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 
control and ensure field works. À map with 
elaborate drawing and high quality can be 
made soon. 
Now the given digital photo-planimetric 
method is five control points to rectify digital 
image in 2000 Japan announced the patent 
"The map drawing's system and method", 
which is a manifestation of the state thought, 
But that method calls nine control points for 
rectification, So the given technology is much 
useful. 
Also in the texbook there is "The photo map 
can be used as relief map" as well as the rules 
saying that in the level terrain arial 
photogrammetry must follow 
Photo-planimetric method. 
3. Theory of five control points for 
rectifying digital image 
It is known to all that the rectification for 
photographs needs five control points, for it 
will be difficult when control points are many 
the requirements for figure of the point's 
costs time and money. 
But the more control points, the easier will be 
the mathematical process of digital 
rectification. As the Japen method which 
found nine control points to rectifying is still 
beyond the capability of field works. Besides, 
the theory of Japanese is linear and triangle 
method. That is simple and can’t afford to 
draw 1:500 scale maps. 
It is difficult for five control points to 
rectifying and ensuring the high accuracy, 
for the requirement of the Interpolation’s 
analysis feature is very strict it should be a 
smooth surface. 
The formula derivation goes as follows: 
As we know that a linear spline is the 
solution of an equation based upon a small 
deflection of an infinite beam. So the surface 
splines are the deformation of an infinite 
plate bending only. The differential equation 
relating bending deflection and the load of 
the plate is 
DV4W=P (1) 
D = flexural rigidity of the plate 
W (x y) — lateral deflection 
P= lateral load 
The hypothesis used as basis goes as 
following: 
1 Deflections are specified at N independent 
points (xi, Yi) i =1...N Here needs to know the 
point loads Pi at these N points. When the 
load is determined, the deflection will be too. 
For example, if we want to know the 
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