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.
1097