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EO-1 often reduce the SNR. To correct

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EO-1 Hyperion:
Hyperion (Pearlmann, 2003) is a hyperspectral sensor on board the NASA Earth
Observer 1 (EO-1) which functioned from November, 2001 to April, 2016. With a
242 channels ranging from the VNIR to SWIR, 400 to 2500 nm, Hyperion images at
a spatial resolution of 30m and a radiometric resolution of 12 bits. Hyperion
data is available as level 1, radiometrically calibrated product (Level 1R) as
well as radiometrically, geometrically corrected and georeferenced data (Level
1GST and 1T). Each of these datasets need to be further corrected before they
can be used to develop products of our interest. Of the 242 bands, some are
highly noisy and a redundancy exists due to the overlap of detecting regions by
the VNIR and SWIR detector. Hence we ignore these bands and the total usable
bands comes down to 196 (1-7, 58-78 and 225-242 are removed). This is followed
by correction due to effects of the atmosphere. The corrections often reduce
the SNR. To correct for this, attempts to separate the noise from the data are
performed using the MNF denoising technique.

RapidEye:
The RapidEye constellation is a set of 5 satellites designed and developed by
Surrey Satellite Technology Ltd in 2008 and later acquired by Planet in 2015.
It provides imagery of 5m/pixel spatial resolution in 5 bands (red, green,
blue, red-edge and near infrared). With an elevation of 630km and a 77km swath,
RapidEye has a revisit time of 5.5 days at nadir. All five satellite sensors
are calibrated similarly leaving no distinction between satellite imagery from
any sensor. The a mosaic of 5 level 3 ortho-corrected imagery was used for this
study. Atmospheric correction was performed using the Quick Atmospheric
Correction (QuAC) technique.

2.2
Study Area

The
study area is the Dhemaji and Lakhimpur region of Assam which is abundant in
rice crop cultivation. Hence, the red edge region is specifically used for
further discrimination within the vegetation class. Dhemaji district of Assam
is bound by Arunachal Pradesh in the north and the river Brahmaputra in the
south. It is a plain area with an average elevation of 104 m above sea level.
Numerous drainage systems originating from the hills of Arunachal Pradesh flow
through Dhemaji to drain into the Brahmaputra. Physiographically, Dhemaji is in
the form of three main sub districts: the piedmont zone where Dhemaji borders
the Arunachal Himalayas,  the active
flood plains near the river Brahmaputra and its tributaries, and the low lying
alluvial belt. With a total geographic area of 323,700 Ha, Dhemaji covers a
variety of socio-geographic features including build up (208 Ha), horticultural
lands (2534 Ha), forest cover (53,225 Ha) and grasslands (97,167 Ha), making it
a perfect study area for the classification techniques aimed towards vegetation.
Five regions were selected across Dhemaji and Lakhimpur and data of Hyperion
and RapidEye taken on October, 2012 were analyzed and regions of interest were
selected based on the LULC map generated at the North Eastern Space
Applications Centre for 2011-2012. Each region and the subsequent classes we
have classified into are summarized below. The regions used for the study are
depicted in Figure 1. Details of training and test samples are available in
Table 2-4.Region 1: This
region depicts mainly the following features in the LULC map. A perennial and
non-perennial drainage system, agricultural lands, fallow lands and dense
plantations surrounding the rural build up near the water bodies. As the rural
build up was evident only in the form of a few pixels in the RapidEye image, we
have selected four classes for this region: (1) water body, (2) vegetation type
1 for agricultural lands, (3) vegetation type 2 for dense plantations
intermingled with rural build up and (4) fallow lands.

Region 2: This
region is geographically similar to region one. There exists a perennial water
body as well as waterlogged regions, agricultural lands, fallow lands and dense
plantations around rural build up. Five classes were selected: (1) water body,
(2) vegetation type 1 for agricultural lands, (3) vegetation type 2 for dense
plantations, (4) fallow lands and (5) water logged wastelands. The similarity
with region 1 was maintained so that accuracies could be checked in varying the
number of classes.

Region 3: Five
classes were selected for this region. However, a larger variety of vegetation
types were selected to check if the red edge bands could accurately assess the
class type. The classes selected are as follows: (1) water body, (2) vegetation
type 1 for agricultural lands, (3) vegetation type 2 for agricultural lands,
(4) dense plantations and (5) barren/fallow lands.

