Roland Geibel 
  
d (P.Q) = min (d, (P,Q), d, (Q.P)) (2) 
Then that pair of segments Po, Qo is fused which has the minimal distance: 
d(Po.Qo) = min (d(P.Q) J. (3) 
Pairs of adjacent segments with minimal distance are fused until this minimal distance d becomes bigger than a 
threshold dy. This threshold dy, is the only parameter to control the procedure. During the initialisation phase the plane 
equations are determined either by all pixels of the 8-neighbourhood or from the best fit with 3 adjacent pixels which 
form a square with the centre pixel. In a post-processing phase very small segments like for example single border 
pixels are added to an adjacent segment. The result of the procedure is the partitioning of the image into disjoint 
segments and the neighbourhood graph of the segments. 
  
Fig. 2: Stepwise fusing of segments after a) 2690, b) 2860, c) 2940, and d) 3050 steps 
The four images in Fig. 2 show intermediate results after 2690, 2860 and 2940 iterations and the final result after 3050 
iterations. Since each iteration fuses at least one pair of segments there can be no more iterations than the number of 
segments in the initial phase, i.e.: the number of pixels of the object. The number of comparisons in each iteration is 
bounded by the number of pixels of the object too. The total effort of the procedure is of quadratic order with respect to 
the number of pixels. 
3 TEST ENVIRONMENT 
The valuation of one or more algorithms requires to process relevant data and to evaluate the results. In order to process 
and valuate a big number of data sets it is suggested to automate the components of the test environment as far as 
possible. To gain a qualitative statement about a procedure task oriented measures must be defined [Hoover et al., 
1996]. 
3.1 Data 
3.1.1 Input data 
In general we discriminate test data by their origin into (i) data of synthetic objects, (ii) data of model objects and (iii) 
data of real objects. In this contribution height data of real objects are used which were recorded by a laser scanner. 
Nowadays airborne laser scanner systems yield sensing ratios of one point per 6m up to 9 points per 1 m^ [Huising & 
Gomes Pereira, 1998]. In this investigation we used data which were recorded with a ratio of 4 points per 1 m°. They 
were used to derive a geocoded equidistant grid which can be depicted as an image. 
3.1.2 Ground truth data 
Ground truth data describe an object in a scene or in image data. If scene descriptions 
are used as ground truth data, then a comparison will also contain the special properties 
of the sensor. Thereon it may be, that objects of the scene are not visible in the image 
because of some properties of the sensor. If the task is to investigate only the procedure 
alone, then the excerption of ground truth data from the image data is suggested. This 
case is called sensed truth [Klausmann et al., 1999]. While for input data of synthetic 
objects and model objects ground truth data can often be obtained automatically input 
data of real objects usually require to derive the ground truth data manually. For 
valuating the segmentation of height data plane areas were extracted manually 
following the visible shape, with areas down to 4 square meters being recorded. Fig. 3 Fig. 3: Ground truth 
shows an example for a manual ground truth segmentation. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 329