157 
_ P U {X,Y,H) 
r ' P 2I (X,Y,H) 
P 3l (X,Y,H) 
c, = 
(4) 
P 4I (X,Y,H) 
P lr (X,Y,H) 
P 2r (X ,Y ,H) 
P 3r (X,Y,H) 
P 4r (X ,Y ,H) 
Because the normalization parameters of left and right image 
are different, the corresponding normalized object space 
(X,Y,H) 
coordinates v 7 are alse inconsistent in expressing, 
which causes it cannot directly solve the equation group by the 
(X Y Hj 
least square method and get ^ ’ ’ 7 . In order to unify the 
form of unknown values as solving the equation group, it needs 
to import the unnormalized original object space coordinates 
(X Y H ) 
v u u-> u ) j nt0 e q Ua tion group to calculate, but not 
the normalized coordinates . 
Linearizes the above formula 4, and imports original ground 
(X Y H ) 
“ ’ “ ’ u , then can get following 
3D coordinates 
formula: 
1 
«'•-AK + _L A a v + 
X,dX 
Y s ,dY 
1 dc, 
—^AX U +—^AY U + 
X s ,dX Y sl dY 
1 dr 1 dr 
-AX +—^AY + 
X sr dX Y sr dY 
l de 1 dc 
—AX H AY + 
X sr dX Y sr dY 
And corresponding error equations are: 
1 
dr , 
dH 
1 
dc, 
dH 1 
1 
dr r 
Z sr 
dH 
1 
dc r 
z~ 
~dH 
AZ u+ r l (X u0 ,Y u0 ,H u0 )=0 
(5) 
1 
dr, 
1 dr, 
1 
dr,] 
dX 
Y sl dY 
dH 
1 
dc, 
1 dc, 
1 
dc. 
x* 
dX 
Y sl dY 
Hs, 
dH 
1 
dr r 
1 dr r 
1 
dr r 
dX 
Y sr dY 
H w 
dH 
- 
1 
dc r 
1 dc r 
1 
dc r 
L*- 
dX 
Y sr dY 
Hsr 
dH 
r, - r, ' 
~AX U ~ 
c, -c,' 
< 
— 
r r -r r ' 
AH u 
c r — C r 1 
(6) 
In the solution of ground 3D coordinates it needs to carry on 
the iterative computation, and the initial values of iteration can 
directly use the normalization parameters of ground coordinates: 
LongOffset, LatOffset, HeightOffs et. 
quickly imported into the iterative computation, and satisfy the 
request of fast localization to the ground objects. 
Having the iteration initial values, it can import them into the 
space intersection model based on RFM, which is constructed 
in before, and carry on iteration during solving the error 
equation group. As soon as the different value of Neighboring 
two coordinates is smaller than the set limit error, then finish 
the iteration, and calculate the optimal solution of original 
object space 3D coordinates (X u ,Y U ,H U ). 
4. EXPERIMENTS AND ANALYSIS 
The experiment data include: one QuickBird panchromatic 
image and part of SPOT5 color image of the same region, some 
1:1,000 topographic maps of this region, 5 GPS control points. 
These two RS images overlay part of same regions. 
Among them, the QuickBird panchromatic image is the whole 
image, and its size is 22888 x 17492 pixels, space resolution is 
0.6m, the RPC and the normalization parameters of this image 
are known; The SPOT5 color image is a small part of the whole 
image, and the size is 3104x4632 pixels, space resolution is 
2.5m, the RPC and the normalization parameters of this image 
are unknown. The original data used in experiments included 
the 1954 Beijing Coordinate System, the 1980 Xi’an 
Coordinate System, and the WGS84 Coordinate System. For 
the sake of utmost make use of an existing original data, it 
needs to unify all calculation data under the WGS84 Geodetic 
Coordinate System. The GPS control points are used to 
compute the conversion parameters between the WGS84 
Geodetic Ellipsoid and the 1980 Xi’an Geodetic Ellipsoid, then 
transforms the plane coordinates and heights obtained from 
1954 or 1980 Coordinate System to the WGS84 Geodetic 
Coordinate System. 
4.1 RFM Model Solution of SPOT5 Image 
Makes use of the 40 GCPs which are selected from the 
topographic maps, and computes the 10 normalization 
parameters of SPOT5 image, then calculates the corresponding 
RPC, constructs the RFM model of SPOT5. 
According to the RPC and normalization parameters, imports 
the ground 3D coordinates of the 40 GCPs and 30 CKPs into 
this RFM, then calculates corresponding residential errors of 
the GCPs and CKPs, finally can get the orientation precision of 
this RFM model for the SPOT5 image, as the following Table 2 
shows: 
This selection method of initial values not only may avoid 
complex formula computation in commonly iteration initial 
values calculation, moreover because these three normalization 
parameters are the known data, they may be conveniently and 
Longitude 
max 
min 
RMSE 
max 
GCP error 
-0.029p 
0.000 p 
0.008 p 
+0.429 
p: pixel 
-0.073 
m 
0.000m 
0.02m 
+1.703 
m 
CKP error 
-11.920 
+0.18p 
2.814 p 
-4.424p 
p: pixel 
-29.80 
+0.45m 
7.035m 
-11.06m 
Latitude 
Plane 
min 
RMSE 
max 
min 
RMSE 
-0.001 p 
0.091 p 
0.429 p 
0.0006 p 
0.092 p 
-0.002m 
0.228m 
1.703m 
0.002m 
0.023m 
-0.0427p 
1.491p 
12.714p 
0.185p 
3.185p 
-0.107m 
3.728m 
31.785m 
0.463m 
7.963m 
Table 2 the SPOT5 image GCP and CKP residential error under RFM model