International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
  
  
  
  
  
  
  
  
  
  
(b) 
Figure 3. Gradient directions 
(a) Circular direction; (b) Radial direction 
After calculating the elevation differences, TEA obtains two 
elevation differences series in both directions ((4) and (5)). 
RC'e nC, RCN RC) (4) 
CC'e ÍCC CC e Cul os (5) 
where RC’ is the elevation differences set in the radial direction 
of the basic unit, and CC' is the elevation differences set in the 
circular direction of the basic unit. In TEA concepts, structural 
lines exist where two-direction gradients intersect. Detected 
candidates are then identified using the intersections between 
the minimum radial elevation differences and the maximum 
circular elevation differences. In the radial direction analysis, 
the first set of candidates are extracted when RC, closes to the 
RC,;. The circular direction analysis then extracts possible 
edge grids from these candidates when CC, is larger than CC, ; 
and CC,+;. The following process compares these collected 
candidates with designed patterns. 
The concept of topological permutations is also used to identify 
structure lines. In this step, 12 patterns are designed to delineate 
the parts of one line, which are compared with designed 
patterns to identify the line grids. These designed patterns are 
shown in Fig. 4. The gray parts indicate the topological 
condition surrounding the nucleus. If the candidate fulfills one 
pattern, TEA determines the candidate to be a part of a structure 
line. Therefore, non-matched candidates can be considered 
isolated noises and removed. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Figure 4. Designed patterns 
2.3 3D Line Formation 
After the detection process, the identified structure lines are 
formed using several adjacent grids. During the subsequent 
process, the Hough transform is employed to group independent 
straight line segments and calculate the parameters of every 
structure line. To preserve the original elevation information, 
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the grids serve as index maps to obtain the original point clouds 
of each selected grid and calculate the linear parameters. 
3. EXPERIMENTAL RESULTS 
The test area was located in Van Heekplein, the Netherlands. 
Two target buildings were selected to evaluate the detection 
ability of the proposed scheme. The first building had several 
flat roofs with multiple elevations, whereas the second building 
contained a parapet on the rooftop. The LIDAR data used in 
this study was scanned by a FLIMAP system in 2007. The point 
density reached 30 points per square meters. Figure 5 shows the 
distributions of the original point clouds for both buildings. 
Because the original point spacing was approximately 20 cm, a 
higher value was used to generate a PDSM during the 
rasterization procedure. The spatial resolution used in this study 
is 25 cm. The elevation constraint is set as 0.5 m. This value is 
a constant for the identification of minimum parapet height. 
  
(b) 
Figure 5. Test datasets for (a) Case I and (b) Case II (Unit: m) 
The PDSM results of the detection process are shown in Figure 
6. In the figure, color-coded boundary pixels denote the 
elevation. During vectorization, the Hough transform was 
applied with TEA to separate the detected edges into several 
independent structure lines (Figure 7). Then, each group of line 
pixels can be used to calculate the linear coefficients. Figures 8 
and 9 show the three-dimensional structure lines developed in 
this study. 
  
  
  
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