The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
v = ASx-(l-l 0 ) 
(7) 
In this study the straight line parameters have to be estimated 
and the accuracy of the estimated parameters is important. The 
covariance matrix of the unknown is computed by 
multiplication of estimated factor variance ( Oq ) and the 
cofactor matrix (N 1 ). 
C X x = 
The diagonal elements of 
C X X = C Otpxoyoz 
(8) 
(9) 
Figure3. Sample of LIDAR range Last Pulse data (endpoints are 
in red colour) 
(X, Y, Z); are object coordinates of the endpoints of the building 
edges. From those the straight line parameters are simply 
calculated according to 
give the accuracy of all line parameters of interest. In order to 
have “tangible” results of the unknown’s accuracy, it is useful 
to calculate a point based accuracy using X, Y, Z coordinates in 
the object coordinate system. 
By using variance propagation rule the covariance matrix of X 
Y Z will be calculated as: 
Cxyz — MCe^yosM (10) 
Where M is Jacobian matrix formulated as follows: 
9-nil- Arc tan(A^/, — ) 
/VAX +AY 2 
</> - vfrctan2(AF/^) 
(12) 
(13) 
'ax 
dX 
dX 
dX 
dx' 
(11) 
*0 
so 
dtp 
dx o 
dyo 
ds 
To 
— ^4>e 
Y, 
M = 
BY 
dY 
dY 
dY 
dY 
s. 
Z, 
60 
dtp 
dx o 
dyo 
ds 
dZ 
dZ 
dZ 
dZ 
dZ 
SO 
dtp 
dx o 
dyo 
ds 
3. METHODOLOGY 
The main goal of this study is the estimation of 3D straight line 
parameters. Those parameters are <f>,9, x 0> y 0 and s as parameter 
of point position on the straight line. 
This is realised by taking advantage of the LIDAR data in a first 
step in which initial values of unknown line parameters are 
calculated and search space for finding corresponding lines in 
the images is significantly narrowed down. In a second step the 
high resolution aerial images are used for extraction the 
corresponding lines and estimating the unknown 3D line 
parameters. 
3.1 Utilizing LIDAR data to calculate initial values of 
unknown parameters 
The main objects used in this study are the buildings, so the last 
pulse range data are used. The endpoints of the building edges 
are interactively measured in the LIDAR data (cf. figure 3 as an 
example). With this measured endpoint coordinates the straight 
line parameters {(/),9, x 0j y 0 , s) are determined. 
By multiplication of the object point coordinates with the 
rotation matrix the line parameters x 0 , yo and the respective 
point position parameter s are found: 
(14) 
The calculated straight line parameters from LIDAR data are 
used as initial values for the next step. 
3.2 Using high resolution aerial images for estimating 
unknown 3D line parameters 
There are three different options for straight line measurement/ 
extraction in/from the images used in the experiments: 
1) Measurement of two fixed points (endpoints of the 
specific straight line). 
2) Measurement of sample of the points on the straight 
line. 
3) Selection of endpoints of the straight lines which are 
automatically extracted. 
Figure 4 shows the measured corresponding endpoints of the 
straight lines in each image. The six unknowns tf>, 9, x 0 ,/y 0 , si 
and s 2 are estimated from the four observation equations (two 
points) related to each image. If n is the number of images, the 
redundancy can be calculated according to r = 4n - 6. Thus 
with two images there is already a redundancy of two. 
Figure 5 illustrates the situation if various points are measured 
on the straight line without any restriction of the point selection 
along the line. 
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