Reference image 
    
«dx 
Ea AE) 
Ll LLL AM EE 
D Lu a uua nu 
/ / Groundel grid 
Figure 2. Geometrically constrained line matching by 
search. 
     
   
EP 
  
The initial position of the line is determined by extracting 
the line segment from the reference image. With the help 
of known orientation parameters and an approximate Z- 
coordinate value the 3-D coordinates for the end-points 
are computed. As the position of the line is fixed on the 
reference image, the position of the line in object space 
has only two degrees of freedom. End-points are 
constrained to move along the collinear rays joining the 
projection centre of the reference image with the 
corresponding image point in the reference image. 
Next the end-points of the 3-D line are incrementally 
changed at chosen intervals and within the given limit. 
After each step, a groundel grid is formed into the object 
space, see Figure 2. This rectangular grid is formed so 
that the current 3-D line belongs to it. Elements in the 
groundel grid are given intensity values, which are 
computed from images by a geometric transformation. 
The geometric transformation contains a spatial 
transformation similar to orthoprojection and a common 
gray-level interpolation. At this point, the intensity values 
in the groundel grid can be normalized into the required 
mean and variance. The first version of the groundel grid 
is computed from the reference image. This grid serves 
as a reference grid with which other grids are compared. 
The groundel grids from other images are computed 
similarly. 
In each step, the difference between the reference grid 
and the search grids is computed. The difference is 
expressed by a mean-square error (03) computed from 
the formula 
-- 
— 
= 
VS S Caisse) 
k=1i=0 j=0 
Imn—1l 
= 
_ 
O4 = 
where 
£,(i,j) intensity of reference groundel grid 
g,(i,j) intensity of search groundel grid 
l number of search images 
m number of column elements in the groundel grids 
n number of line elements in the groundel grids. 
The search step in which the mean-square error is at its 
minimum is the best match in the terms of least squares 
matching. 
Geometrically constrained line matching by search can 
be utilized in the matching of planar faces. The planar 
face of interest is extracted from the reference image. 
Two edges of the face are matched to the other images 
using the method described. From these two matches the 
equation of the plane in object space is computed. After 
this the final vertices of the planar face are determined by 
computing the intersections between the plane in object 
space and the set of rays coming from the reference 
image. Plane matching can also be implemented using 
least squares matching by search. In this case, it will still 
be reasonable to limit the search space by first matching 
one of the edges of the planar face by line matching. For 
example, a roof face would have only one degree of 
freedom if the correct position of the top of the roof is first 
searched. 
4. DISCUSSION 
Boundary models are generally applied in CAD/CAM 
software. Modelling tools in these packages are not 
usable as such in photogrammetric mapping. However, 
the kernel software defining and handling the geometric 
data structure can be the same in both applications. Only 
the high-level tools handling the geometric model have to 
be specialized e.g. by writing an application-dependent 
layer of tools above the kernel. 
The use of boundary models in building extraction does 
not require that the geometric model of the building is 
always created from nothing. In practice, it is reasonable 
to have predefined models for the most common types of 
building. The use of predefined models is similar to the 
use of parametric models. However, there is one 
significant difference between these two approaches: 
parametric models can be modified only through their 
parameters, while boundary models offer general 
editability. Parametrization of a new building class at the 
moment of extraction could be extremely useful in many 
cases. 
The accomplishment of many geometric tasks can be 
embedded inside the tools editing the data structure. 
These include generation of eaves by moving wall 
elements inwards, automatic completion of a model after 
‘a minimum number of features have been extracted and 
the preservation of the geometric integrity of the solid 
model. Some of these tasks cannot be implemented in a 
general way relevant to all different object types. 
However, the use of a common basis upon which this 
functionality can be built is beneficial. 
216 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996 
Th 
en 
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