2.3.2 Modelling of Basic Belief Assignment BBA: The
definition of BBA relates to the application and the character of data source. In this paper, change detection is considered as a
classification problem of detecting the categories of land-cover change vectors. The BBA can be calculated based on the
confusion matrixes of every classified image, this approach has been proved to be feasible for classification
Elouedi Z., 2010 .
The classification process provides the classified image
t
T
, which means each pixel in the images gets a detected class, the
detected class before and after change forms a detected change vector, denoted as
,
x y
. The unavoidable classification error makes the detected change vector
,
x y
imprecise. It is reasonable to believe that the detected change vector is not
absolutely reliable, and may correspond to other possible real change vector
,
a b
as denoted in section 2.2. In order to measure the belief value of a detected change vector,
the confusion matrixes
t
p
and
1 t
p
correspond to the pre- and post-change classified image
t
T
and
1 t
T
should be converted to the prediction positive rates as follows:
1 1
1
, ,
, ,
, ,
t t
x a
t x
t t
y b
t y
p x a
P p
x a p
y b P
p y b
2
Where , 0,1,2, ,
a x p
, 0,1,2, ,
b y q
,
t
p x a
,
1
,
t
p y b
= elements in the confusion matrixes
t
p and
1 t
p , which represent the amount of
pixels classified as class
x
and
y
while their ground- true class are
a
and
b
. Assigning the belief value of a detected change vector
,
x y
to all the possible real change vectors ,
a b
as follows:
1
, ,
,
a b
t x
a t
y b
m P
P
3
Where ,
a x
, ,
b y
, {
, }
a b
.
According to Dempster-Shafer’s theory, the summation of the BBAs should satisfy
equation
1, denoting that:
,
a b
a b
M m
4 Then the BBAs should be normalized as follows:
1 1
, ,
, 0,
: ,
,
a b
t x
a t
y b
t x
a t
y b
a or b
m P
P M
a b
m m
P P
M m
5
2.3.3 Evidential Fusion based on Combination Rules: The
Kategori