Effects of Hyperspectral Data Transformations on Urban Inter-class Separations using a Support Vector Machine
Raja M. Kamil Raja Ahmad
This study investigated the performance of different data types used in a hyperspectral data classification process. Data in the form of spectral reflectance, first derivative spectra and wavelet coefficients were used as inputs for the Support Vector Machine (SVM) algorithm used to classify five different classes. The first derivative spectra gave a lower classification accuracy (35.6%) than the spectral reflectance (82%) and the use of wavelet coefficients further improved the classification accuracy to 100%. Proper selection of the wavelet transformation method, the mother wavelet, the number of vanishing moments and the decomposition level could improve classification accuracy. In summary, wavelet coefficients could maximise discrimination capability as compared to the spectral reflectance and first derivative spectra.
Received: April 23, 2010;
Accepted: July 05, 2010;
Published: July 27, 2010
The availability of various remote sensing data provides an opportunity for users to fully utilise the data to achieve their goal with a maximum success rate. These opportunities arise because remote sensing technology has been used in many applications including mapping, the military, meteorology, agriculture and others. Different types of data have their own usefulness. Multispectral data with high spatial resolution is suitable for mapping and hyperspectral data is more suitable for subtle discrimination.
Hyperspectral data have been widely used because of their capability in discriminating
between subtle variations among similar features and they could improve the
users capability for gaining a greater understanding of various features.
Although, it has been extensively used in agricultural applications (Rao
et al., 2007; Gong et al., 2002;
Mutanga et al., 2004; Chappelle
et al., 1992; Hansen and Schjoerring, 2003),
hyperspectral data have also been extensively used for urban and sub-urban applications
(Heiden et al., 2007; Bassani
et al., 2007).
Several methods such as clustering (Gomez-Chova et al.,
2009; Oldeland et al., 2010) or indices (Oldeland
et al., 2010; Huang et al., 2009;
Kuckenberg et al., 2008; Devadas
et al., 2008) are possible for discriminating between one feature
and others. Classification (Laverington, 2010; Wang
and Sousa, 2009; Lucas et al., 2008; Wilson
et al., 2004; Castro-Esau et al., 2004)
is also one of the methods used to discriminate between features. There are
several factors that can contribute to the success of a classification process,
including the selection of data type for use as input for the classification
(Koger et al., 2003; Yang
et al., 2009; Ouma et al., 2008),
the selection of the optimal band (Phillips et al.,
2009; Keshava, 2004; Murakami,
2004; Serpico and Moser, 2007) and the use of classifiers
(Shafri and Ramle, 2009; Clark et
al., 2005; Yang et al., 2009; Erbek
et al., 2004; Ali et al., 2009; Nelson,
1981). These are the major factors that will impact the classification accuracy.
For hyperspectral data, the original data are normally in the form of the spectral
reflectance. Exploitations or transformations of the original data could be
performed to improve the classification results. Calculating the spectral derivative
is one of the transformations that can be applied to the reflectance data and
several studies have shown that derivative data could achieve better results
than the reflectance data (Tsai and Philpot, 1998; Han,
2002). Wavelet transformations can also be used as a data transformation
method and have been used for applications like feature extraction, image compression,
feature detection and others (Hsu, 2007; Koger
et al., 2003; Galford et al., 2008;
Bruce et al., 2002; Loum
et al.,2007; Ping et al., 2009; Raju
et al., 2008).
study area and the AISA image
However, the best data type has yet to be determined for use in classifying
different urban-area features while using data from an Airborne Imaging Spectrometer
for Application (AISA). This is particularly important in the Malaysian context
because AISA is currently the only airborne hyperspectral sensor available through
a commercial data provider. Thus, this study focused on determining the effects
of data input selection on the classification of inter-class features by using
MATERIALS AND METHODS
The data used in this study were acquired in November 2009 over an area in Kuala Lumpur, Malaysia (Fig. 1a). With a pixel size of approximately 1x1 m, the AISA image covers a spectral region of 400-1000 nm with a spectral resolution of approximately 5 nm for 128 bands. The AISA image used in this study is shown in Fig. 1b.
The three major steps involved in this study were image processing, data transformation and classification. The general methodology of this study is shown in Fig. 2.
Image processing: The AISA image required processing before feature
extraction could be made. The image was converted to reflectance because it
was collected in radiance mode to minimise the effects of the atmosphere. The
conversion method used was a log-residual method in ENVI software. After the
conversion to reflectance was made, a Minimum Noise Fraction (MNF) transformation
This step minimised the noise in the image. Twenty seven first-MNF bands were
used to obtain a de-noised image that had less noise than the original image
obtained using the Inverse MNF method. Next, the Pixel Purity Index (PPI) was
performed to find the pixels of highest purity in the image that represent certain
Feature extraction: The feature extraction was performed based on the PPI result. Five features were selected for further processing: vegetation, water, road, concrete and rooftop. One hundred pixels were extracted from the de-noised image for each feature. Each pixel represented the signal for that particular feature. Those signals were used for further processing. Figure 3 shows the average spectral reflectance for the selected features.