3 METHODOLOGY

A
Hyperion strip over the Dhemaji and Lakhimpur districts of Assam taken on
October, 2012 was used. RapidEye images over the same region for October, 2012
at similar local times were mosaicked and subsetted to the same areal extent as
the Hyperion data. This was followed by georeferencing the Hyperion data set to
the RapidEye data set using control points. Once both datasets were prepared,
the processing in the form of bad band removal was performed for Hyperion and
atmospheric corrections were performed on both Hyperion and RapidEye images. The
corrected and georeferenced images were fused using the Gram-Schmidt
hyperspectral sharpening method. See the original Rapid Eye image, Hyperion
image and fused image in Fig 2 a ,b and c respectively. The spectral
characteristic of the region is as observed in Fig 3 a ,b and c.Hyperspectral
datasets require significant denoising for enhanced spectral understanding.
Hence, the Minimum Noise Fraction Transformation as implemented by Green et al,
1998 was used. This is implemented using the concept of principle components.
The Eigen values and Eigen vectors of the image are obtained and ordered (See
Fig 2). The image is then projected onto the Eigen space to decorrelate the
bands and noise whitening is performed. The noise related Eigen value are
discarded and the signal rich Eigen-images are employed for the inverse that
gives us the denoised image that is used for classification.

A
spectral subset of the fused image and the Hyperion image in the red edge
region was also considered to understand if a red edge based classification
depicts superior results in the case of vegetation classification.Multiple
previous studies have been performed using fusion of hyperspectral or
multispectral images and panchromatic high resolution images (e.g. Pohl, 2013,
Akhtar et al, 2014, Yokoya et al, 2017). Yakoya et al, 2017 has further
performed a comparison of results for the different fusion methods for a
variety of datasets including AVIRIS, HyDICE etc. Many fusion algorithms exist
which vary in the accuracy either resulting in spatial or spectral distortions
(Zhang et al, 2007; Yakoya et al, 2012; Qian and Chen, 2012). Recent years have
seen more sophisticated attempts at the hyperspectral fusion challenge. Chen et
al., 2014 performed fusion by dividing the multispectral image into individual
bands and hyperspectral image into segments of bands centred around a
corresponding multispectral band and performed pan sharpening on each segment.
In this study, we use the Gram Schmidt spectral sharpening method (summarized
in Laben and Brower, 2000 and Maurer, 2013). This involves the hyperspectral
image combined via a linear combination by using weights to represent it as a
panchromatic image.

                                                                                               

         …
(1)

This
is followed by the Gram Schmidt orthonormalization of the vectors in the N
dimensional space where each band represents an N dimensional vector where N is
the number of pixels. This procedure decorrelates the bands. The
orthonormalization procedure involves the pan band taken as the first vector (v1).
It follows the general formula as follows where ui is the
orthonormal vector and vi is the original vector:

                                                            u1=v1
                               …
(2)

                                     

              … (3)

This
is followed by replacing the averaged panchromatic image with the high spatial
resolution panchromatic image and performing an inverse Gram Schmidt transform
(similar to the forward transform). This gives us the fused product.

In
order to check for the validity of the fused product, point to point spectral
correlation was investigated between the fused data and the Hyperion data and
the correlation coefficient and regression coefficient were calculated.

3.2
Classification

Five
regions within the Dhemaji-Lakhimpur region was considered. Classification was
performed using ROIs derived from the LULC map as archived by the North Eastern
Space Applications Centre and visual examination of the images. Hyperspectral
classification techniques are adversely affected by the Houghes effect due to
which the required number of training samples for larger number of bands
increases to maintain the accuracy. Breunig et al, 2011 suggest that the SVM,
SID and SAM classifiers do not demonstrate a reduction in accuracy. Hence, two
classifiers were used for the purpose: Support Vector Machines (SVM) and
Spectral Angle Mapper (SAM). Classification was performed on the three segments
using RapidEye, Hyperion and the fused result of RapidEye and Hyperion and the
results were assessed by comparing the kappa coefficient and accuracy
assessment.

