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Title
Mapping without the sun
Author
Zhang, Jixian

280
x'=x+ax=
MP,LM)
p 2 (p,l,h)
+ AX
Y=Y+AY=
MP,LM)
M p ,LM)
+ AZ
(3)
The adjustable functions and AT are typically
polynomials of the image coordinates X and Y. Such methods
are known to be particularly applicable to a system with a
narrow field of view imaging a relatively flat area (Ian Dowman,
2000). However, refinements to the RPC camera model are
required that will be valid for systems with a large field of view
and moderately hilly terrain (Jack Grodecki, 2003). In order to
further improve the accuracy of the sensor model, more
correction items can be added in image space.
T Z
Figure2. Adjustment of object space coordinate system
Different from traditional approach of translating, rotating and
scaling imaging parameters that describe the sensor system to
remove the biases in the measured imaging parameters, the
object space coordinate system may be mathematically rotated,
translated and scaled in an attempt to remove the biases in the
biased. The adjustment of the object space coordinate system
may be implemented as an adjustment of object space
coordinates before the application of the given RFM by using
nine physical parameters. Therefore, refining the RFM then
only requires adjustments to nine physical parameters and
processing of significantly fewer GCPs. The RFM with the set
of coefficients is then applied to the set of new object space
coordinates to result in a pair of image space coordinates. One
refined RFM defined as the follow equations can be adopted:
Since the sensors of Beijing-1 small satellite are a linearity
pushbroom CCD camera, the focal plane is one line of detection,
in contrast to frame camera, wherein the focal plane is a two
dimensional image plane. If the flight direction is perfectly
oriented in the north-south direction, a more correct formulation
for refinements to RFM of a pushbroom camera is detailed
below.
p
>0'
1+5,
0
0 "
"hi
"hi
~P
>'
L'
=
4
+
0
1 + ^2
0
"hi
"ha
L
+
L
H'
A.
0
0
1+S3
."hi
"hi
"hi.
H
H
However, it is very unlikely that the flight direction is oriented
perfectly in the north-south direction. This lack of perfect north-
south orientation may be accounted for by skewing the latitude
and longitude coordinates by an orientation angle on the
skewing the latitude and longitude coordinates and then reverse
skewing the latitude and longitude coordinates by the same
orientation angle[27SUN].
p
^0
cos 9
sin#
0'
1 + 5,
0
0
m u
m n
«7,3
0
P t
L
=
A,
+
-sin#
COS#
0
0
1 + $2
0
A«,,
m n
"hi
L,
+
0
H
H 0
0
0
1
0
0
l + s,
m >:
m„
H
0
where
# = arctan
ÔP
av
,8P
p t '
cos#
sin#
0'
P'
L,
=
-sin#
cos#
0
L
H s
0
0
1
H
In practice, most of the object space coordinates can be in a
linear measurement for easting or northing. So equation (4) and
related equations can be simplified to minimize the use
engineered parameters and thus provide a more generalized
solution. With small rotational angles including pitch angle 60 ,
roll angle ^ , and yaw angle K and scaling factors
equation can be rewritten as the follow equations.
P
M
cos y
sin^
0"
'•*1
-K
CO
'0'
M
L
=
4
+
-sin?'
cosy
0
K
S 1
-

4
+
0
H'
A.
0
0
1
-CO (p
s i -
H
0
L =
H
where ^ °’ °’ °‘ are translating factors of physical parameters;
(sl,s2,s3) are scaling factors of physical parameters; Both of
them are acted for adjusting latitude, longitude and height,
respectively ( m wi m \2, m M, m n, mm i\t m n," 1 33) arg
rotating factors that are organized in a rotational matrix
determined from physical parameters which are called
rotational angles including pitch angle ^ ; ro n angle ^ , and
yaw angle ^ . The rotating factors are determined from the
rotational angles in more than one relation. One standard
relation expresses as follows (Sun Jiabin, 2003):
m,, m, 2 m, 3
i"n "hi “a =
m,, my,
which may be expanded and generalized as:
P =a 0 +q-P+a 2 -L+a } -H+P
• L — /?Q+^’.P+ô,'Z/+7y//+/.
H —c 0 +c l -P+c 2 -L+c i -H+H
From which 12 adjustable coefficients the equations may be
identified. However, not all of the 12 coefficients are
independent. The 12 adjustable coefficients are determined
based on the nine physical parameters including three
translation factors, three rotation angles and three scaling
factors through equations (4) and (5) before simplification and
equations (8) after simplification.
To improve the geometric accuracy of refinement to the RFM, a
given set of GCPs may be added to the refined method. So,
optimizing the 12 adjustable coefficients for a given sensor can
begin with initializing the physical parameters and calculating
the initial values of the adjustable coefficients. This kind of
orthorectification based on RFM can diminish the influence of
Po
l + s.
0
0
"’ll
m n
m,.
~P~
4
+
0
l + s 2
0
m u
m 22
m 2 .
L
A.
0
0
1 + s,
_m 3 ,
m 12
H
COS COS AC — COS 40SÜ1AC+ sin ç>sin COCOS AC sin ty sin AC+cos COS ty sin AC COS ^7COS AC+sin^siniysin AC —SUI Ç/COS AC+COS ^JSÛl ÛASÜl AC
-sin ¿y sin