International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
produced is used as reference for positional 
improvement and updation. 
In the other project the digital vector data was not available. The 
existing maps are scanned and 2D Vectorization of the features 
carried out for subsequent use in the positional accuracy and 
updation process. 
accuracy 
2. POSITIONAL ACCURACY IMPROVEMENT (PAI) & 
TRANSFORMATION REQUIREMENT 
2.1 PAI 
This process assumes existing data is relatively correct and 
Geometric/Absolute accuracy is within specified tolerance 
limits. In this process, attempt is made to improve the accuracy 
of existing data. The user must specify the amount of 
displacement required at several well distributed points 
throughout the map using the available information form ground 
survey or latest orthophoto or stereo model. 
Positional Accuracy Improvement (PAI) requires a special kind 
of transformation to the vector data to improve the overall 
accuracy with minimal change to the following accuracies. The 
allowable limit varies depending upon the scales of data sets, 
but the basic principles remains the same. 
Relative accuracy: lt is a measure of how close is the distance of 
a line measured on map agrees with the corresponding distance 
measured on ground. 
Absolute accuracy: lt is a measure of how close is the co- 
ordinate of a point on map agrees with the corresponding co- 
ordinate of the point measured on ground. 
Geometric fidelity: It is a measure of how closely the feature on 
the map matches the real-world shape and alignment 
2.2 POSSIBLE SOLUTION FOR PAI 
In order to maintain the relative, absolute and geometric 
accuracy within required tolerance limits while carrying out 
transformation, is rather complicated. Solution can be achieved 
in 2 steps 
1. Identifying required displacement 
2. Applying special transformation for PAI 
Again it may not be possible to notice the amount of shift 
required at all the places through out the map, especially where 
accuracy matters the most. The amount of shift has to be 
identified on raster Orthophoto, where it can be identified. 
The solution for special transformation for PAI can be 
divided into two parts. 
I. Defining the smallest area, which will act as 
transformation unit. 
2. Defining transformation formulae, which ensure smooth 
transition across such unit areas. 
2.2.1 Defining unit area for transformation. 
One kind of transformation can't ensure that the displacement at 
all points is same as desired. Traditional affine transformation 
can ensure this in side a triangle and projective transformation 
can ensure the same inside a quadrangle. Expansion, geometric 
contraction and dilation of the affine transformation do work in 
a particular direction but the requirement of the project is quite 
complicated. For example expansion is an affine 
transformation, in which the scale is increased and it is opposite 
of the geometric contraction. This is not the single requirement 
because apart from scaling it has to take care of rotation and 
UA 
translation. Since controlling the amount of displacement across 
the edges of the triangle is more complicated, it was decided to 
divide the whole area into small triangles based on Delauney 
triangulation, which will lead to a better control of smooth 
transition across the edges. 
2.2.2 Defining Type of transformation. 
Many of the traditional approaches used for PAI are based on 
one of the following possible methods. 
1. Inverse distance function 
2. Inverse square of distance, (acts like potential field). 
3. Affine transformation. 
Type | & 2 transformation approach will simply not work for 
such transformation in side a triangle as there is a need to 
guarantee the smooth transition across edges. Type 3 uses 
differential scaling in different directions, making it difficult to 
control scaling factor throughout the map. 
So the need is to opt for a simple weight based transformation 
solution, which will localise the transformation in the triangle 
(the effect of displacement should not be distributed over the 
complete map). The requirements are as follows 
1. At corners resultant displacement should be same as 
specified displacement 
Smooth and gradual change across such unit areas 
Transformation should be smooth inside the triangle 
Retain existing relative, absolute & geometric 
accuracy 
SH N 
Out of few possible solution for defining distribution of Weights 
inside a triangle following methods were tried 
l. Weight proportional to distance from opposite 
sides 
Weight proportional to the area of triangle 
formed with other 2 vertices 
[9] 
3.1 TRANSFORMATION USING WEIGHT 
PROPORTIONAL TO DISTANCE FROM OPPOSITE 
SIDES 
  
P 
(Figure -1 Weight proportional to distance from 
opposite sides) 
The Weight of displacement vector at point T are calculated as 
follows 
Inter 
WtA 
WiB 
WiC 
Whe 
ABC 
T= 
Wt- 
This 
good 
foun 
unifc 
unifc 
Henc 
woul 
edge 
trian; 
23 
of tr 
The \ 
WtA 
WiB 
WiC 
Wher 
ABC 
T=A 
Wt 
Th 
distar 
ends) 
additi 
throu, 
where