# Full text: Mapping without the sun

```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
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