3.2.1 Spectral Angle Mapper (SAM) Classifier:
SAM is a classifier that compares the similarity between the test and training
samples by considering the spectrum to 
be a D dimensional vector where D is given by the number of bands. The
training samples are either the laboratory spectra in the form of spectral
libraries that have been resampled to the dimensionality of the test samples.
Alternately, they are obtained from known regions within the satellite imagery
that is being classified. This study uses ROIs as obtained from a ground survey
performed in the Dhemaji and Lakhimpur district in 2012. Spectral similarity is
estimated by calculating the angle between the test and training spectrum
vectors.

                                               

           …
(4)

Larger
angles suggest dissimilarity. An advantage SAM has over other traditional
classifiers is the independence from intensity values permitting regions of
shadow to also be classified accurately.

3.2.2 Support Vector machine (SVM)
Classifier: Support Vector Machine based
classification is a well recognized classification technique where an N-1
dimensional hyperplane is used to separate the data by maximizing the margin
between them. The hyperplane is called the optimal hyperplane and the data
points closes to the hyperplane are the constraining factors and are called the
support vectors. This suggests that SVM is a linear classifier. However, to
account for non linear classification, SVM can be used alongside kernels such
as polynomial, radial basis function, sigmoid etc. This study utilizes two
commonly used kernels which have demonstrated significant success in the past (Gordon,
2004). The mathematical form of the polynomial kernel is given as below:

                                               

   … (5)

Here,
x is the input, xi is the support vector and d is the degree of the polynomial
to be used. See below for the radial basis function kernel expression:

                                               

     … (6)

There
are two parameters of concern that can be tweaked: the gamma parameter and the penalty
parameter. The gamma parameter depicts the influence of the training sample
with smaller values causing far reaching influence. The penalty parameter or
the misclassification trade off parameter affects the smoothness of the
decision boundary. Larger values cause over fitting.  

3.2.3 Maximum Likelihood Classifier
(MLC): MLC  is based on the
Bayes law following posterior=prior*likelihood/evidence given by:

                                          

            … (7)

 

             

             … (8)

Generally, the prior probability of the for a class
? is assumed to be a constant or expected to be equal to each other and the
evidence, P(x), is usually common to all classes, therefore Lx is
dependent on P(x/?). Classification is performed such that the likelihood of x
belonging to a class ? is maximized. Sampling
should be such that the estimation of the mean and covariance is reflective of
that of the population. The maximum likelihood method is not useful when the distribution of the
population does not follow the normal distribution.

 

 

4. RESULTS AND DISCUSSION:

4.1
Spectral Characteristics of the Fused Product:

From Figure 3, we observe that the Gram Schmidt
spectral sharpening leads to an offset in the intensity values of the fused
product. In order to study if any distortion occurs or if the difference lies
solely in the offset, we have performed a correlation test on the data set. Ten
random regions were selected from both the Hyperion image and the fused image.
The average spectra of each region was computed and a scatter plot was used to
check for the correlation. Very high correlation was observed with an average
Pearson coefficient of correlation as 0.98 and a regression coefficient of
0.96.Multiple
previous studies have been performed using fusion of hyperspectral or
multispectral images and panchromatic high resolution images (e.g. Pohl, 2013,
Akhtar et al, 2014, Yokoya et al, 2017). Yakoya et al, 2017 has further
performed a comparison of results for the different fusion methods for a
variety of datasets including AVIRIS, HyDICE etc. Many fusion algorithms exist
which vary in the accuracy either resulting in spatial or spectral distortions
(Zhang et al, 2007; Yakoya et al, 2012; Qian and Chen, 2012). Recent years have
seen more sophisticated attempts at the hyperspectral fusion challenge. Chen et
al., 2014 performed fusion by dividing the multispectral image into individual
bands and hyperspectral image into segments of bands centred around a
corresponding multispectral band and performed pan sharpening on each segment.
In this study, we use the Gram Schmidt spectral sharpening method (summarized
in Laben and Brower, 2000 and Maurer, 2013). This involves the hyperspectral
image combined via a linear combination by using weights to represent it as a
panchromatic image.                                                                                               

         …
(1)

This
is followed by the Gram Schmidt orthonormalization of the vectors in the N
dimensional space where each band represents an N dimensional vector where N is
the number of pixels. This procedure decorrelates the bands. The
orthonormalization procedure involves the pan band taken as the first vector (v1).
It follows the general formula as follows where ui is the
orthonormal vector and vi is the original vector:

                                                            u1=v1
                               …
(2)

                                     

              … (3)

This
is followed by replacing the averaged panchromatic image with the high spatial
resolution panchromatic image and performing an inverse Gram Schmidt transform
(similar to the forward transform). This gives us the fused product.

