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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
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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
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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