bits with 0 values are likely to be found in the former numbers,
because of the existence of more surrounding pixels having the
same intensity as the central one. However, 0 values dominate
also in case of heterogeneous neighborhoods having a central
pixel with larger intensity values than its surrounding pixels.
To counterbalance this drawback, a variation of the local binary
patterns algorithm is also tested, termed local ternary patterns
(Tan and Triggs, 2007), with the incorporation of a third value in
labeling neighboring pixels. In this case, if a pixel intensity dif-
fers within a predefined range +d from the central pixel it takes
value 1. If it is larger or smaller than the central pixel by more
than d, it takes value 2 or 0, respectively. In addition, depending
on the value of range d, the measure may handle noise and poten-
tial inaccuracies of the data, up to a certain degree. The created
number is now expressed in the ternary system instead of the bi-
nary, i.e. having number three as basis. The more homogeneous
textures are expected to be represented by numbers close to the
one having all its bits equal to 1.
Following the same notion, another variation can be introduced
from the combination of local binary and ternary patterns, by as-
signing value 0 to the pixels whose intensity differs less than a
range +d from the central one and value 1 otherwise. In this
measure, the more homogeneous a patch, the smaller its measure
value is expected to be.
4 RESULTS AND DISCUSSION
To evaluate the performance of the proposed measures in esti-
mating vegetation height and discriminating between LPH/MPH
and TPH habitat classes, different versions of the measures were
applied to all patches of low/mid and tall phanerophytes on Le
Cesine site, extracted from the available habitat map, for each
band of the Quickbird image. 52 LPH/MPH and 99 TPH patches
were totally considered. For each patch, each measure was calcu-
lated on a per pixel basis and then averaged for the pixels of the
patch.
The discriminatory power of each measure for a specific band
was tested in two ways. At first, Student's t-tests were applied
to compare the measure values for LPH/MPH and TPH patches.
Under the null-hypothesis that the values of LPH/MPH and TPH
patches come from the same distribution, one-tailed tests were
performed to assess our expectation that LPH/MPH patch values
are significantly smaller than TPH ones. In addition, the ability of
the measures to create correct classification of the LPH/MPH and
TPH patches was evaluated with a decision tree classifier based
on the CART (Classification And Regression Tree) methodology
(Breiman et al., 1984). A CART tree consists of binary nodes,
each one examining whether the value of a patch for a specific
measure is smaller or larger than a certain value. In addition, at
the end of the training process, CART trees are pruned, i.e. the
number of their nodes is reduced to a certain degree, in order to
increase their generalization performance with data non belong-
ing to the training set.
Table 1 summarizes the results of the evaluation of the texture
analysis measures. Different parameters were tested for each ap-
proach, resulting in different instances of each measure. À clas-
sification tree was created for each measure in each band. For
the training of each tree a random subset of 30 LPH/MPH and 50
TPH patches was selected; the non-selected patches were used
for testing the classification accuracy of the tree. The ratio of
the correctly classified patches to the total number of the test set
patches is recorded in the table. In addition, the p-value resulting
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
from each t-test is drawn, indicating the probability that a differ-
ence between the LPH/MPH and TPH mean values as large as or
larger than the one observed can occur, assuming that the null hy-
pothesis is true. The lower the p-value, the larger the probability
that the null hypothesis is wrong and, thus, the measure values
for the LPH/MPH patches do not come from the same distribu-
tion and are significantly smaller than the TPH ones.
Two versions of the local energy measure appear in Table 1: in
LEI, a window of 3 x 3 pixels around each pixel was used for the
calculation of the variance, while in LE2, a window of 5 x 5 pixels
was used. In LH1 and LH2 versions, the local entropy was calcu-
lated in 9 x 9 pixel windows. The data were quantized in 8 bins
for each individual window in LH1, while in LH2 quantization
in 8 bins was applied to the whole region from the beginning. A
quantization in 8 bins of the whole region and a selection of 9 x 9
pixel windows as the small ones, were applied in ‘LHR’ versions
of the calculation of the local entropy ratio. In LHR1 and LHR2
the small windows were included in the calculation of the local
entropy of the large windows. In LHR1, 13 x 13 pixel windows
were selected as the large ones, while in LHR2 their dimensions
were 21 x 21 pixels. In LHR3 and LHR4, the same parameters as
in LHR1 and LHR2, respectively, were used, with the difference
that the inner window pixels were excluded from the calculation
of the local entropy of the outer windows. Rotation invariant and
rotation variant local binary patterns were calculated for radius 1
in LBP1 and LBP2, respectively. In LBP3 and LBP4, the same
parameters were used, with the radius changing to 2. The ‘LTP’
and ‘LTBP’ versions were the same as the respective ‘LBP’ ones,
with the only difference being that the ternary system and the
modified binary approach were adopted, respectively.
As observed, most p-values resulting from the t-tests are signif-
icantly smaller than the 5% level of significance usually used in
assessing the null hypothesis (Chatfield, 1983). This provides a
strong evidence against the null hypothesis that the mean values
of the measures for LPH/MPH and TPH patches are almost the
same and strongly supports our theoretical assumption that the
values of the LPH/MPH patches are significantly smaller than
the TPH ones. The smaller the p-value for a specific measure
instance, the higher the confidence that this instance can lead to
clear discrimination of low/mid and tall phanerophyte patches.
As far as the used Quickbird bands is concerned, it is observed
that all visible ones performed almost equally well and outper-
formed the near-infrared (NIR) band in discriminatory power.
Among them, values extracted from the green band, seem to pro-
vide better results for most measures. Regarding the measures
tested, the local ternary patterns, ‘LTP’, and the modified local
binary patterns, ‘LTBP’, instances seem to outperform all other
measures in the visible bands, with the latter appearing slightly
better. The local entropy ratio measure, on the other hand, ap-
pears robust in all bands and provides satisfactory results even
in the NIR band, especially in the implementations where the
outer window is significantly larger than the inner one, LHR2
and LHRA.
The top performing measures as far as the t-test is concerned,
include the implementation of the rotation invariant local ternary
patterns with radius 1, LTP1, as well as the modified rotation vari-
ant local binary patterns approach with radius 2, LTBP4, both cal-
culated in the green band, with p-values of the order of magnitude
of 107??, As expected, these results are in accordance with the
CART classification assessment results, where LTP1 and LTBP4
instances in the green band present the highest rates in correctly
classifying LPH/MPH and TPH patches based on their height.
The instance that outperforms all others in classification accu-
racy is the modified rotation variant local binary pattern approach
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