DEFORESTATION AROUND THE WORLD - India Environment Portal

174
w
k
pi
iC k
Deforestation Around the World
The k w is regarded as the zeroth-order cumulative moment of the kth class Ck. and the
means for classes is
i. pi
uk
(3)
w
iCk In the case of bi-level thresholding, Otsu defined the between-class variance of the
thresholded image as:
Where
And
k
2* ( ) 2 ( ) 2
B
w 1
u
1
u T
w 2
u
2
u
T
(4)
M
T
k
k
k1
M
wk 1
(6)
k1
Assuming that there are M-1 thresholds, {t1, t2, …, tM-1}, which divide the original image
into M classes: C1 for [1,…, t1], C2 for [t1+1, …, t2], … , Ci for [t i-1+1, …, t i], …, and CM for
2
[tM-1+1, …, L], the optimal thresholds {t1*, t2*, …, tM-1*} are chosen by maximizing B as
follows
then
{ t *, *,..., *} arg { 2
1
t
2
t
M1 Max
B
( t
1
, t
2
,..., t
M1
)}
1 t
1
... t M1
L
2 M
( )
2 2 M
2
B
wu
k k
u T
wu
(8)
k k
k1 k1
A threshold value tOtsu developed by Otsu is the one that maximizes vart between-class, or
equivalently minimizes vart within-class.
Min1 t
Var
1
t
tOtsu t L withinclass arg ( )
t arg Max ( Varet )
Otsu t L between class
where L is the number of gray levels in each band, in our images L is 256 because each pixel
is represented with eight bits.
(2)
(5)
(7)
(9)