the shadow of a wall is changeable, according to the bearings 
of wall features o, and the solar azimuth a, thus, the second 
weighting factor to be considered is given by 
cos(n /2-j, —a, |), if 0xl, -a,|«n/2 
cos, -a.,| - n /2), if n/2X|, -a,|«n 
) if x <ja, -a,|<3x/2 
cos(fot, -a,|- 31/2), if 3 sk, -a, «2n 
cos(3n / 2 - lo, m 
  
In order to carry out image-and-map registration, the vector 
data of the cadastral parcels with walls have to be provided by 
spatial information systems and then converted into image 
space, according to the imaging geometry and/or the processed 
level. If the header data of Quickbird images gives relatively 
good approximate geographic location of each corner, say on 
the order of 10m, it is possible to start image-and-map 
registration with no human intervention at all. However, 
selecting a reference point manually identifiable both on map 
and in image could speed up registration. The U-shape model 
of intensity profile of a shaded wall is certainly not secured to 
find an unique location for image-and-map registration, 
therefore, the geometric characteristics of all polygons, i.e., all 
of the given parcels with walls, have to be taken into account. 
Then, all of the searching results of polygons are compared 
with each other to filter out any candidate locations whose 
geometric structure is not conformal to the vector data. In other 
words, most of the polygons should have the best match at the 
candidate locations with the same magnitude of translation and 
rotation. 
2.3 Image-and-Map Registration Error Modelling 
Automation of photogrammetric practices are mainly based 
upon prior knowledge derived from the manual operations, 
therefore, error modelling on image-and-map registration has 
to start with the analysis of the errors resulted from manual 
operations. In case of the registration of a vector map and a 
geometrically rectified image, the errors of registration may 
result from various aspects. Errors coming from a rectified 
image include residuals of rectification o;, random errors in co- 
ordinate measurements of  features/points Om and 
misplacements of the identified features oy, such as walls, with 
respect to the expected boundary lines. On the other hand, 
errors resulted from a vector map contain residuals of 
surveying adjustment o, and the error of digitisation of 
cadastral maps o4. Obviously, image-and-map registration is a 
process of linear combination of two types of data, and the 
resultant error G, is propagated and derived as 
  
2 
2 2 2 2 
e. = Jo} £0 +0 tal +0, (2) 
The magnitude of rectification error o; depends upon the 
imaging geometry, algorithms of rectification, ground 
control/DEMs, and the terrestrial flatness. Since the advanced 
satellite optical sensor produces images of 0.6m GSD, it is not 
always available to derive DEMs of excellent accuracies on the 
order of deci-meter, and the production of ortho-rectified high- 
resolution satellite imagery of good quality is not guaranteed. 
However, the rectification of satellite images over flat areas 
does not necessarily need DEMs, and the proposed algorithm 
for image-and-map registration is primarily aimed at flat areas 
   
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
at this stage. Ground control is also not essential, provided 
that on-board satellite positioning systems gives good 
approximation of geographic locations for images. Thus, the 
imaging geometry of the satellite sensor and the algorithm 
to be used in rectification has to be considered. Assuming 
that the rotational angles in across-track direction (pitch) 
and in vertical direction (yaw) are relatively small and 
neglected, the first author proposes a simplified equation to 
calculate the relief displacement d, resulted from undulated 
terrain surface in oblique satellite images regarding to the 
rotational angles in along-track direction (roll). It is given 
as 
(f —r tan (Xf tan’ +r) 
H 
Hf {1 + tan? 1 (3) 
(00055) un 
if t — 0, then. d, & A 5—— —— — zh-— 
He lc 
if H>>h, then d, «A 
where H= flying height, /-difference of elevation, f= focal 
length, r= tilt angle (roll), r=radial distance from center to 
an arbitrary point in image space. It can be calculated that 
an elevation difference of 10m over the entire imaging area 
may result in difference of relief displacement less than 0.3 
pixels, in the case of the Quickbird imagery. This modest 
displacement is due to the imaging geometry of extremely 
narrow angular filed of view and relatively flat terrain. 
Since the cadastral parcels are located at relatively flat 
areas, where terrain variations are under 10m, the 
magnitude of rectification error o; is relatively insignificant. 
The second factor of errors oy, is caused by random errors 
in co-ordinate measurements of features/points and is 
related with the image sampling and re-sampling 
procedures. It is obvious that a line feature of ground 
distance of 1 GSD in a basic (raw) image taken (sampled) 
by a satellite sensor may be sampled by 2 pixels in a 
standard image, i.e., the blurred edges of the line features 
in a rectified and re-sampled (standard) image convey 
deviations up to 2 pixels. The third factor of errors or is due 
to intentional misplacements of the identified features, such 
as walls, in respect to the expected boundary lines. 
Regulations of local governments demand some extent of 
retreat in setting up walls regarding to the exact boundary 
lines of a cadastral parcel to give way to the surrounding 
roads and sidewalks. The extent of the retreat of wall is up 
to 3 m, or 5 pixels in Quickbird imagery, contributing the 
major error to the results of image-and-map registration. 
The forth factor of errors is the residuals of cadastral 
surveying and adjustment c, conveyed in the vector data of 
cadastral parcels. The residuals of cadastral surveying 
practices and adjustment computations are on the order of 
centimetres, which is certainly much better than one GSD 
of any advanced satellite optical sensor available. That is 
also the reason why cadastral maps are proposed to provide 
ground control for image-and-map registration. 
In case that digitization for existing cadastral maps, instead 
of surveying by using total-station or electronic distance 
measurement (EDM) instruments, are the sources of vector 
data, the fifth factor of errors o4 is resulted from the 
process of digitization. The scale of cadastral maps is 1/500 
(urban areas) or 1/1,000 (rural areas) for the new version of 
cadastral maps in Taiwan and is 1/600 (urban areas) or 
  
   
     
    
  
    
  
    
   
    
   
  
   
    
    
   
   
  
   
   
     
    
   
    
  
  
  
  
     
    
  
   
   
   
   
    
   
  
   
   
   
   
   
  
    
  
  
  
   
    
    
   
  
     
    
  
      
   
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