Chapman, David 
  
  
Random sampling of quadric Least-square fit 
X. Ye Ze l m n R X, Y. Ze l m n R 
Pipe1 740.90 -2315.08 369.43 0.93 0.36 -0.01 95.39] 737.00 -2300.00 366.00 0.93 0.36 -0.01 84.70 
741.00 -2320.00 369.00 0.93 0.36 -0.01 95.40| 395.00 -2420.00 364.00 0.92 0.38 -0.04 79.60 
679.00 -2320.00 359.00 0.91 0.43 -0.03 75.00! 676.00 -2330.00 365.00 0.94 0.35 0.01 82.70 
Pipe2 121.82 -624.10 1210.43 0.34 -0.94 0.01 61.41 119.00 -626.00 1200.00 0.34 -0.94 0.00 52.30 
20.30  -329.00 1220.00 0.33 -0.94 0.03 69.40 14.80 -332.00 1190.00 0.33 -0.94 0.02 50.60 
84.50  -516.00 1210.00 0.34 -0.94 0.01 63.70 80.20 -518.00 1200.00 0.34 -0.94 0.01 52.60 
Pipe3 749.00 -2150.00 -476.00 0.92 0.39 -0.03 28.20] 751.00 -2160.00 -493.00 0.93 0.38 -0.03 40.70 
507.00 -2240.00  -632.00 -0.64 -0.29 -0.71 26.90| 526.00 -2250.00  -644.00 -0.64 -0.29 -0.71 45.40 
  
  
  
  
  
Table 2. Comparison of initial values from quadric fit using random sampling and least-squares cylinder fit 
5 RESULTS OBTAINED 
A large number of planar and cylindrical objects were extracted from the range-image data. As anticipated the system 
exhibited some degradation when attempting to recover data from specular reflectors such as the metal cabinets and 
aluminium pipe lagging such areas are visible in the intensity image showing areas where the sensor has saturated 
(figure 4a). The mask image (figure 4c) image also shows the masking of sections of the range image which, although 
unavoidable in any active triangulation system, are minimised by the short baseline employed in the Biris sensor. 
  
  
  
  
Figure 4 a,b,c. 256 x 1024 Biris intensity, range and mask images (indicating missing or null data). Note dark highlights 
on piping indicating specular reflections of laser stripe. 
Typical RMS errors for cylinder fitting were of the order of 1-2mm and demonstrated good overall agreement with 
photogrammetric measurements. The measurement strategy involved the identification of major structures which were 
extracted as planes or cylinders and then removed from the dataset (figures 5 & 6). In this way it was possible to extract 
the majority of the equipment items and the majority of pipes with radii greater than 40mm. On diffusely reflective 
surfaces such as the brickwork walls good range data was obtained and it was possible to recover the structure of the 
surface morphology from a 2-3 metre stand off (figure 8). Small-bore piping could not be reliably extracted and the 
software did not permit the extraction of more geometries such as circular-torii or complex parts such as valves. These 
structures were left as isolated clouds of points in the final output. Analysis of the range data as a function of incident 
angle with respect to the surface normal of a range of reflective surfaces indicate that, as expected, range observations 
  
  
  
126 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 
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