Data transformation: The methodology for data transformation is shown in Fig. 4. Three major steps were involved in this process and included spectral derivative conversion followed by wavelet conversion of the spectral reflectance and derivative data using a Continuous Wavelet Transform (CWT) and a Discrete
Wavelet Transform (DWT). Selection of the mother wavelet was also performed along with selection of the number of vanishing moments and the level of decompositions.
The original spectral reflectance data can be transformed into other types
of dimensional data by applying mathematical operations. Using transformed data
may provide better information and understanding than using the original data.
For instance, the spectral derivative enhances the spectral differences in certain
parts of the spectrum, removes multiplicative factors and reduces the effect
of the soil background (Tsai and Philpot, 1998; Gong
et al., 2001).
||Average spectral reflectance for vegetation, water, road,
concrete and rooftop features
All of the spectral reflectance samples used in this study were transformed
into first derivative by using Eq. 1 (Dawson
and Curran, 1998).
where, FDR is the first-derivative reflectance at wavelength i, R(j) is the reflectance at wavelength j, RÆÆ(j+1) is the reflectance at wavelength j+1 and Δë is the difference in wavelength between j and j+1.
Wavelet transformations were then applied to the spectral reflectance and the first-derivative data. A wavelet is a mathematical function used to divide a given function (or signal) into different scale components and a wavelet transform is the representation of a function by wavelets. Wavelets have advantages over traditional Fourier transform for representing functions that have discontinuities and sharp peaks. Wavelets also have advantages for deconstructing and reconstructing a signal. Discrete Wavelet Transform (DWT) and Continuous Wavelet Transform (CWT) are two types of wavelet transformations.
There are several types of mother wavelets and each mother wavelet has its
own characteristics. The mother wavelets are different in terms of their orthogonality,support,
regularity and symmetry.
||Flowchart for the methodology of data transformation
||Wavelet families representing (a) Haar, (b) Daubechies, (c)
Symlet, (d) Coiflet, (e) Biorthogonal, (f) Reverse Biorthogonal and (g)
|| Example of a three-level DWT decomposition
As a result, wavelet coefficients vary according to the selection of mother
wavelet. This study uses only seven mother wavelets (Fig. 5a-g):
Haar, Daubechies, Symlet, Coiflet, Biorthogonal, Reverse Biorthogonal and Discrete
Both DWT and CWT were used in this study. Each spectral reflectance and first-derivative spectrum was transformed or decomposed into wavelet coefficients with nine levels of decomposition. For DWT, each decomposition process produced two types of coefficients, the approximation coefficient (cA) and the detail coefficient (cD). Their values are illustrated in Fig. 6. Only the detail coefficient from each level was used as an input for classification. DWT and CWT were tested to determine the best method of wavelet transformation for use in distinguishing features.
Both the spectral reflectance and the first derivative data were decomposed using the selected wavelet families to study the effects of mother wavelet selection on discrimination capability and to investigate which of the mother wavelets performed best. Haar, Daubechies (db1-db20), Symlet (sym1-sym20), Coiflet (coif1-coif5), Biorthogonal (bior1.1-bior6.8), Reverse Biorthogonal (rbio1.1-rbio6.8) and Discrete Meyer (dmey) are the seven mother wavelets that were tested in this study. They were decomposed, level-by-level, up to level nine. Since the transformation was applied to both the spectral reflectance and the first-derivative spectra, the analysis generally produced two groups of wavelet coefficient data. One group contained the wavelet coefficients derived from the spectral reflectance dataset and the other group was derived from the first-derivative dataset. The classification of datasets containing the spectral reflectance, the first-derivative and the wavelet coefficients were performed after the wavelet transformation process was completed.
Support vector machine classification: Classification was one of the
methods used for information extraction. Various supervised and unsupervised
classification algorithms may be used to assign data to one possible class.
The choice of classifier (i.e., decision rule) depends on the nature of input
data and the desired output (Jensen, 2005).
of the SVM process in two-dimensional space. Blue dots represent data
from group 1 while red dots represent data from group 2
The Support Vector Machine (SVM) method was selected because it is considered
the most suitable classifier for handling limited samples (Chi
et al., 2008). SVM is a supervised learning method used for classification
and regression. It constructs a separating hyperplane between two sets of data
in n-dimensional space. The hyperplane will maximise the margin between the
two data sets. A good separation is achieved by the hyperplane that has the
largest distance separating the neighbouring data points of both classes. Larger
margins will lower the generalisation error of the classifiers.
