ISPRS Commission III, Vol.34, Part 3A ,,Photogrammetric Computer Vision“, Graz, 2002 
  
  
Figure 4-b. Extracted Roof Regions (Building 2) 
4. LIDAR DEM REFINEMENT 
For each plane, the contributing points are used to adjust the 
plane parameters. The L1 norm (Marshall, 1998) is used in 
this step to update the plane parameters. Ll norm 
minimization is a robust estimation technique that has the 
ability to perform well in the presence of outliers. The 
updated parameters serve as the plane parameters at this 
stage. The elevations of all points that contribute to a certain 
plane are taken as observations, while the unknowns are the 
plane parameters. 
The next step is to apply the geometric constraints of the 
building roofs. The first constraint is the horizontal plane 
constraint. The plane parameters are checked to find if any 
plane has small slope values, i.e. the values of the parameters 
a and b are negligibly different from zero. In this case the 
plane is assumed horizontal. The second constraint is the 
symmetric constraint. Each two adjacent planes are checked 
to find if they satisfy a slope symmetry condition, as one 
would expect in a conventional gabled roof. The previous 
constraints are used to update the plane parameters. The 
mathematical description for horizontal planes is shown in 
Equation (2). The complete mathematical description that is 
used to find the parameters of two symmetric planes is 
shown in Equation (3). 
Zyà 7 9X gg 7 P Yga -c=0 2) 
a=0 AND h=0 
Where n is the number of points in the region. 
Zax 7 4; X nd 7 biYya — 6j z0 
Z md — A; X m —D ; Ym —Cj =0 (3) 
a; +a; =0 OR b+b;=0 
Where n is the number of points in region (i), m is the 
number of points in region (j). The overdetermined system is 
solved by least squares. The adjusted plane parameters are 
then used to refine the LIDAR DEM points. Each point 
elevation is refined based on the new plane parameters. 
Figure 5 and Figure 6 show the LIDAR DEM before and 
after the refinement. 
A - 105 
Figure 6. The Original and Refined DEM for Building 2 
5. ROOF BORDERS EXTRACTION 
The roof region borders are extracted after finding the roof 
regions. Roof border points are points that have at least one 
point of its 8-connected neighbors not from the same region 
(Rosenfeld and Kak, 1982). Figure 7-a and b show the 
extracted roof region borders.