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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
  
entities. Using this procedure, for the determination of the edge 
pixels of a geometric feature is only necessary the search of the 
maximum values in the accumulated table. 
In the location of straight lines (y - m: x ^n, p-x:cos0 * y: 
sen 0 ), the Hough transform is based in the transformation of 
the XY image plane into a mn image space (according the 
original formulation of the Hough transform) or into the pf 
"space (Duda and Hart, 1973) (figures 1 and 2). Using this 
procedure, all the lines that can be defined by one point A are 
transformed into two values (0,0) —or m,n values if the original 
Hough expression is applied— These couples of values will be 
stored in parametric form into the accumulated table increasing 
a unit the corresponding storage cell according the 
discretization parameters. 
  
g^ X 
Figure |. Parametric representation of a line 
(mn and p,0 space) 
  
Figure 2. Hough transformation for line extraction. a) synthetic 
images showing a set of blocks, b) edge detection, c) Hough 
transformation partial results (p,0 accumulative matrix), d) 
selection of the edges that belong to the same line 
In the case of the circles, the nonparametric equation of the 
curve to locate can be written like FORMULA, where () and r 
are the center and the radius of the circle, respectively. In this 
case, the parameters space is now a 3-dimensional space (x,y,r). 
Consequently, there will be necessary to define a storage cell of 
3 dimensions -N x M x NR- (figure 3). 
2.1 Edge operator 
For the edge point extraction, a Canny filter has been used. 
Previous to the filter application, a noise reduction process is 
carried out. Usually, in order to solve this problem, which can 
169 
affect to the edge detection quality, a gaussian filter with a c 
value between 1 and 3 is applied. The c value is dependent on 
the noise level of the image. 
  
m —————--- 
  
Figure 3. 
Once the image noise is reduced, the edge operator itself begins 
with the gradient calculation in all the image pixels. For this 
calculation, filtering based on first and second derivate are 
usually applied. In this paper, the Sobel operator has been used 
in order to obtain the gradient direction Gx and Gy. The 
gradient module and direction for each pixel of the image can 
be obtained using the following expressions: 
|G [= Gx” + Gy? 
6 = arctan (Gy/ Gx) 
  
In most cases the characteristics of the photogrammetric images 
produce a large number of extracted edges so several pixels can 
be related to the same edge. In order to avoid this problem and 
simplify the problem, it is necessary to reduce the total number 
of pixel that are considered as edge pixel. Using this procedure 
we obtain edges that are defined by a edge pixel chain. The 
procedure applied to this selection is the local maximum 
(suppression of non-maximum). The resulting edges will have a 
thickness of a single pixel. Finally, a binarization process is 
carried out in order to debug the extracted edges and minify the 
noise influence in the edge extraction. 
3. APPLICATION 
3.1 Interior Orientation Process Automation (OIA 
Program) 
3.1.1 Metric cameras images 
There are several methodologies for the inner orientation 
process automation (see Schenk, 2000 for a comparison and 
analysis of the different methods applied to metric images). In