The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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Table 4 summarizes the performance measures obtained by 
applying each of the three methods to the data in pixel level. 
The performance measures of the methods in object level are 
given in Table 5. As can be seen, the Bayesian maximum 
likelihood method yields the highest detection rate and the 
lowest false negative rate in both pixel level and object level. 
The Dempster-Shafer method and the minimum distance 
method perform better in terms of the false positive rate. For 
both methods the false positive rate is about 5 times lower than 
that of the maximum likelihood method. A comparison of the 
performance of the methods in pixel level and in object level 
reveals that the detection rates and the false negative rates are 
slightly improved for all methods in object level, whereas the 
false positive rates are still better in pixel level. 
s 
t 
{B} (s) 
{T,L,G} (1-s) 
{T> (t) 
{0} St 
{T} t(l-s) 
{B,L,G} (1-t) 
{B} s(l-t) 
{L,G} (l-s)(l-t) 
Table 1 
. Combination of evidence s (from DSMle-DTM) with t 
(from DSMfe-DSMIe). 
sot 
{B} 
- s(l -1) 
(1 - St) 
{T} 
t(l -s) 
(1 - St) 
{L,G} 
u 
(1 s)( 1 -1) 
(1 - St) 
{T,G} 
(u) 
{0} 
su(l - t) 
(1-st) 
{T} 
tu(l - s) 
(1 - St) 
{G} 
u(l -s)(l -t) 
(1-st) 
{B,L} 
(1-u) 
{B} 
s(l-t)(l-u) 
(1-st) 
{0} 
t(l - s)(l -u) 
(1-st) 
{L} 
(l-s)(l-t)(l-u) t) 
(1-st) 
Table 2. Combination of evidence u (from NDVI) with sot 
(combination of s and t). 
Class hypothesis 
Combined evidence (sotou) 
{B} 
s( 1 -t)( 1 -u) / (1 -t+tu-su) 
{T} 
(l-s)tu / (1-t+tu-su) 
{L} 
(1 -s)( 1 -t)( 1 -u)/( 1 -t+tu-su) 
{G} 
(1 -s)( 1 -t)u/( 1 -t+tu-su) 
Table 3. Combined evidences for simple class hypotheses. 
DSMfe-DSMIe 
NDVI 
Fig. 3. Evidence assignment functions for the Dempster-Shafer 
method. 
A B C 
Fig. 4. Cleaning of the binary building image using 
morphological operations. A. Binary building image; 
B. Morphological opening removes small objects, 
but also smoothes out building boundaries; C. 
Morphological reconstruction retrieves the building 
boundaries. 
By visual inspection of the results in Fig. 5 and Fig. 6, it can be 
observed that building objects detected by the application of the 
methods in object level are relatively larger than those detected 
in pixel level. A superimposition of the detected buildings on 
the reference boundary map showed that in pixel-based results 
many building pixels at the boundaries of buildings were 
missed. This explains the better detection rate and false 
negative rate of the object-based results. 
An examination of the detection results also suggests that when 
the detected buildings are to be compared against a map for the 
purpose of change detection, the Dempster-Shafer results 
provide better signals for an operator, as compared to the 
Bayesian results, due to the much lower rate of false positive 
signals. 
Qi?f G Q - 
tJ 
Q tf 
=*£>**** 
Fig. 7. Manually extracted building boundaries used as 
reference data for the evaluation of detected 
buildings.