The spectral reflectance, the first derivative of spectral reflectance, the wavelet coefficients derived from the spectral reflectance and the wavelet coefficients derived from the first-derivative spectra were used as inputs for SVM classification. Fifty samples from each group were used as a training dataset. To eliminate any potential bias, only the remaining separate samples were used as testing dataset. The performance of the spectral reflectance, first-derivative and all-wavelet coefficients data were evaluated based on the classification accuracy (Fig. 7).
RESULTS AND DISCUSSION
First derivative transformation: The values of the spectral reflectance
data depend on many factors including sun illumination. Use of the first-derivative
data has an advantage over use of the reflectance data because it minimises
the effects of sun illumination. Several studies have established the usefulness
of the first-derivative data for separating classes more effectively than the
reflectance data (Tsai and Philpot,1998;
||First-derivative spectra of the spectral reflectance of each
Figure 8 shows the first-derivative spectra of the average
spectral reflectance for each class.
Wavelet coefficients: Different wavelet coefficient values were obtained
from the decomposition of different mother wavelets. There were also differences
in wavelet coefficient values obtained from the spectral reflectance and first-derivative
spectra. Although, the spectral reflectance and the first derivative spectra
were decomposed using the same mother wavelet, their wavelet coefficient values
resulting from decomposition were different. It has been suggested for some
time that the use of spectral derivatives can reduce the illumination and other
effects, thus, the use of spectral derivatives as input data may offer further
benefits when applying wavelet analysis (Blackburn and Ferwerda,
2008). In addition, the number of vanishing moments used for the decomposition
also affected the resulting wavelet coefficient values. Figure
9 shows an example of the wavelet coefficient values obtained from spectral
reflectance data and first-derivative spectra obtained from a vegetation sample.
Generally, the coefficient values of each mother wavelet varied because of different
characteristics the mother wavelets. The coefficient values derived from first-derivative
spectra were also smaller than the coefficient values derived from the spectral
reflectance. More visualization of wavelet transformation of spectral reflectance
and first-derivative using DWT and CWT methods by Blackburn
and Ferwada (2008).
Classification results: The performance of all data types that were tested in this study was assessed by their classification accuracies. Generally, higher classification accuracy indicates better feature discrimination.
The classification results of the spectral reflectance and the first-derivative
data are shown in Table 1. The classification accuracy for
the spectral reflectance was higher than the classification accuracy of the
||An example of Haar, Daubechies and Symlet coefficient values
obtained from a spectral reflectance sample and its derivative spectrum
using the DWT method and a nine-level decomposition. (a) Spectra reflectance,
(b) First derivative spectra, (c, d) Haar coeddicients, (e, f) Daubechies
coefficient and (g, h) Symlet coefficient
||Classification accuracies of reflectance and first-derivative
The classification accuracy achieved by using spectral reflectance was 82%
and the classification accuracy of first derivative was only 35.6%. The classification
accuracy drops significantly when using derivative-transformed data. Several
other studies also obtained similar results in which the classification accuracy
of derivative is lower than the classification accuracy of spectral reflectance
(Jones et al., 2010; Li
and He, 2008; Zhang et al., 2006). For this
study, the derivative spectra could not improve the discrimination capability
and had worse discrimination capability than the spectral reflectance. The low
classification accuracy achieved by using the derivative data may be caused
by noise in the spectra because the spectral derivative is very sensitive even
to small variations in the data. This factor was believed to have contributed
to the low overall classification accuracy achieved when using derivative spectra.
The classification accuracy for wavelet coefficients can vary with the selection
of transformation method, mother wavelet, number of vanishing moments and decomposition
level. Some of the mother wavelets gave higher classification accuracies than
the original dataset, while some gave lower classification accuracies. This
difference shows that not all mother wavelets were suitable for feature discrimination.
