——M——RRR 
num size of the 
ze respectively 
ipplication. The 
width selection 
ughness (or the 
V size increase 
an the minimum 
hresholding the 
| the adjacency 
onnected pixel; 
isclassification, 
te thin lines ani 
ig segments and 
| and the chang: 
minate the small 
of the required 
as housing, this 
old. 
1 in equation (J 
lly) zeros, whik 
width is done 0 
f the edge pixels 
be done pixel bj 
rtical compone 
n). The standat 
pplying the end 
ange. Each pit 
e number of fac 
into building « 
- of pixels in ff 
size, the sized 
iold value. It hi 
ling and adjacell 
Michel Morgan 
  
Change in slope 
The slope (or the inclination) and the orientation (or the azimuth) are computed from the DSM using the Sobel operator 
in two perpendicular directions. The standard deviation of the slope and orientation for each pixel is determined based 
on the filter coefficients used and applying the error propagation rule. By applying the Laplacian filter to the slope 
image, the values of the resulting image should be (ideally) zeros for the pixels inside the planar roof faces. As 
mentioned before, segment shrinkage is used to avoid the contribution of the boundary pixels in the classification, and 
the classification is done pixel by pixel within each segment. Again, the standard deviation of slope change is computed 
by applying the error propagation rule. The threshold value of each pixel in the resulting image can be defined based on 
the standard deviation of the slope change. Each pixel is then classified as face pixel or vegetation (or edge) pixel. It is 
again a binary classification. By counting the number of face pixels in comparison with the total number of pixels for 
each segment, the segment is classified into building or vegetation. This threshold can be calibrated based on the prior 
knowledge about the face area, chimneys size, and the pixel size. 
It has to be mentioned that classification of flat buildings based on the orientation will fail because the orientations of 
the pixels of the flat buildings have random-like values. Therefore, a prior knowledge about the building roofs should 
be available to select the best criteria for classification. However, not considering the change in orientation in the 
segment classification is more conservative. 
3.3 Building Extraction 
3.3.1 Identifying roof faces 
3.3.1.1 Connected component labeling 
The strategy for identifying building faces is to connect adjacent pixels (based on 8 directions) of the same slope and/or 
the same orientation. Because the slope and orientation values contain errors, threshold values should be considered for 
the change in slope and orientation between the adjacent pixels. The threshold value can be defined based on the 
standard deviation of the difference of the slope and orientation between the adjacent pixels. Pixels are then segmented 
into sub-segments within the building segment. 
Having more than one criterion for connecting pixels leads to better results (as comparable with having many bands in 
image classification). However, connecting adjacent pixels based on the orientation will lead to unexpected results in 
the case of flat roofs. Therefore, connecting adjacent pixels is used based on slope and orientation for sloping roofs, and 
based on slope only for flat roofs. Therefore, prior knowledge about the building roofs is used to select the criteria for 
the segmentation. However, if the pixel slope value is larger than a certain value (theoretically zero) both slope and 
orientation have to be used, otherwise only the slope has to be used. The mentioned value is chosen based on the 
standard deviation of the slope or based on prior knowledge about the minimum slope of the sloping roofs. For 
example, if the minimum slope of the sloping roofs is 30°, a value of 15? can be used as long as the standard deviation 
of the slope is less than 15 °. The suggested method for connecting adjacent pixels is meant to work also in the cases 
where horizontal and sloping faces are contained in the same building. 
33.1.2 Majority filtering 
After applying the connected component labeling, several sub-segments within the building segment are identified. To 
correct for the small sub-segments, which may be caused by the chimneys or other “disturbances”, a majority filter is 
used. The size of the window of the majority filter can be chosen based on the knowledge about the chimney size and 
the pixel size. Alternatively an iterative majority filter of small window size (e.g. 3 pixels by 3 pixels) can lead to the 
same result without this pre-knowledge. Iterated majority filtering is then applied till stability is reached, i.e. till no 
more changes happen. It has to be noted that the majority filter has to be constrained to make sure that the building 
boundaries do not shift. In other words, we have to keep the building segment unshrinked and unexpanded. Face 
segments before applying the majority filter are assumed to have only random errors in the height values. After 
applying the majority filter more non-random errors (in the height values) in the reclassified pixels will exist. The 
height values of those reclassified pixels will not be considered for extraction of the height and slope information of the 
faces. However they are used for extracting planimetric information. Another advantage of the mentioned 
reclassification is to determine the adjacency information among roof faces. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 619