ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
251 
3 further filtered 
based on the 
dates shown in 
sides of edge 
the shape of 
je segment and 
if two templates 
imbination with 
; edges. 
me length. The 
rst extended to 
cribed above is 
s considered to 
candidates of 
|th of conjugate 
: edges in other 
ole edges as a 
ase, the above 
s. 
Calculation 
>y the following 
r when in the 
to each other 
other edges. 
jltiple edges B, 
table edges in 
threshold, and 
e pair {A,B} is 
t there are no 
copied in step 
ihest similarity 
RAINT 
ebb’s rule for 
. This process 
mpetition and 
ping between 
le left stereo 
t is applicable 
rated in Fig.6. 
a in image A 
A shift vector 
id the optimal 
or is modified 
area. These 
operations are repeated at each local area. The final result 
becomes a nonlinear mapping between these two images. 
For competition process it is very important to use the 
appropriate correlation function. Normally absolute value of 
difference between template area's brightness is used in terms 
of computational cost. To enhance object’s features, pre 
processing processes are necessary. The complexity Index (Cl) 
calculated by Eq.2 and Eq.3 proposed by Kosugi et al. [5] is a 
good example. Cl is capable of improving CEM objected for 
urban area. This has been ascertained by verification test. 
V 2 / 
dx 1 dy 1 
a=I 
av ! / 
dx 
ÔV 2 / 
dy 
Eq. 2 
Eq. 3 
The method of consensus operation depends on processed 
object. For example, it is efficient to use spline function for the 
matching objected for mountainous topography. Convergence 
property in matching by consensus operation mainly depends on 
the range of consensus area, shape of area, method of 
weighting. In this study we apply cross-shape consensus area 
and use median shifting vector as a consensus result. 
The balance of competition and consensus operation is also an 
essential factor. If the influence of competition is too large, the 
number of mismatch area will increase. On the contrary, if the 
degree of consensus is too strong, matching results will be too 
smooth. Therefore these parameters must be adjusted properly 
according to the number of iteration. 
Object Point 
X 
Image A OOOfOOO 
Image B o cfo O C5& O 
Search Area 
-cr 
Update of 
-Initial Search Point 
-Search Area 
-Consensus Area 
Competition 
Consensus Phase 
Fig.6 The Principle of CEM 
5.2 Extension of CEM with Edge Constraints 
CEM is a very effective approach for smoothly transforming 
object’s matching. Since our target is for stereo matching in 
urban area, we make use of edge constraints to improve the 
performance of CEM. 
Global search in initial stage of competition phase is very 
important, because if it fails to find approximate matching 
positions in large area, CEM cannot recover such errors due to 
its characteristics. We can avoid this problem with edge 
matching results described in Section 4. Up to now, to avoid of 
error in initial global search has been executed such as using 
more extensive area in competition phase, utilization of edge 
segment will offer alternative approach. 
Conjugate edge segments gives shifting vectors and can be 
used as immovable area in both competition and consensus 
operation. This constraint brings prevention against deforming of 
some building’s edges. 
Furthermore, edge segments that are detected with the 
approaches described in Section 3 but not matched at Section 4 
can also be used as efficient information in consensus phase. 
Because most of the edges detected in Section 3 are regarded 
to have nearly linear shift vector except for occluded region by 
collinear condition. The rules of edge constraint applied in CEM 
are as follows. 
(i) Conjugate edge segments are immobile in competition and 
consensus operation. 
(ii) Non-conjugate edge segments have uniform parallax shift. 
(iii) Parallaxes of points put between edges don’t exceed 
those edges. 
6. EXPERIMENTS AND RESULTS 
6.1 Experimental Environment 
Experiments have been performed with stereo aerial imageries 
of urban area. Fig.7 shows a small portion of the stereo images. 
The image sizes are 700 x 700 respectively and the resolution is 
about 20 cm per pixel. There are several occluded areas and 
hidden regions in the shades. 
Left Image Right Image 
Fig.7 A Pair of Stereo Images 
6.2 Edge Detection Results 
Fig.8 and Fig.9 show edge tracing results derived from images 
processed by SUSAN operator and Haar’s wavelet respectively. 
Similarly Fig. 10 and Fig. 11 show the results of segmentation 
operation of edge tracing. The final results of edge segment 
matching are illustrated in Fig. 12 and 13. From the experiments, 
both approaches produce almost valid results, however we 
observe that SUSAN operator can detect more valid edge than 
wavelet does. This is because that at the stage of calculating 
binary edge images with wavelet, some of the important 
information on edges was lost by binarization process. On the 
other hand in SUSAN, edge components are detected by linking 
interest feature points, so that the points with weak interest 
feature can keep edge’s information. We would try to apply this 
concept for using in wavelet operation as feature works. 
Fig.8 The Edge Tracing Results by SUSAN Operator