International Archives of the Photo 
  
  
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4. DATA PROCESSING 
Data processing for generating a precision building model from 
the acquired sensory data involves two main processes, 
registration and modelling. 
4.1 Registration 
Each data set is defined in its own local coordinate system. To 
combine such data sets, we should determine the relationships 
between the coordinate systems. Registration aims at defining 
about an absolute coordinate system the local coordinate system 
in which each data set (either laser scanner point clouds or 
digital camera images) is expressed. Registration is based on 
the reference points. 
4.1.1 Mathematical model for registration of point 
clouds: we establish a model graph for the point clouds 
acquired at all the positions, as shown in Fig. 3. The model 
graph includes each point cloud as a node and represents the 
existence of overlap between two point clouds as an arc. Each 
arc incorporate a transformation represented as T; , which 
establishes relationship between two coordinate systems in 
which two point cloud are defined. It makes it possible to 
convert a point cloud into the coordinate system of another 
points and vice versa. The final goal of the registration is to 
convert each point cloud into an absolute coordinate system 
denoted as G. This transformation is denoted as T;; . Both 
kinds of transformation, 7; and 7j; are classified into 3D 
similarity (or called rigid-body) transformation that have three 
parameters for rotation, (0,9, «) and three parameters for 
translation, (x, y,.z,) ). defined as 
x; XG *, 
YN; = R( , 0, K) Ya + X , ( ] ) 
z ZG =, 
! 
where R(w,#,x) is a 3D rotational matrix defined as 
1 0 0 cosó 0 sing | |cosK — sink 0 
0 coso -Ssino/ 0 1 0 ||sik. cosk .O 
0 sino  coso —sing 0 cosó 0 0 | 
  
  
  
  
  
  
  
  
  
  
  
  
Figure 3. A model graph for point clouds 
erammetry, Remote Sensing and Spatial Inf 
ormation Sciences, Vol XXXV. Part B7. Istanbul 2004 
    
41.2 Mathematical model for registration of images: we 
establish a model graph for the images acquired at all the 
positions, as shown in Fig. 4. The model graph includes each 
image as a node and represents the existence of overlap 
between two images as an arc. Each arc incorporate a 
transformation represented as Rj which establishes relative 
orientation between two images (Ii, Ij). The final goal of the 
registration is to establish the exterior orientation E;; between 
each image and an absolute coordinate system. With the 
exterior orientation, we determine where a point in the object 
space appear in an image based on the collinearity equations 
> I (Xg T Xo y + (Ye = Yo )» t (Zg —- Z9) 
ll Xe -Xo}n te 7 Yon am la 
hes Kg = XI +g = Yorn * Uo = Zo 
Er (Xe - ‘alu * (Y; - Yos * (Zo - Zo)'s 
where (x;,y;) is the image point corresponding to the ground 
boint. (X&,YG.Zg defined in an absolute coordinate system; 
G^*JG G J , 
(Xo, Yo, Zo) are the coordinates of the position of the camera; 
and (r,) is an element of the rotational matrix composed by 
three rotation angles (&,ÿ,Æ) indicating the orientation of the 
camera. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
^a x 
Rai | | Ros 
x ® 
| Eacı Esc 
14 Ru [3 
  
  
  
Figure 4. A model graph for images 
4.1.3 Parameter estimation using block adjustment: We 
estimate the transformation parameters associated with the 
registration of point clouds and images using block adjustment. 
The main characteristic of the block adjustment is simultaneous 
determination of the transformation parameters of the entire 
data sets rather than sequential determination of the parameters 
of each individual data set. We establish a set of non-linear 
equations associated with the entire data sets. This set includes 
the transformation parameters as unknowns and the coordinates 
of some points in the data sets as observations. Some points 
among the points used as observations are also measured by à 
total station to provide their coordinates in an absolute ground 
coordinates. These points serve as control points that relates the 
data expressed in local coordinate systems to the ground 
coordinate system. In case of the example in Fig. 2, four sets of 
3D similarity transformation parameters for the point clouds 
and four sets of exterior orientation for the images are to be 
estimated. 
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