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Similar to LBP
u2
P;R
, the mapping from LBP
P;R
to LBP
riu2
P;R
, which has P+2
distinct output value, can be implemented with a lookup table.
2.2. Rotation invariant variance measures (VAR)
A rotation invariant measure of the local variance can be
defined as [24]
VAR
P;R
¼
1
P
X
P1
p ¼ 0
ðg
p
uÞ
2
ð7Þ
where u ¼ 1=P
P
P1
p ¼ 0
g
p
. Since LBP
P;R
and VAR
P;R
are complemen-
tary, their joint distribution LBP
P;R
=VAR
P;R
can better characterize
the image local texture than using LBP
P;R
alone. Although Ojala et
al. [24] proposed to use only the joint distribution LBP
riu2
P;R
=VAR
P;R
of LBP
riu2
P;R
and VAR
P;R
, other types of patterns, such as LBP
u2
P;R
, can
also be used jointly with VAR
P;R
. However, LBP
u2
P;R
is not rotation
invariant and it has higher dimensions. In practice, the same (P, R)
values are used for LBP
riu2
P;R
and VAR
P;R
.
2.3. LBP variance (LBPV)
LBP
P;R
=VAR
P;R
is powerful because it exploits the complemen-
tary information of local spatial pattern and local contrast [24].
However, VAR
P;R
has continuous values and it has to be quantized.
This can be done by first calculating feature distributions from all
training images to get a total distribution and then, to guarantee
the highest quantization resolution, some threshold values are
computed to partition the total distribution into N bins with an
equal number of entries. These threshold values are used to
quantize the VAR of the test images.
There are three particular limitations to this quantization
procedure. First, it requires a training stage to determine the
threshold value for each bin. Second, because different classes of
textures may have very different contrasts, the quantization is
dependent on the training samples. Last, there is an important
parameter, i.e. the number of bins, to be preset. Too few bins will
fail to provide enough discriminative information while too many
bins may lead to sparse and unstable histograms and make the
feature size too large. Although there are some rules to guide
selection [24], it is hard to obtain an optimal number of bins in
terms of accuracy and feature size.
The LPBV descriptor proposed in this section offers a solution
to the above problems of LBP
P;R
=VAR
P;R
descriptor. The LBPV is a
simplified but efficient joint LBP and contrast distribution
method. As can be seen in Eq. (3), calculation of the LBP histogram
H does not involve the information of variance VAR
P;R
. That is to
say, no matter what the LBP variance of the local region, histogram
calculation assigns the same weight 1 to each LBP pattern.
Actually, the variance is related to the texture feature. Usually the
high frequency texture regions will have higher variances and
they contribute more to the discrimination of texture images [8].
Therefore, the variance VAR
P;R
can be used as an adaptive weight
to adjust the contribution of the LBP code in histogram
calculation. The LBPV histogram is computed as
LBPV
P;R
ðkÞ¼
X
N
i ¼ 1
X
M
j ¼ 1
wðLBP
P;R
ði; jÞ; kÞ; kA ½0; Kð8Þ
wðLBP
P;R
ði; jÞ; kÞ¼
VAR
P;R
ði; jÞ; LBP
P;R
ði; jÞ¼k
0 otherwise
ð9Þ
Fig. 3. Uniform LBP patterns when P=8. The black and white dots represent the bit values of 1 and 0 in the 8-bit output of the LBP operator.
Z. Guo et al. / Pattern Recognition 43 (2010) 706–719708