Digital Signal Processing Reference
In-Depth Information
where,
H
k
is the
k
th
histogram bin. Next, we introduced a fuzzy classification
technique in order to reclassify ambiguous pixels, which mainly appear on the borders
of bins (Fig. 3). Indeed, the automatic pixels classification into a histogram provides
K
equally spaced containers, what leads to decrease the certainty of the correct
belonging of a pixel into a bin, especially for those on the area
χ
“shared” by two bins
(Fig. 3). Thus, our strategy consists to define a fuzzy membership degree
µ
B,Ci
(j)
, for
each pixel
j
in each channel
C
i
, to the bin
B
to which pixel
j
belongs by default, as
well as its fuzzy membership degrees
µ
B-l,Ci
(j)
(
l
∈
{-1,1}
) to the neighboring bins
B-1
and
B+1
(3). This returns to define, relatively to each binary matrix
HEC
i
, a fuzzy
membership matrix
MC
i
, where each pixel
j
has three fuzzy values (3) depending on
its position in the corresponding bin. In fact, such that if
EC
i
(j)≤ EC
i
(c
B
)
then
l=-1
else
l=1
, the membership degrees of pixel
j
to bins
B-1
,
B
and
B+1
are defined as
follows:
|
EC
( )
j
−
−
ECc
(
) |
(3)
μ
(
j
) 1
=−
i
i
B
,
μ
() 1
j
=−
μ
(
j
)
and
μ
() 0
j
=
,
BC
,
B l
+
,
C
Bi
,
B
−
l
,
C
|
EC
(
c
)
EC l
(
)|
i
i
i
i
B
i
B
,
B
+
l
where,
c
B
is the central pixel of bin
B
which belongs to color channel
C, l
∈
{-1, 1},
l
B,B+1
(
resp.
l
B,B-1
) is the local-entropy on the limit between bins
B
and
B+1
(
B-1
and
B
). For example, supposing that the red component of the input image is composed of
four pixels (
S=4
); where
ER
1
(j=1)=2.2, ER
1
(j=2)=3.9, ER
1
(j=3)=0.5
and
ER
1
(j=4)=4.45
; which will be classified into five bins (
K=5
) varying from
0
to
5
, so
that
ER
1
(c
B=k
)=0.5*k
for each
k (
∈
{1,2,…,K})
. Thus, the fuzzy local-entropy
classification of these pixels allows to obtain the fuzzy matrix
MR
as illustrated by
Fig. 4.
Fig. 2.
Outline of the proposed histogram matching technique
Then, the fuzzy classification technique divides pixels into two groups. The first
group contains the pixels with high membership degrees (≈1) to the default bin B.
