The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
where x, y = map coordinates 
x', y' = image coordinates 
e 0 , fo, Ci, fj, gi, e2, f2, g2 = point based projective 
transformation parameters 
r 0 , s o> r i> Si, tj, r 2 , s 2 , t 2 = line based projective 
transformation parameters 
a, b = line parameters in ground coordinate system 
a’,b’ = line parameters in pixel coordinate system 
The projective transformation presented in equation 5 uses line 
coefficients of equation 2. There exists an equation applying the 
line equation 1 and the same projective parameter set as with 
point based transformation, presented in (Weerawong,1995), 
see equation 6. 
d'* \e { * cos«' * cos a" + /, * sin a'* cos«" 
+ e 2 * cos a' * sin a" + f 2 * sin a'* sin or" 
-d"*(e 0 *cos a' + / 0 *sina") ] 
+ g x *cosa" + g 2 *sm.a"-d n = 0 
e x * sin cc' * cos cc" — f x * cos«'* cos a" (6) 
+ e 2 * sin a'* sin a"-/ 2 * cos«'* sin a n 
- d" * (e 0 * sin a' - f 0 * cos a') = 0 
However, in our implementations the equation 6 was 
numerically too unstable with our data set and we could not get 
estimation to converge. On the other hand, the implementation 
of line parameters based on equation 2 and transformation 
based on equation 5 was successful and was the one used in this 
experiment. 
3. DATA SET AND TEST ARRANGEMENT 
The implemented estimation model was tested with QuickBird 
image acquired in spring 2006 in area of Vierumaki locating in 
southern part of Finland. The image was full image covering 
16.5kmx 16.5km area and landscape was was typical 
agricultural area including two small residential areas. The 
image consisted only multispectral channels and was 
preprocessed on the standard level resulting an upscaled image 
with 1.66m pixel size. 
As ground data topographic database from National Land 
Survey of Finland was used. From digital vector database road 
lines were selected as target vectors. The data was delivered as 
ESRI shape files. In database only centre line of the road was 
recorded. In order to filter out suitable straight lines from 
polyline spaghetti an own algorithm was programmed in EASI 
script language of PCI Geomatica software package. For the 
control lines only straight line segments longer than 100m were 
accepted. In filtering process all lines were examined taking 
care of straight line segment which extended over road 
junctions. In direction of successive line vector only 2.5 deg 
difference was allowed. 
Correspondent line features were digitized from image 
manually. An alternative way would have been to apply some 
algorithm dedicated to road extraction, but since there was not 
such an algorithm available in software package and the 
primary goal in this investigation was to study accuracy of 
transformation with straight lines, the manual approach was 
considered to be adequate. 
Altogether 30 lines were selected and measured from image. In 
addition 20 check points were measured in junctions of road 
network. The points selected consisted a fairly even distribution 
on an image. From 20 check points four were used as ground 
points for the purpose of comparison of point wise and line 
based methods. The remaining 16 points were used in both data 
sets as check points for testing an accuracy of transformation. 
Image measurements could be observed within precision of 
pixel or half a pixel. For the part of the topographic database 
location accuracy of road network was reported to be 3m on 
average, with higher level road network the location accuracy 
was apparently better fhan this, but with forest truck roads 
worse. Unfortunately, also line segments from lower level 
road network had to be used especially in forested area in order 
to get a proper line segment constellation. 
4. RESULTS AND ANALYSES 
The pixel observations of road line segments were used in 
estimation of line parameters of image lines. The same 
procedure was applied for node points of polylines filtered out 
from road network. These line parameters were then treated as 
observations of projective transformation in LSQ adjustment 
according to equation 5. Respectively, four check point pairs 
were used in LSQ adjustment of point wise projective 
estimation according to equation 4. All estimation procedures 
were programmed as MATLAB code. 
In computation of line based projective transformation some 
numerical instability was noticed. Therefore it was considered 
to be necessary to get both data sets centered before line 
parameter estimation in order to stabilize the computation. 
Similar approach has been earlier presented in (Heikkila,1991). 
The final adjustment was also computed in this shifted 
coordinate frame. In projective line adjustment the inverse of 
posterior line parameter variances from line estimation were 
used as weights in LSQ adjustment. After solving line 
projective parameters the equivalent point based parameters 
were computed according to equation 7. 
This parameter set was then used to calculate forward and 
backward projective transformation in check point pairs in 
order to verify the accuracy of transformation, see table 1. In 
order to compare point wise and line based transformation four 
ground points were used to compute point based projective 
transformation and equivalent accuracy assessment was 
performed in same 16 check points, see table 2. 
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