The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
Optimized Spectral Angle Mapper classification of spatially heterogeneous
dynamic dune vegetation, a case study along the Belgian coastline
Bertels Luc1, Bart Deronde1, Pieter Kempeneers1, Walter Debruyn1, Sam Provoost2
1. Flemish Institute for Technological Research, Remote Sensing and Earth Observation
Processes, Boeretang 200, B-2400 Mol, Belgium; e-mail: luc.bertels@vito.be
2. Institute of Nature Conservation, Kliniekstraat 25, 1070 Brussel, Belgium
ABSTRACT
Vegetation classification starting from hyperspectral images is a widely used technique for
material identification and mapping. The unknown pixels are assigned to a certain vegetation type
whose reference spectrum is derived from the hyperspectral imagery by means of Regions Of Interest
(ROIs). The standard Spectral Angle Mapper (SAM), available in most image processing software
packages, uses the average spectrum of each ROI. This implies that the spectral variability within
each ROI, denoted as the intra-class variability, is not retained. To preserve the intra-class
variability, an Optimized Spectral Angle Mapper (OSAM) was developed consisting of two parts.
Firstly an Optimal Spectral Library (OSL) is generated which preserves the spectral variability
present within each ROI. This library can be considered as ‘optimal’ since it contains the spectra
that classify all pixels of a certain class correctly, without misclassifying pixels which do not belong to
that class. At the same time, for each reference spectrum, a maximum spectral angle distance is
calculated which is used in the second step to avoid misclassifications. Secondly, all image pixels are
classified using the reference spectra stored in the OSL, taking into account the calculated maximum
spectral angle distance. This means that each pixel will be assigned to the class of the reference
spectrum for which the smallest spectral angle value was calculated with the actual pixel spectrum.
Accuracy assessment was done using a part of the ROIs for training, while the remaining part of the
ROIs was used for validation. An overall accuracy of 53% was obtained when using the standard
SAM. When using the Optimized Spectral Angle Mapper, an overall accuracy of 64% was obtained.
Keywords: Hyperspectral; Classification; Spectral Angle Mapper; Optimized Spectral Angle
Mapper.
I. INTRODUCTION
The dynamic dunes along the Belgian coast are important natural ecosystems with
respect to nature conservation. They are the habitat of several rare and unique plant
species and wildlife. Besides their biological value they serve as a natural seawall
protecting the hinterland against storms and floods. An accurate and thorough knowledge
of the distribution of plant species in the dynamic dunes is a critical component for
managing these dunes and preserving their biological diversity. Various public
institutions need detailed and regularly updated vegetation maps of the active dunes, salt
marshes and mudflats along the Belgian coast for managing the area. The ‘Administratie
Waterwegen en Zeewezen’ of the Flemish Government uses vegetation maps of the
dynamic dune areas to estimate the strength of the seawall and to decide whether specific
protection measures are necessary. The Administratie Waterwegen en Zeewezen is also
responsible for the public management of several nature reserves in the dunes. In
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
addition, the Institute of Nature Conservation is carrying out ecological research in the
coastal dunes for over 15 years. It supports and monitors the conservation actions taken
by the Nature Division of the Flemish Government, which is responsible for the
ecological management of the coastal dunes.
The main purpose of this research was to develop a new method for efficient, detailed,
objective and cost-efficient vegetation mapping. A test area located at the west coast of
Belgium, called ‘De Westhoek’, was selected for which data cubes were obtained from
the AISA Eagle sensor. The data was collected in July 2004 with 32 spectral bands in the
VIS-NIR region and a pixel resolution of 1 m x 1 m. Classification of the test site was
performed using 12 vegetation types and 4 non-vegetation types. Endmember spectra
used for classification training were extracted from the hyperspectral imagery using 221
Regions Of Interest.
II. SPECTRAL ANGLE MAPPER (SAM)
One of the most applied strategies for material mapping is the use of similarity
measures. This study makes use of a deterministic similarity measure to compare an
unknown pixel spectrum with a library of reference spectra. Spectral Angle Mapper
(SAM), is a common distance metric, which compares an unknown pixel spectrum t to
the reference spectra ri, i = 1, ..,K, for each of K references and assigns t to the material
having the smallest distance:
Class t   arg min d t , ri 
(1)
1 i  K
The reflectance spectra of individual pixels can be described as vectors in an ndimensional space, where n is the number of spectral bands. Each vector has a certain
length and direction. The length of the vector represents brightness of the pixel while the
direction represents the spectral feature of the pixel. Variation in illumination mainly
effects changes in length of the vector, while spectral variability between different
spectra effects the angle between their corresponding vectors, (Kruse et al., 1993).
Figure 1 depicts a pair of three-dimensional spectra and indicates the Spectral Angle, ,
created by them that SAM quantifies. The more similar the two spectra are, the smaller
the spectral angle between them. The spectral angle can have values between 0 and 
and is calculated by the formula given in (2).