Koger et al. (2003), Zhang
et al. (2005) and Bruce et al. (2002)
got similar result pattern when classifying using different mother wavelet coefficients
data sets. Koger et al. (2003) studied on detecting
pitted morningglory in soybean using wavelet analysis. The classification accuracies
were varied for most of the mother wavelets. Only several mother wavelets gave
same accuracy. This indicated that classification accuracy is depending on the
selection of mother wavelet. Selecting the number of vanishing moments was also
as critical as the selection of the mother wavelet. This result is shown in
Figure 11 shows the maximum accuracy of every level while
using wavelet coefficients derived from reflectance and spectral-derivative
data with DWT transformation. In general, the maximum accuracy increased with
the number of decompositions used. The accuracy for one-level decomposition
was lower than the accuracy at higher-level decompositions. This result may
be due to the noise occurring at every level. Lower decomposition levels may
contain more noise than the higher decomposition levels.
||Classification accuracies achieved with the Daubechies wavelet
while using different numbers of vanishing moments
||Maximum classification accuracies achieved from each level
of decomposition while using the DWT wavelet coefficient. This data was
based on the maximum accuracy for each level, independent of the mother
wavelet, the number of vanishing moments and the level of decomposition
The coefficient values at lower decomposition levels were small and smaller
coefficient values were often assumed to be noise in the data. Besides that,
the number of coefficients at a lower decomposition level was greater than the
number of coefficients at higher decomposition levels. Wavelet coefficients
at lower scale are sensitive to narrow or local spectral features because they
are derived from high-pass filters, which is similar to the derivative spectra
(Zhang et al., 2006). Those factors could affect
classification accuracy with regard to the selection of decomposition level.
Figure 11 also suggests that the classification accuracy
while using wavelet coefficients derived from reflectance was higher than the
accuracy of wavelet coefficients derived from derivative-spectra.
||Classification accuracies when using the Daubechies wavelet
with different numbers of vanishing moments
An exception was the three-level decomposition. This result shows that wavelet
coefficients derived from spectral reflectance are more reliable for discriminating
between features than wavelet coefficients derived from derivative spectra.
Maximum classification accuracy could be achieved by using wavelet coefficients
derived from the reflectance when using a five-level decomposition. Wavelet
coefficients derived from derivative spectra only gives maximum accuracy when
using wavelet coefficients with a seven-level decomposition.
The same pattern of results was also achieved when using wavelet coefficients
that had been transformed using CWT transformation (Fig. 12).
Lower classification accuracy was achieved when using lower levels of decomposition
and wavelet coefficients derived from reflectance gave better classification
accuracies than wavelet coefficients derived from derivative spectra. The only
difference between DWT and CWT was that the CWT transformation could not produce
wavelet coefficients that provided a maximum classification accuracy of 100%
(as with DWT).
||Classification accuracies of the reflectance, the first-derivative
spectra, the best wavelet coefficients of reflectance and the derivative
This result showed that the DWT transformation was much better than the CWT
transformation for discriminating features.
The classification accuracy for wavelet coefficients derived from first-derivative spectra did not produce better accuracies than wavelet coefficients derived from the spectral reflectance. This may have been due to noise contamination in the original data, thus resulting in poor classification results. However, there was an improvement in classification accuracy for wavelet coefficients of derivative spectra compared to the classification accuracy of the derivative spectra. This result proved that wavelet transformation could be used as one of the transformation method for improving the output result and achieving a maximum success rate.
The overall accuracy of the data types analysed in this study is summarised in Table 2. The spectral reflectance gave better classification results than the derivative spectra. Furthermore, the wavelet coefficients of the spectral reflectance and the derivative spectra may maximise the classification accuracy. The results using Symlet 12 and reflectance data can be considered better as it requires only five-level decomposition compared to the use of Haar wavelet with derivative spectra that requires eight-level decomposition. Decomposition to a higher level would demand more processing time. Thus, Symlet 12 with a five-level decomposition transformed from reflectance data by using the DWT transformation was the best wavelet coefficient for discriminating between features.
Although this study has proven that Symlet 12 is the best wavelet coefficients
in discriminating between features, this wavelet will not guarantee to give
the best results when applied to other data sets. Previous studies by Bruce
et al. (2002), Koger et al. (2003)
and Zhang et al. (2005) and have shown differences
in terms of the performance of the best mother wavelet achieved from their studies.
In summary, the selection of data types was essential to achieve the desired output with minimum error. The selection of wavelet transformation method, mother wavelet, number of vanishing moments and level of decomposition also played an important role in achieving better results. This study showed that the first-derivative spectra do not necessarily provide better classification accuracies than the spectral reflectance data. Some of the mother wavelets derived from spectral reflectance or from derivative spectra resulted in lower classification accuracies than the original dataset and some of the mother wavelets produced improvements in the classification results. This study showed that the potential of using wavelet-transformed data for discriminating features with a maximum success rate. Better ways of dealing with noise could be investigated to utilise the spectral derivative fully in future studies using this data.
The authors would like to thank the Ministry of Higher Education Malaysia for the research grant and UPM for providing a graduate scholarship to aid in the completion of this research. Aeroscan Precision (M) Sdn. Bhd. is also acknowledged for providing the test data.
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