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Figure 2: Measurement of straight lines 
minimizing the sum of the square distances of projection beams of points on this line and the line itself (Andresen, 91). 
Initial values for the non-linear minimizing problem are generated with the two-plane intersection method. 
The two approaches of straight line measurement are easily extended to aquire position and shape of cylindric objects 
(e.g. pipes and vessels): 
Two points of the visible edge of the cylindric object lead to a plane in space touching tangentially the object. The two 
planes at either side lead to a center-plane. The centerline of the cylindric object falls into this center-plane, so the center- 
planes of two images have to be intersected to obtain the objects centerline (Fig. 3 A). Assuming errorless data the object’s 
radius is the perpendicular distance to the tangential planes. A reasonable radius from eight edge-points in two images 
is obtained as the mean-value of the distances of the eight projection-beams to the centerline. The edges are found using 
Hough-transformation in manually selected rectangular segments (Fig. 3 B). 
  
Figure 3: Measurement of cylindric objects (A) and digital edge detection (B) 
The statistically exact solution to measure shape and position of cylindric objects has been shown by ANDRESEN in 
(Andresen, 91). It minimizes the residuals of the radius and the projection-beam—centerline—distance directly leading to a 
radius and centerline-coordinates for the cylindric object. 
While ANDRESEN’s method has been successfully used for measurement of large-scale cylindric objects (vessels) it 
failed frequently for low-scale objects as pipes due to deficient orientation and imagepoint data. The simple method of 
intersecting centerplanes proofed to be stable in either case. 
The method of intersecting centerplanes is easily extended to measure position and shape of conic objects (Fig. 4). While 
the centerline of the object is calculated analogously the radius of the cone is a linear function of the centerline-position. 
The parameters of this funtion are obtained from eight (or more) projection-beams in two (or more) images by linear 
regression. 
This set of feature-measurement-technics is used to obtain position and shape information which are completed to the 
entire plant-model with CAD-—modelling-technics. 
2.2 Modelling 
The modelling of process plants with computer-aided-design technics (CAD) is highly dependend from design rules for 
this plants. Design rules determine the choice and position of plant-components. This will be illustrated by the following 
examples: 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 109