CMRT09: Object Extraction for 3D City Models, Road Databases and Traffic Monitoring - Concepts, Algorithms, and Evaluation 
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(c) Vertical/Hypsometric Difference (absolute values) 
(d) Vertical Difference among the HTP (absolute values) 
I 
L 
I 
\Ki;j 
• * >lJ 
I 
(e) Vertical Difference 
Jk, I ^ 4 
(f) Vertical Difference among the HTP 
(g) Vertical False Positives among the HTP (h) Vertical False Negatives among the HTP 
Figure 4: Vertical/Hypsometric Difference between the Extracted Buildings and the Ground Truth 
roof’s inclined planes (©* = (h m ,ui,U2,u}3,u}4))- These four 
angles (Figure 2) along with the implicitly derived dimensions of 
every building’s footprint (from E 2 d) can define the roof’s height 
at every point (pixel) h r (x, у): 
h r (x,y) = 
min [D(P U Pm); T>(P 2 , Pm); X>(P 3 , Pm)i P(P 4 , P m )] (3) 
= min [di tan u>i; cfetanu^; (fetanc^; dj tan cj 4 ] 
where V: is the perpendicular distance between the horizontal 
plane P m and roof’s inclined plane Pi.4. The distance for e.g. 
between Pi and P m in Figure 2 is the actual roof’s height at that 
point (x, y) and can be calculated as the product of the tangent 
of plane’s Pi angle and the horizontal distance di lying on plane 
Pm- V(Pi,P m ) is, also, the minimum distance in that specific 
point comparing with the ones that are formed with the other three 
inclined planes. 
Utilizing the 3D information from H -either from point clouds or 
from a height map- the corresponding energy E3D that recovers