The constrained relationships. between different objects, 
can be introduced by attaching or nesting the individual 
(parametric) objects to one another. Both methods, nesting 
as well as attaching, define a fixed geometric relationship 
between two objects: they can share an edge, have com- 
planar sides or the like. Nesting an element also introduc- 
es a hierarchy in the model which can be used as a means 
to provide different levels of detail. A more detail descrip- 
tion of the modelling concept is given in (Hirschberg, 
1996). 
3.2. Feature measurement 
The feature measurement employed in DIPAD is a semi- 
automatic routine, where a generic object model is used to 
detect the features described by this model. Therefore, 
only relevant features (as defined by the user) are extract- 
ed and redundant or useless informations are reduced to a 
minimum. The use of a priori knowledge makes explicit 
assumptions, that allows the checking of whether or not 
these assumptions are fulfilled in the images. The three- 
dimensional position of the object is derived by a simulta- 
neous multi-frame feature extraction, where the object 
model is reconstructed and used to triangulate the object 
points from corresponding image points. 
Although boundaries of objects are only a small percent- 
age of the whole image content, they have major impor- 
tance for the description of object discontinuities. This 
routine takes advantage of this knowledge, by first locat- 
ing the edges of the features to be measured and then de- 
riving the vertices as intersections of appropriate lines. 
This routine consists basically of three loops (see Fig. 2). 
First an internal loop performs the feature extraction in 
2D-space, based on the radiometric information given by 
the digital imagery. An external loop allows the determi- 
nation of object coordinates from multi-frames, and final- 
ly an orientation loop provides for the estimation of the a 
priori unknown camera parameters (interior/exterior ori- 
entation) by a bundle adjustment. 
3.2.1 Internal loop 
The approximation of object space features transformed 
into image space are used as starting values for the two-di- 
mensional automatic extraction algorithm. It is based on 
the assumption that discontinuities or rapid changes in the 
intensity of the image signal often occur at the physical 
extent (edges) of objects within the image. 
Local searches are carried out at regular intervals along 
directions perpendicular to the approximate (a priori) 
  
  
| CAD Model 
  
  
  
| 3D-FEX 
  
  
  
  
performed in: image space 
[1 object space 
Figure 2: General data flow of feature measurement 
550 
boundary. A Sobel edge operator (Eq. 1) is applied to each 
of the discrete points along each of these perpendicular di- 
rections. 
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Every pixel is assigned a gradient value, which is a vector 
containing the amplitude and the direction. The spatial 
gradient amplitude is given by: 
e(j,k) = Ag, G. K^ * g,G; K^ (Eq. 2) 
The direction of the spatial gradient with respect to the 
row axis IS: 
gc(J, k) 
e, I 
For each such direction, the pixel with the highest ampli- 
tude within a user defined search window, starting from 
the approximate line, is pre-selected as an edge pixel. This 
pixel has to be confirmed by applying the same search 
window, now starting from the previously selected pixel. 
This procedure continues until the selected pixel remains 
at its position. 
6(j,k) = arctan -n«0«mn (Eq. 3) 
The subpixel position of the edge is then determined by 
fitting a second-order polynomial (parabola) in the direc- 
tion of the gradient. The maximum point of the fitting 
curve corresponds to the subpixel position of the edge (see 
Figure 3). 
The coefficients (co, c, c2) of the parabola 
fu) = CotCp utc, u (Eq. 4) 
image intesity 
   
  
image coordinates (u) 
  
   
  
parabola 
gradient amplitude 
image coordinates (u) 
Figure 3: Estimation of edge point with subpixel 
precision 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
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