and treetop-based spectra were extracted for tree species clas-
sification in this research.
The redundancy of full hyperspectral datasets is not ef-
ficient or reliable due to the Hughes’ phenomenon, which
arises when the ratio between the number of training samples
and the number of features is small (Hughes, 1968). There-
fore, optimal spectral subsets are necessary to be selected for
maximizing the discrimination of target features (Jones
et al
.,
2010). In this study, a stepwise spectral discriminant analysis
(
SDA
) based on the Wilk’s lambda method was carried out us-
ing
SPSS
(ver. 22) to reduce the dimensionality of the hyper-
spectral data. Wilk’s Lambda is a multivariate analysis of vari-
ance, and it corresponds to the ability of each band to separate
tree classes. The less the Wilk’s lambda, the greater the separa-
bility between classes (George
et al
., 2014). To assess the lost
information in selecting optimal bands, both full bands (312
bands) and optimal bands (6 bands) were used to classify tree
species with the same samples and
SVM
algorithms.
Structural Feature Extraction from Lidar Data
The structure of a tree crown is defined as the distribution of
all the plant elements (e.g. leaves, twigs, branches, etc.) and
their geometric properties (e.g., size, shape) within the tree
crown (Wang and Jarvis, 1990). The structural properties have
a significant effect on radiation absorption, photosynthesis,
and transpiration, and they can be derived from the discrete
lidar data (Fassnacht
et al
., 2014; Wang and Jarvis, 1990).
As the most basic and intuitive attribute, tree height plays
an important role in forestry and forest ecology (St-Onge
et
al
., 2004), and many other features, such as the biomass and
DBH
, were also calculated (Ørka
et al
., 2009). Therefore, tree
heights were chosen as the first structural feature for tree spe-
cies classification.
Crown shape is another feature suited to distinguish spe-
cies because it is more invariant to life stages and can capture
between-species variability in crown morphology (Alves,
2002; Antin
et al
., 2013). The three-dimensional (3D) shape
signature was developed by Osada
et al
. (2002) to measure
geometric properties of the 3D object. A 3D shape signature
describes a probability distribution sampled from a shape
function measuring geometric properties of a 3D object.
Therefore, it can reduce the 3D matching problem to the
comparison of 2D probability distribution. In this study, the
shape signature measuring the frequency distribution of the
heights at random points on a crown surface was derived,
and then the shape index, one-dimensional expression of
shape signature in measuring geometric properties of the 3D
object, was further calculated for tree species classification.
In particular, when the number of random points, such as
5,000, was determined, the points within a crown scale were
randomly selected and their heights were extracted from the
crown surface, and then the values were sorted and put into
user defined histogram bins, such as 100, to illustrate the
height frequency. Based on the height shape signature, the
shape index was calculated using the following equation:
SI
i b b
i
m
i
m
= ×
=
=
∑ ∑
1
1
(
) /
i
i
(1)
where,
m
is the number of bins, is the number of points in bin
i.
In addition to
SI
, a third index, coefficient of variation (
CV
)
describing the height dispersion within a crown scale, was
developed.
CV
is known as relative standard deviation (
RSD
)
measuring the variability of a series of numbers independent
of the unit (Abdi, 2007). Comparing with the absolute vari-
ability of standard deviation,
CV
is a helpful statistic in com-
paring the degree of variation from one data series to another
with considerably different means.
CV
is defined as the ratio
of the standard deviation
σ
to the mean
E
:
CV
E
=
σ
(2)
where
E
n
X
n
X E
j
n
j
n
=
=
−
=
=
∑ ∑
1
1
1
0
2
j
j
and
σ
(
) ;
n
is the number
the samples;
X
j
is the height of the sample
j
.
Data Fusion and Classification
In order to assess the contribution of different structural fea-
tures to tree species classification, treetop height (
TH
), shape
index (
SI
), and coefficient of variation (
CV
) were integrated
with the optimal treetop-based spectra respectively. The fused
datasets consisted of the following four variables.
1. Optimal hyperspectral bands (Spectral only)
2. Optimal hyperspectral bands + tree height (Spectral +
TH
)
3. Optimal hyperspectral bands + shape index (Spectral +
SI
)
4. Optimal hyperspectral bands + coefficient of variation
(Spectral +
CV
).
Among the total 198 trees included in this study, 20 percent
to 25 percent of trees were randomly selected from each of the
four groups as training data set and leaving others as testing
data for the crown-level tree species classification. As a result,
12 out of 51 ash trees, 12 out of 59 maple trees, 14 out of 70
oak trees, and 9 out of 18 other species were set aside for
model training, leaving 39 ashes, 47 maples, 56 oaks, and 9
other species for accuracy assessment.
We applied a non-linear support vector machine (
SVM
)
classifier in the classification process.
SVM
has been proven
better than conventional approaches in performing classifi-
cation in complex environments, as it finds a hyperplane to
maximize the margin between different classes (Petropoulos
et al
., 2012). Linear hyperplane is only efficient for linearly
separable samples, while non-linear hyperplane derived from
a variety of kernel functions can represent more complex
shapes and operate in a high dimensional space. In this re-
search, the radial basis function (
RBF
) kernel
SVM
was chosen
due to better performance and less number of required param-
eters. Based on the
ENVI
User’s Guide (2008), the parameters
of γ is the inverse of the number of the spectral bands, which
were set as 0.0032, 0.167, and 0.143 respectively for the clas-
sification based on 312 bands, 6 optimal bands, and 7fused
bands. C controls the cost of misclassification on the training
data, which was set as 100. The number of pyramids and the
classification probability threshold were set as zero to force
the imagery processed at the full resolution and each pixel
belongs to a class.
Performance of the fusion methods were compared with
the results obtained by hyperspectral only, based on the over-
all accuracy (
OA
), producer’s accuracy (
PA
), user’s accuracy
(
UA
), and the Kappa (
K
) statistic (Petropoulos
et al
., 2012).
In addition, the McNemar test
(Lu et al
., 2014; Zhang
et al
.,
2013) at a 95 percent confidence level was employed in
SPSS
statistics, which can evaluate the statistical significance of
differences in accuracy among the four fusion methods.
Results
Individual Tree Identification
Treetops in the study area were first detected using the local
maximum method on the lidar-derived canopy height model.
Due to the inaccessibility of trees in private properties for
498
August 2018
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
