sheets 
selected to millimeter grade in geography space. 
Generally, the geography space precision must be 
superior to the ground resolution of the images. 
The experiment adopts the latest digital vector line drawing 
with 1:500 scale of Liaoning Technology University mapped in 
2000 to select obviously features, and all the positions selected 
are building comers. There are 30 control points and 15 
checking points as shown in Figure 1. 
3.2.2 Selection of rectification methods: The geometric 
correction software used in the experiment is ERDAS 8.5 that 
provides several kinds of image mathematical model for 
correction as shown in Table 2. 
least number 
Method 
of 
ground control 
Notes 
points 
Helmert 
2 
affine 
Affine 
3 
first-order 
polynomials 
Project 
4 
projection 
transformation 
2nd order 
6 
second-order 
affine 
polynomials 
3rd order 
10 
third-order 
affine 
polynomials 
4th order 
15 
4 th -order 
affine 
polynomials 
5th order 
21 
S^-order 
affine 
polynomials 
6th order 
28 
b'b-order 
affine 
polynomials 
Table 2. Algorithm of images geometric correction 
Theoretically speaking, the polynomials orders used in the 
geometric correction using ERDAS are allowed from 1 to n, 
and the number of least controls points must be provided in 
Equation (2). 
(f + l)x(/ + 2) 
m = 
2 
(2) 
where t is the polynomials order. 
There are 30 GCPs Selected in the experiment and 6 kinds of 
different correction methods are applied, such as Affine, 2 nd - 
order, 3 rd -order, 4 th -order, 5 th -order, and 6 th -order. Meanwhile, 2 
discrepancy points are rejected according to residual error along 
the axes XoxY that more than one pixel. 
3.3 Evaluation of the plane precisions 
3.3.1 Root mean square (RMS) error of the GCP: The 
RMS errors of simple-points and the total RMS errors of 28 
points are calculated separately by applying six polynomials 
from one to six orders, because the data mount of the RMS 
errors of simple points is too large, only the total RMS errors by 
six kinds of different polynomials for geometric correction 
listed in Table 3. 
Figure 1. Distribution of control points and checking points