In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
543 
out of this window to deal only with candidate building edges 
and to decrease the number of unnecessary edges. From these 
edges, the rectangle that represents the building is reconstructed. 
For each possible building location, we put an initial virtual box 
on (xb, Vb) coordinate with 9 = 0 angle. Here, 9 is the slope of 
the rectangle. Then, the edges belonging to the virtual box are 
swept outwards, until they hit to building edges. After our vir 
tual box stops growing, we calculate the energy Eq. The energy 
of the detected box shape is defined as the sum of minimum dis 
tance between virtual building edge pixels and real building edge 
pixels in perpendicular direction as given below; 
Ee = 'Y^min(sqrt((x v {i)-x e (j)) 2 -(y v {i)-y e (j)) 2 )) (1) 
i= 1 
Here, Ee is the calculated energy in 9 direction. (x v (i),y v (i)) 
represent coordinates for ith pixel on the edges of the virtual box 
shape. (x e (j),y e (j)) represents the yth pixel on the real build 
ing edges. For same seed-point, we put an initial virtual box and 
start growing again for all 9 e [0,7r/6,7r/3, tt/2, 27t/3, 27r] 
angles. As we increase step sizes here, we can obtain more ac 
curate approximations, however we need more computation time. 
After calculating Ee for 9 & [0,7r/6, n/3, 7t/2, 27t/3, ..., 2-7t] an 
gles, we pick the estimated box which has smallest Ee energy as 
detected building shape. Since buildings are generally in rect 
angular shapes, it makes sense to extract rectangular shapes on 
buildings. Main advantage of using Box-Fitting approach is that 
approximate building shape still can be found even the building 
edges are not well-determined, or even if there is not a closed 
shape. However, other region growing algorithms fail to extract 
an object shape in these cases. 
In Fig. 2, we represent our original Jeddai sample image, and 
B(x,y) binary image which holds detected approximate build 
ing shapes. As one outcome of using the Box-Fitting approach, 
we can reject some false seed-points if the virtual box can not 
converge to a shape in this region. We also reject the detected 
box-shape if its area is very small (less than 100 pixels), or if its 
area is very large (more than 5000 pixels) since it can not repre 
sent a real building considering image resolutions. As a result, 
we also verify building appearance using Box-Fitting algorithm. 
In the next part, we use detected approximate building shapes to 
refine the DEM. 
(a) (b) 
Figure 2: (a) Original Jeddai test image, (b) Detected approxi 
mate shapes using box-fitting approach (B{x, y) binary image). 
4 ENHANCING BUILDING SHAPES IN DEM 
After finding approximate building shapes from the panchromatic 
satellite image, we try to enhance DEM data using this informa 
tion. For this purpose, we first calculate gradient magnitudes in 
DEM to investigate discontinuities. To find gradient magnitudes, 
we use smoothed gradient filters in x and y directions as below, 
9x{x,y) = ~exp(- X 2 ^2~~) (2) 
2 I 2 
, \ ~y , x +y ^ 
9y\ x i V) = 2~ ex P( 20*—' 3 
where a is the smoothing parameter and equal to 0.5. Although 
our method is fairly robust to this parameter, one may need to 
adjust it according to the resolution of DEM. We calculate the 
smoothed gradients for the DEM data E(x, y) as, 
E x (x, y) = g x (x,y) * E(x,y) 
(4) 
E y {x, y) = g y (x, y) * E(x, y) 
(5) 
where * stands for a two-dimensional convolution operation. We 
calculate gradient magnitudes of image as, 
G(x, y) = \f E x (x,y) 2 + E y (x, y) 2 (6) 
If a pixel in G(x, y) has a higher value than td, we assume there 
is a significant discontinuity. Here, td threshold value is obtained 
by Otsu’s automatic thresholding approach (Otsu, 1979). After 
detecting significant discontinuities in the DEM, we pick each 
rectangle and investigate the corresponding region. If there are 
discontinuities in the DEM pixels where rectangle have edges, 
we assume the inside of this rectangle as a building rooftop. In 
order to eliminate noise that appears on building rooftops, we cal 
culate only one height for each rectangular building. To calculate 
an approximate building heights, we pick DEM values which are 
inside of the detected rectangular region and calculate their mean 
value. Then we set each pixel, which exists inside of the rectan 
gular region, to the calculated mean value. As a result, we have 
only one height value for each detected building. In the Experi 
mental Results section, we analyze effects of choosing mean and 
median of DEM values as a building height. 
We assume that there may be buildings in the DEM which are 
missed in previous building detection and shape approximation 
steps. Therefore, after removing reconstructed building pixels 
from DEM we make a post-analysis on it. If there are regions 
with high values for a large area, we assume that they can be 
missed buildings and insert them to our final result after smooth 
ing their DEM values with a [9 x 9] size median filter to remove 
the noise on DEM. We picked this median filter window size af 
ter extensive tests on our test image dataset. If window size is 
chosen larger, this post-processed buildings will have smoother 
edges. On the other hand, if window size is chosen smaller, me 
dian filtering process can not be adequate to remove noise within 
DEM. In this post-analysis, if a region has very high value (more 
than 40 meters) we remove this region from DEM since it can not 
represent a building. In this way, we also eliminate errors in the 
DEM which occur because of stereo image matching errors in the 
DEM generation process. 
5 EXPERIMENTAL RESULTS 
To test the performance of our proposed method, we use a test im 
age data set of Jedda city. We use DEM which is generated from