ıbul 2004 
| based on 
decision 
measures 
(28) 
(29) 
tively are 
- Cr ‚and 
(30) 
31) 
lefined in 
r selected 
pectively 
applying 
efined as 
n DMDF 
cheme in 
methods 
)empster- 
jns. Then 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
we compared the decision fusion results, considering their 
commission and omission classification errors those defined as 
follows: 
A(l-mn,./Sn. 35 
eo Cj A( n,/Y No ) ( ) 
ec, A(17 n, /En;) (36) 
In which, eo, and ec, respectively are the omission and 
t i 
commission classification errors for C; data class (Petrakos ef 
al., 2000, Rashidi& Ghassemian, 2003). In addition, the total 
commission and omission errors and reliability factor (re, ) 
for all data classes are defined as follows: 
M 
eo, AM™ Yeo, (37) 
= el 
| M 
ec AM E ec, (38) 
Fey All = 0-S(ec, * €O,, )} (39) 
The experiments have done for more than 15 available remote 
sensing data classification results. In all of these experiments, 
we have found that the DMDF performances are higher than 
other methods. In this section we show the decision fusion 
results related the data described in example (we called C12 
data). In tables 3 and 4, there are comparisons for percentages 
of the omission and commission classification errors for the 
final classification in different methods versus data classes. In 
addition, Figures 4 and 5 and table 5 show the percentages of 
the total omission and commission errors and reliabilities for all 
data classes of data. 
Table 3. The decision fusion methods omission error 
percentages (€O, ) for C12 data. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
3 sd le i 
un NOM 
7 e [= | [£ S S 
o = cz & A A a 
Corn 1.64 0.45 13.3 2.41 2.11 2.89 
Soybeans 0.43 0.62 6.31 3.05 0.47 2.63 
Woods 77.8 75.2 94.0 36.0 50.9 23.9 
Wheat 23.8 30.0 7].5 20.9 30.6 14.6 
Sudex 2.12 1.92 11.6 3.95 3.32 3.56 
Oats 38.2 54.1 62.9 30.6 Sil 13.6 
Pasture 2.15 2.14 47.5 2.14 2.14 0.32 
Hay 25.8 35.1 66.6 16.5 32.8 15.4 
Unclassified 2.25 5.56 1.41 3,53 3.58 3.68 
  
  
Table 4. The decision fusion methods commission error 
percentages (eC, ) for C12 data. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
> > 
v + Es = S n 
NE pere eget put e 
o ES DEE PR IE 
Corn 8,15 3567 | 7.32 1.87 3.52 1.69 
Soybeans 20.1 | 112} 509 3.19 7.82 1.92 
Woods 14.0 | 5.7 25.4 55.0 6.84 15.7 
Wheat 75 16.4 | 50.1 11.4 pt 14.4 
Sudex 3.51 | 6.09 | 6.76 2.59 2.84 2.67 
Oats 31.6 | 15.8 | 34.3 23.9 13.2 36.0 
Pasture 2.74 | 2.44 | 8.84 2.44 2.44 4.88 
Hay 26.8 | 8.61 1 45.3 14.6 9.06 15.8 
Unclassified 15.1 | 8.04 | 30.4 7.6 [ii 7.29 
  
545 
  
  
  
  
  
  
> 
zo 
$9. GB: 
9 d 
3 m 
N = 
eges 
e c 
= N 
c — N = 
= O oo © 
eg Ll. ^ rj = w oo 
ta | D © 
= a 
[1 
= 
go © T T T T T 1 
G > = E oO Z 2 
< > > ir L = 
= z < G = 9 
A m = = = 
A = => 
> 
z 
Figure 4. The total omission errors for the decision fusion 
methods. 
OT 
01 
JAN ssi 
NV | 888 
NVISIAVE B= 
1 10119 UOISSIUILUWIOS [EJO] 
95BJUIIIAC 
AGING | UH 
(N2O)SG ] 262 
(Nd)SQ ] oe 
S 
Figure 5. The total commission errors for the decision 
fusion methods. 
Table 5. The reliability factors for the decision fusion methods. 
  
  
  
  
  
  
  
  
  
Methods Reliability (C12 
data) 
MVF 0082.55 
Rank %84.20 
Bayesian %64.70 
DS(CM) 7086.36 
DS(PM) 9086.56 
DMDF % 89.70 
  
  
Considering the mentioned results in the tables and figures, it is 
cleared that the DMDF method, has lower commission and 
omission errors and higher reliability than other methods. This 
superiority is raised from the better combination rules and 
extraction the new tools such as commission. and omission 
errors distribution vectors in the DMDF algorithm. Another 
important point about the presented method is that, we just need 
to hard decision for extraction the commission and omission 
errors matrixes of classifier results as the fuser inputs, while the 
other methods such as rank based and Bayesian methods, need 
soft decisions which are high volume data and complex inputs. 
Therefore, we confirm that the new method has a desirable 
condition for all classes in commission and omission errors, and 
reliability viewpoints. Of course, for any data fusion and 
classification, we should note that we have to evaluate the 
commission and omission errors of the whole classes jointly, 
and improving in only one of them is not sufficient. So, table 5 
shows that the DMDF is superior in this aspect(reliability) 
comparing the all other methods. 
5. Conclusion 
In this article, we described at first, the most useable methods of 
decision fusion such as MVF, rank based, Bayesian inference 
and Dempster-Shafer theory of evidence. Meanwhile, we