Agriculture Reference
In-Depth Information
ground scene. Second, the relative brightness of a single pixel in different bands can
be inaccurate if compared with the spectral reflectance of the corresponding region
on the ground.
Geometric errors can be generated by rotation, the curvature of the Earth and
mountains, and the height, speed, and instability of the platform. Some distortions
are predictable—for example, the effects of the Earth
s rotation and camera angles.
Therefore, they can be calculated and systematically corrected for. Satellites have
sophisticated on-board systems that record very slight movements. This informa-
tion is mainly used to correct the satellite
'
s position, but can also be used to
geometrically correct the images. Geometric distortion can, for example, cause a
certain number of pixels to move from one scan line (i.e., the detection line of the
scanner) to the next.
Engineers and physicists have developed many techniques to correct these
distortions. This section is not intended to be an in-depth description of geometrical
pre-processing techniques. See Jensen (
2004
) and Richards and Jia (
2006
) for more
details on this topic.
The polynomial maps method is often used to correct geometric distortions,
because all the image distortions may not be eliminated during the automatic
correction pre-processing phase and a manual correction may be required.
We must assume the existence of a
correct
map that is geometrically correct,
where each point is uniquely identified by its Cartesian coordinates (
'
). Suppose
that the coordinates of the pixels in an image can be expressed as functions of (
α
,
ʲ
α
,
ʲ
)
such that
i
¼
f
α; ð ;
ð
4
:
1
Þ
and
j
¼
g
α; ð :
ð
4
:
2
Þ
These functions can be written in quadratic form as
2
2
i
¼
c
0
þ
c
1
α þ
c
2
ʲ þ
c
3
αʲ þ
c
4
α
þ
c
5
ʲ
ð
4
:
3
Þ
and
2
2
j
¼
d
0
þ
d
1
α þ
d
2
ʲ þ
d
3
αʲ þ
d
4
α
þ
d
5
ʲ
:
ð
4
:
4
Þ
However, we often do not know a priori the terms
c
r
and
d
r
, for
r
, 5, so they
must be estimated. The estimate can be obtained by comparing certain landmarks
on the Earth with the deformed image. These points are well known in advance, and
are usually represented by the intersections of roads, airports, and highways. We
refer to these places as ground control points. Equations (
4.3
) and (
4.4
) show that
we require a minimum of six ground control points for a second order
polynomial map.
¼
1,
...
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