Roland Geibel 
  
2.4 The USF-procedure (University of South Florida) 
The procedure of Hoover et al. [1996] proceeds in two steps: First for each pixel the normal vector is estimated, then the 
region growing itself starts. For the investigation a window of size at least 5x5 is laid around each pixel. For the 
estimation of the normal for each pixel a sub-window is made centred around the pixel and eight other sub-windows in 
horizontally, vertically and diagonally shifted directions. For all of these sub-windows the normal vector and a residual 
is computed. The normal vector with the smallest residual is taken as the normal vector of the centre pixel. For pixels in 
the interior of a segment this residual will be small. Noise or a near by edge produce a big residual. Thus a small 
residual can be a hint for the interiorness inside a planar segment. 
The pixel with the smallest residual is taken as seed point for the region growing process. Criteria for the addition of a 
further pixel to a growing region are (i) the four-neighbourhood, (ii) the angle between the pixels normal and the region 
grown so far, (iii) the distance between the new pixel to be added and the plane equation of the region grown so far and 
(iv) the point-to-point distance between the pixel and its neighbours in the scene. This way a region grows pixel-wise at 
its border. If no more pixels can be added to a region the next best pixel available (based on its residual) is taken as the 
seed pixel for the next region. Too small regions are discarded and their pixels play no further role. 
2.5 Qualitative valuation of the procedures by an example 
For a first qualitative valuation the procedures were installed and tested with the data in hand. For that purpose it was 
necessary to modify source code and the data to make the data types, the data formats and the different image formats 
compatible. Several interfaces for camera models present in the original source code could not be used. The results of 
the segmentation by the different procedures are displayed in Fig. 1. 
  
  
Fig. 1: Results of the segmentation procedures: a) Burns, b) UB, c) WSU, d) USF 
The result of the procedure Burns (Fig. 1a) shows a heavy sectioning of the areas, caused by the sensitivity of the 
gradient to noise by the small 2x2 window. Since the procedure Burns makes the segmentation only based on gradient 
orientation adjacent areas of same orientation but different slope can not be discerned. Since gradients are only 
considered if they have a certain absolute size horizontal areas can not be detected either. Since the aim is to find edges 
the decision about intersecting concurrent segments is determined by their length and not the number of pixels which 
would be desirable. Remarkable in Fig. 1b) are the horizontally directed segments, resulting from a supposed line 
structure of the scanning system which however was not present. The result in Fig. 1d) shows extraordinarily many 
small segments in the border area and a very big part at the border of the segmented object and between the segments 
considered as unsure. This is due to the operating mask being small with respect to the resolution of the data. Since the 
results produced with the data present seem not satisfactory a further segmentation procedure was developed and 
implemented. 
2.6 The FOM procedure 
This procedure is based on the stepwise growing of similar areas from single pixels up to big regions. Beginning with a 
masking made in advance the knowledge about the separation into background and foreground is used. The procedure is 
marked out by a special distance measure and a continuing recalculation of the plane equations. Thereon the distance 
measure is not determined from derived features of the segments but directly from their pixel sets. For the calculation of 
the distance measure between two adjacent segments P, Q the Euclidean distance dg is determined for all pixels p of 
segment P to the plane of the other segment Q. The distance d, of one segment P to Q is calculated as 
d,(P,Q) = maxpep (dg (p, Plane(Q))] (1) 
whereas the symmetric distance measure between P and Q is taken to be the minimum of both values: 
  
328 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
  
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