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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
This procedure starts from big circles and proceeds to small 
circles until all appropriate candidates in the accumulator will 
be put in a list. 
  
Figure.6. The structure of accumulator for circle hypotheses. 
3.2.1 Constructing a minimal convex covering for a set of 
extracted circles: It is a standard procedure of computational 
geometry. The only modification of it in our application is 
connected with a fact that we deal with circles but not with 
points. Due to this fact, the convex covering should consist the 
arcs of circles as well as segments of lines between them. 
However, we use the approximate computational scheme that 
allows representing the convex covering just as a closed 
polygon without arcs. This approximate procedure is performed 
in three steps: 
e Find the minimal convex covering to a set of circle centers; 
e Find the mass center of vertices of this covering 
e Expand this covering by translating the cach its points by 
vector from mass center with length of circle radius at this point 
Our experiments have demonstrated that the precision of such 
approximation is appropriate enough for this application. 
  
Figure. 7. Minimal convex polygon (blue) as an expansion of 
minimal convex covering for set of centers (red). 
3.2.5 Reconstruction of non-detected circles: As we state 
in the previous section, our approach is based on an assumption 
that all cuts (circles) lay approximately in one plane. However, 
it the real cuts may not satisfy this condition. Therefore, on the 
ortho transformed image some cuts will screen the other cuts. If 
the big cut screen the small cut, the small become "invisible" 
for the detection algorithm due to low number of visible points 
on its contour. Fortunately, these «invisible» objects make the 
“holes” in the entire structure of the circle set. In our algorithm, 
the holes inside the covering polygon are detected to recover the 
lost cuts (circles). 
Sometimes this recovering algorithm fails, when it try to fill the 
hole from one lost circle by two or even three smaller circles (if 
the environment allows such decision). However, the estimation 
of sum of cuts' areas still better that for the case without 
recovering of lost circles. 
3.2.6 Computation of required area parameters: Finally, 
three basic characteristics of the bundle are calculated: 
e The number of cuts in a bundle 
e The total area of cuts in a bundle 
The area of bundle bounded by a minimal convex polygon. 
  
  
  
  
  
Circles Number=53 
Bundle Area.- 26786.2 [mm2]! 
Circles èrea= 127731 [mme] 
  
  
Figure. 8. The final result of the computations. 
3.2.7 Manual measurement mode: The system designed for 
working in off-line mode to process previously acquired and 
stored images in automated, semi-automated or manual mode. 
In semi-automated mode software recognize any single circle in 
the orthophoto and find its diameter and area. To find the area 
of single cut operator has to mark it by mouse click. The 
recognized circle is displayed and its parameters are shown in 
message box. The result of semi-automated cut extraction is 
shown in Fig 9 in “Transformed” window and 
“Measurements” message box. Operator also can delete false 
recognized cuts (if any) and store results in report file. 
In manual mode operator can perform any 3D measurements 
basing on given stereo pair. He can measure 3D coordinates of 
spatial poin* marking it in the left. and right image. For 
determining distance between two spatial points the 
corresponding image points have to be marked in the left and 
right image. Fig.9. illustrates distance measurement. Markers #1 
and #2 determine the diameter of the same cut as extracted in