Full text: Mapping without the sun

Orientation Model 
same orientation models 
various orientation models 
Extent of Complexity 
simple, long researching history 
complex, many problems, little research 
Suitable Scope 
Table 1 the differentiation and affiliation between traditional and generalized stereopair 
Its practical significance can be described as: (1) Opens the 
source: Maximum limit uses the existing image sources, and 
expands the information content; (2) Saves money: Saves the 
expensive expense; (3) Increases effect: Realizes the fast 3D 
information extraction and target reconstruction. 
The orientation model of image decides which kind of models 
should be used in space intersection. The common orientation 
models have the following types: Polynomial Model (PM), 
Collinearity Equation Model (CEM), Affine Model (AM), 
Direct Linear Transformation (DLT), and Rational Function 
Model (RFM). Among them, RFM has already become the 
main orientation model for high resolution imagery. Comparing 
with other models, the RFM has following advantages: (1) 
independence from sensors or cameras; (2) suit for any kind of 
coordinate system, and free form the coordinate system; (3) 
can imitate rigorous models of any existing sensors or cameras. 
According to the above advantages, this paper takes the RFM 
as the basis of generalized stereopair space intersection and 
makes the principle deduce and analysis. 
In the construction of generalized stereopair, the 
different-source images have the different sensor models and 
imaging techniques. In order to unify all these different sensor 
models under the identical kind of model, therefore takes the 
RFM as the image orientation model for each single image to 
construct generalized stereopair. And all these kind of space 
intersection models constructed by this method are all based on 
the RFM model. 
3.1 Mathematics Model of RFM 
mathematics expressing of RFM: 
r _ P\(X,Y,H) 
P 2 (X,Y,H) (1) 
^ P 3 (X,Y,H) 
P 4 (X,Y,H) 
m ] m 2 tfi 3 
P(X,Y,H) = £'£ j Y j a ijk X i Y J H k 
i=0 y=0 k=0 
— a x + a 2 X + a 3 Y + a 4 H + a s XY + a b XH 
+ a 7 YH + a,X 2 + a 9 Y 2 + a l0 H 2 + a n XYH In this 
+ a n X + a X2 XY + a x4 XH 2 + a l5 X 2 Y 
+ + a xl YH 2 + a xs X 2 H + a X9 Y 2 H + a 20 H 3 
Y, C image coordinates after normalization; 
X, Y, H ground coordinates after normalization; 
a,, b t , c,, d t Rational Polynomial Coefficients of RFM 
3.2 Solution Method of RPC 
The solution method of RPC can be divided into two kinds: the 
first kind is the solution which has nothing to do with the 
terrain. This method is under the sensor rigorous physical 
model known condition, and establishes the image grid and the 
corresponding ground 3D grid, then calculates the RPC by the 
least square method according to the grid corresponding 
coordinates; The second kind is the solution with terrain. This 
method is suitable for the situation of sensor rigorous physical 
model is unknown, and needs to select 40 or more GCP, then 
calculates the RPC by the least square method according to 
these GCP ground 3D coordinates and corresponding image 
3.2.1 Solution of Normalized Parameters 
Before solves the RPC, in order to strengthen the stability of 
normal equation coefficient matrix, and avoids having the rank 
defect matrix, it needs to firstly carry on normalization 
processing to the GCP ground 3D coordinates and the 
corresponding image coordinates, and causes the coordinates 
normalized between -1.0 and+1.0. The method of 
normalization processing is stated as following formula 2 and 
normalization of the image coordinates: 
if the size of image is 2m x 2n, an( j t ^ e pj xe j coordinates of 
image center is ( m ’ n \ then the corresponding normalization 
parameters of image coordinates can be calculated by following 
SampOffset = m,LineOffset = n, ^ 
Samp Scale = m,LineScale = n 
normalization of the ground 3D coordinates: 
S'[Longitude V Latitude V Height 
LongOffset= , LatOffset= , HeightOffet = — (3) 
n n n v ' 
LongScale= maj^|Longtitud^ - LongOffsdf \Longtitud& m - LongOffs^j 
LatScale= ma^Latitud^. - LatOffsdf | Latitude - LatOffsdf) 
HeightScai = mat^Heigh^ - HeightOffet| |Height - HeightOffe\) 
According to above formula, the 10 normalization parameters 
of image coordinates can be calculated, then the ground 
coordinates (X,Y,H) and corresponding image coordinates 
(r )C ) after normalization can be calculate by these normalization 
parameters. Finally, the RPC also can be solved by these 
coordinates after normalization under the least square method. 
3.3 Generalized Stereopair Space Intersection Model Based 
on RFM 
When the orientation model of left and right image to construct 
the generalized stereopair are all RFM, then the corresponding 
space intersection mathematical model can be described as the 
RFM+RFM model, and its mathematical formula is:

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