The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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(Figure.5 (a)). The criterion of classification is the orientation 
( U V in building model coordinate system, where V = U +90°) 
of the corresponding edges constructing the comer. As a result, 
building shape can be represented by a comer sequence. Base 
on the classification, the example shape comprised of right 
angle in Figure.5 (b) can be represented by a tag sequence, 
which is ABDBCDAC (starting from the red comer in left 
bottom). In this way, the shape of the buildings in imagery can 
be expressed fully and readily. 
B, c 
A D 
► 
x 
(a) 
(b) 
Figure.5 (a) comer classify (b) shape representation by tag 
sequence 
4,3 Matrix search based on Hough transform 
The boundary of building obtained in section 4.1 is not very 
regular. To obtain the two perpendicular line sets without 
fragmentation, Hough transform (P. V. C. Hough, 1962) is an 
ideal alternative as its robustness. Peaks corresponding to these 
perpendicular line sets in Hough space ( p , 6 ) where 
0 < 6 < K and -^(nf +r?) <p<J(n?+r?) for an image of m by n 
pixels will have the same value 0 X 0 2 (the dominate 
orientations, 0^—6-,+ 90° ), causing peaks of two columns 
aligning vertically in Hough space. All peaks in the two 
columns surpassing a threshold in Hough space produce two 
lines set which are perpendicular to another. A node matrix 
whose elements are intersection nodes of two perpendicular line 
set can be determined. However, the type of the node can not be 
determined. We take the following case in Figure.6 as an 
example to demonstrate our schema to this issue. There are 9 
edges which form a 3 X 3 node matrix. The 3 red lines is not the 
building edge. In order to remove these false lines, a buffer 
around each line between two nodes is constructed. We 
compute the average grey value of the two rectangles in each 
side of the edge. If the difference of the average grey value 
exceeds a predefined threshold, we can safely suppose that the 
edge is not a building edge. By this criterion, some false edges 
will be removed out. After this process, the comer type can be 
determined by the criterion in previous section. Obviously, 
building shape information is contained in the node matrix. To 
retrieve the building-related node sequence, a search is 
implemented from all the A type nodes. A search for the next 
right angle comer in the sequence is carried out by scanning 4- 
beighbor element in the matrix. In this case, the desired node 
sequence is ABCACDA (search from the left down comer) 
which is the aimed tag sequence of the search. However, in the 
present of significant mount of right angles, it is likely that 
more than one sequence, which is identical to the required 
sequence, will be found. The selection of the final tag sequence 
is based on the similarity between the desired sequences and the 
searched sequence. The searched sequence with largest 
similarity may be the same as the desired sequence. 
(b) 
Figure.6 (a) Matrix construction (b) search result 
5. RESULTS AND DISCUSSION 
In all these experiments, processing was carried out in the 
Visual C++ 6.0 environment using real world imagery. In 
addition to these experiments, complexity analysis and 
conclusion is also discussed in this section. 
5.1 Experiment result 
To improve the capability of grow algorithm, median filter is 
first allied to the image. The pixel value of the seed point which 
is manually selected by the user needs to be the same as the 
average of all the pixels in the building region. If the pixel 
value of the seed point is large than the average, the region 
obtain via the grow algorithm may be not very precise. In 
addition, the threshold in the grow algorithm is very important. 
If it is very large or small, the growing result may be not the 
same as the building region. This is depicted in Figure.7.