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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B4, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
symmetrical deflection of the origin point 
when the load is P, use the equation (1) 
Where X= rcos 6 
Y=rsin 0 
And we get 
W(r) = A+ Br?+(P/16 1 D)r2.1nr? (2) 
In the equation (2), A, B are undetermined 
coefficients while P is point load. To continue 
the derivation that will set two hypothesis: 
1 Deflection is symmetrical at the points with 
load. 
2 The surface splines will be flat if far away 
from the applied loads. 
The deflection of the whole splines is the 
summation of the equations (2): 
Pe 
Means Wr(r) = 
IM 
A+ Br2+(P/16 x D)r?.Inr? 
p 
(3) 
And after deduced and combined we get 
N 
W(x, y) =A+Bx+Cy+ 
i=l 
Fr nr; 
(4) 
Here 
r? —(x-x)2* (y-yj? 
Equation (4) need to solve N+3 unknown 
quantities. 
Here N = 5 so add 3 equilibrium 
equationsand then form 8 linear equations, 
153 
and get the final answer. In this way which 
can correct the image point by point while 
avoid its translating and rotating, that is due 
to. the function of the equilibrium 
equations.Formula (5) is equilibrium 
equations. 
YFi=XXiFi =X YiFi=0 (5) 
4. Function of the software 
This software can work as a rectifying 
apparatus and make image map 50cmx50cm 
from aero photograph based on five control 
points. The name is *five points method". It's 
easy to operate, anyone who can use PC 
works with it smoothly: there's no special 
skill for operation and the data to enter is 
little. It’s easy to find an appropriate PC, for 
any ordinary PC can do the job. 
The processing steps are as following: 
1 Scan the photo or image into PC 
2 Enter the coordinate of the control points 
3 Identify the control points on the photo or 
image (recognition of control points) 
4 Supply mapping scale 
5 Rectifications 
6 Get photo map 
5 Examples