In
order to check for the validity of the fused product, point to point spectral
correlation was investigated between the fused data and the Hyperion data and
the correlation coefficient and regression coefficient were calculated.

3.2
Classification

Five
regions within the Dhemaji-Lakhimpur region was considered. Classification was
performed using ROIs derived from the LULC map as archived by the North Eastern
Space Applications Centre and visual examination of the images. Hyperspectral
classification techniques are adversely affected by the Houghes effect due to
which the required number of training samples for larger number of bands
increases to maintain the accuracy. Breunig et al, 2011 suggest that the SVM,
SID and SAM classifiers do not demonstrate a reduction in accuracy. Hence, two
classifiers were used for the purpose: Support Vector Machines (SVM) and
Spectral Angle Mapper (SAM). Classification was performed on the three segments
using RapidEye, Hyperion and the fused result of RapidEye and Hyperion and the
results were assessed by comparing the kappa coefficient and accuracy
assessment.

3.2.1 Spectral Angle Mapper (SAM) Classifier:
SAM is a classifier that compares the similarity between the test and training
samples by considering the spectrum to 
be a D dimensional vector where D is given by the number of bands. The
training samples are either the laboratory spectra in the form of spectral
libraries that have been resampled to the dimensionality of the test samples.
Alternately, they are obtained from known regions within the satellite imagery
that is being classified. This study uses ROIs as obtained from a ground survey
performed in the Dhemaji and Lakhimpur district in 2012. Spectral similarity is
estimated by calculating the angle between the test and training spectrum
vectors.

                                               

           …
(4)

Larger
angles suggest dissimilarity. An advantage SAM has over other traditional
classifiers is the independence from intensity values permitting regions of
shadow to also be classified accurately.

3.2.2 Support Vector machine (SVM)
Classifier: Support Vector Machine based
classification is a well recognized classification technique where an N-1
dimensional hyperplane is used to separate the data by maximizing the margin
between them. The hyperplane is called the optimal hyperplane and the data
points closes to the hyperplane are the constraining factors and are called the
support vectors. This suggests that SVM is a linear classifier. However, to
account for non linear classification, SVM can be used alongside kernels such
as polynomial, radial basis function, sigmoid etc. This study utilizes two
commonly used kernels which have demonstrated significant success in the past (Gordon,
2004). The mathematical form of the polynomial kernel is given as below:

                                               

   … (5)

Here,
x is the input, xi is the support vector and d is the degree of the polynomial
to be used. See below for the radial basis function kernel expression:

                                               

     … (6)

There
are two parameters of concern that can be tweaked: the gamma parameter and the penalty
parameter. The gamma parameter depicts the influence of the training sample
with smaller values causing far reaching influence. The penalty parameter or
the misclassification trade off parameter affects the smoothness of the
decision boundary. Larger values cause over fitting.  

3.2.3 Maximum Likelihood Classifier
(MLC): MLC  is based on the
Bayes law following posterior=prior*likelihood/evidence given by:

                                          

            … (7)

 

             

             … (8)

Generally, the prior probability of the for a class
? is assumed to be a constant or expected to be equal to each other and the
evidence, P(x), is usually common to all classes, therefore Lx is
dependent on P(x/?). Classification is performed such that the likelihood of x
belonging to a class ? is maximized. Sampling
should be such that the estimation of the mean and covariance is reflective of
that of the population. The maximum likelihood method is not useful when the distribution of the
population does not follow the normal distribution.

 

 

4. RESULTS AND DISCUSSION:

4.1
Spectral Characteristics of the Fused Product:

From Figure 3, we observe that the Gram Schmidt
spectral sharpening leads to an offset in the intensity values of the fused
product. In order to study if any distortion occurs or if the difference lies
solely in the offset, we have performed a correlation test on the data set. Ten
random regions were selected from both the Hyperion image and the fused image.
The average spectra of each region was computed and a scatter plot was used to
check for the correlation. Very high correlation was observed with an average
Pearson coefficient of correlation as 0.98 and a regression coefficient of
0.96.