of an DLBP
P;R
pattern is defined as the number of spatial transitions
(bitwise 0/1 changes) in that pattern
UðDLBP
P;R
Þ¼js
0
ðp
P1
; p
c
Þs
0
ðp
0
; p
c
Þj þ
X
P1
n¼1
js
0
ðp
n
; p
c
Þ
s
0
ðp
n1
; p
c
Þj: ð8Þ
For example, DLBP
P;R
pattern 11111111 has a U value of 0 and
00010000 of 2. The uniform DLBP
P;R
pattern refers to the uniform
appearance pattern which has limited transition or discontinuities
(U 6 2) in the circular binary presentation, which is similar to the
uniform LBP
P;R
pattern [12]. It was verified that only ‘‘uniform’’ pat-
terns are fundamental patterns of local image texture.
Since the rotation invariant DLBP descriptor discards the color
intensity information with constant DLBP
riu2
P;R
value (see Fig. 4) and
color is still an important feature for color texture classification,
combining both DLBP
riu2
P;R
and color intensity values is expected to
be a very powerful measure to classify the color texture images.
We firstly construct a color index space (representative color
set), then project the all color pixels of the original image into the
color index space and obtain an index image. In order to ensure
meaningful comparison among different color texture images, the
set of representative colors, that is, the color index space, has to
be image-independent. To this end, we adopted uniform quantiza-
tion of the color space: n samples are taken on each axis of the color
space, resulting in a color index space of N ¼ n
3
colors. Provided
that the original images are given in the RGB space, we considered
a good practice to do uniform quantization in this space. Fig. 2
shows the resulting color index spaces with 8, 27, 64 and 125 ele-
ments. Once the color index space has been computed, each color
pixel of an original image is assigned the index of the nearest color
in the color index space (herein we used the Euclidean distance to
determine the nearest color). Sequential scanning of the original
image gives rise to an index image.
Then, we compute the joint distribution of the DLBP
riu2
P;R
and color
index values. For each pixel p in color image, the DLBP
riu2
P;R
value is
computed by Eq. (7) and the color index value (IðpÞ) is obtained
by projecting the pixel into the color index space. As shown in
Fig. 3, we then compute their 2-D histograms MS
DLBP
2D
which
are computed by:
MS DLBP
2D
ðl; kÞ¼
X
M1
m¼0
X
N1
n¼0
dðDLBP
riu2
P;R
ðp
mn
Þ; lÞdðIðp
mn
Þ; kÞ; ð9Þ
with
dðx; yÞ¼
1; x ¼ y
0; otherwise
ð10Þ
where M N represents the image size, p
mn
is the pixel on location
ðm; nÞ; l ¼ 0; 1; ...; P þ1; k ¼ 0; 1; ...; K 1; P is the number of the
pixels in the considered local neighborhood and K is the number
of the color index. After that, we normalize the whole MS
DLBP
2D
.
The 2-D histogram captures the joint distribution of the color infor-
mation and DLBP
riu2
P;R
values. The intensity of each cell in the 2-D his-
tograms corresponds to the frequency of some DLBP
riu2
P;R
value on a
specified color index value. In this 2-D histogram, each row corre-
sponds to the DLBP
riu2
P;R
distribution of the specified color index value.
To obtain a simpler and more discriminative descriptor,
the 2-D histogram, MS
DLBP
2D
ðl; kÞ, ðl ¼ 0; 1; ...; P þ 1Þ and
ðk ¼ 0; 1; ...; K 1Þ, is further encoded into a 1-D histogram.
Given the joint distribution of the color index value I and DLBP
riu2
P;R
,
as shown in Fig. 3, we extract each row of the 2-D histogram to
form a 1-D sub-histogram h
k
ðk ¼ 0; 1; ...; K 1Þ. That is, we
regroup the DLBP
riu2
P;R
value into K sub-histograms h
k
, each
sub-histogram h
k
corresponding to the DLBP
riu2
P;R
distribution of the
color index value I
k
. Then concatenating all these 1-D
sub-histograms h
k
ðk ¼ 0; 1; ...; K 1Þ, we have the 1-D histogram:
MS
DLBP
1D
¼fh
k
g; k ¼ 0; 1; ...; K 1, which is used to characterize
the color image.
Different from the DLBP
riu2
P;R
descriptor in which the histogram is
obtained only from the total number of the pixels with same
DLBP
riu2
P;R
value, we regroup these pixels with the same DLBP
riu2
P;R
value
based on the color index values to form the 1-D histogram
MS
DLBP
1D
. Fig. 4 shows that two images with the same DLBP
riu2
P;R
histogram have different MS DLBP
1D
histograms.
The entire process of the rotationally invariant features for color
textures can be summarized as follows (see Fig. 3): (1) establish-
ment of an image-independent color index space; (2) color index-
ing; (3) obtainment of the index image; (4) calculation of the
DLBP
riu2
P;R
image; (5) computing the joint distribution of the
DLBP
riu2
P;R
and index image; (6) calculation of the DLBP
riu2
P;R
histogram
of each index color; (6) concatenation of the resulting DLBP
riu2
P;R
his-
tograms, that is, the MS
DLBP
1D
histogram. In the following
Fig. 1. An example of the computation process of the DLBP
8;1
code in RGB color space. Firstly, the color distances between the center pixel and the neighborhood pixels are
computed. Then we divide the color distance into two levels (0 and 1), here, the threshold is set at h ¼ 0:025 by training. Finally, the DLBP
P;R
code is obtained by using Eq. (3).
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
G. Lian / J. Vis. Commun. Image R. 31 (2015) 1–13
3