1 
  cos 






i 1

n
n
2
2 
ti  ri 

i 1
i 1

n
tr
i i
(2)
With n = the number of spectral bands, t = the reflectance of the actual spectrum and r =
the reflectance of the reference spectrum.
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
β3
t

β2
r
β1
Figure 1 Visualization of the Spectral Angle, , between two spectra, t = target spectrum, r =
reference spectrum, using three bands β1, β2, β3.
Classification is performed by calculating the spectral angles between the reflectance
spectrum of the target pixel and the reference spectra. Each pixel will be assigned to the
class according to the lowest spectral angle value.
III. OPTIMIZED SPECTRAL ANGLE MAPPER
Ideally, the reflectance spectra of a vegetation type should not vary, but in reality,
they do, due to a number of factors, i.e. phenological stage, weather conditions, soil
conditions, shadows, Bidirectional Reflectance Distribution Function (BRDF) effects,
etc. The standard Spectral Angle Mapper (SAM), available in most image processing
software packages, uses the average spectrum of each Region Of Interest (ROI). This
implies that the spectral variability within each ROI, denoted as the intra-class variability,
is not retained. To preserve the intra-class variability, an Optimized Spectral Angle
Mapper (OSAM) was developed consisting of two parts as shown in Figure 2.
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
Hyp.
Hyp.
File
File
Hyp.
File
Roi
Roi
Roi
1
Optimal
Library
Generation
Optimal
Spectral
Library
2
Optimized
SAM
Classification
Classified
Image
Figure 2. The optimized SAM classification.
In the first step an Optimal Spectral Library (OSL) is generated which preserves the
spectral variability present within each ROI. This library can be considered as ‘optimal’
since it contains the spectra that classify all pixels of a certain class correctly, without
misclassifying pixels which do not belong to the class under consideration. In the second
step, all image pixels are classified using the reference spectra stored in the OSL. This
means that each pixel will be assigned to the class of the reference spectrum for which
the smallest spectral angle value was calculated with the actual pixel spectrum.
The algorithm was tested on AISA EAGLE images, acquired over the Belgian
coastline in July 2004. The imagery was collected in 32 spectral channels in the visual
and NIR spectral range of the electromagnetic spectrum and with a spatial resolution of
1m. The radiometric and geometric correction was performed by the operator of the
AISA sensor, while the atmospheric correction was performed in house with the help of
ATCOR4.
A. Generating the optimal spectral library
The pixel spectra of the different vegetation types, also named vegetation classes
C  C1 , C 2 ,..., C k , where k is the number of different vegetation classes and which are
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
collected by the ROIs, are stored in a spectral library S  s1a , s 2b ,..., s kj . Where s1a is the
pixel spectrum of class C1 and 1  a  nC1 , with nc1 the number of pixel spectra in C1.
Similarly skj is the pixel spectrum of class Ck and 1  j  nck , with nck the number of pixel
spectra in Ck. When creating the optimal spectral library, each spectrum in the spectral
library S is considered as reference spectrum s(r) for which the spectral angle values, ,
are calculated against all the target spectra s(t) in the same spectral library S. Both, s(r)
and s(t) are N dimensional vectors, where N equals the number of spectral bands, with
1  r , t  M and M the total number of spectra in the spectral library S. The result is a
two-dimensional M by M matrix X with its elements defined as:
X (r , t )   ( s(r ), s(t )), 1  r , t  M
(1)
For each reference spectrum s(r), with 1  r  M , two vectors are defined. One vector,
v(r), contains all intra-class spectral angle values, the other vector, w(r), contains all
inter-class spectral angle values and this implicates: X(r )  v(r )  w (r ) . When s(r) is a
spectrum of class Ci these vectors can be written as:
v(r , t a )   ( s(r ), s(t a )), 1  t a  M : s(t a )  Ci
(2)
(3)
w(r , t r )   ( s(r ), s(t r )), 1  t r  M : s(t r )  Ci
Here s(ta) is the target spectrum which belongs to the same vegetation class Ci as the
reference spectrum s(r) and s(tr) is the target spectrum which does not belong to the same
vegetation class Ci as the reference spectrum s(r). The set of inter-class vectors
M
W  w(r )r 1 , is used to create a vector, μ, containing the minimum spectral angle value
found in each inter-class vector w(r), with elements:
 (r )  arg _ min w(r), 1  r  M
(4)
Subsequently, the values in μ and the intra-class vectors V  v (r )r 1 are used to define a
vector ε, containing the effectiveness value for each reference spectrum s(r). The
effectiveness value ε(r) is the number of intra-class spectral angle values found in v(r),
less then the corresponding spectral angle value μ(r). What follows is an iterative process
to create the Optimal Spectral Library (OSL):
M
For all Ci
Iterate until no reference spectrum s(r) left which is a member of Ci
Create a vector εi, containing the effectiveness values for the
spectra s(r) in Ci
Locate the maximum value in εi
Store the corresponding reference spectrum s(r), minimum spectral
angle value μ(r) and effectiveness value ε(r) in the OSL
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
Remove the spectra with a spectral angle value μ(r), less then
μ(r) just stored in the OSL and which are a member of Ci
from X.
s11 … s1n1
C2
C1
s11 … s1n1
C2
…
s21
Ck
s2n2
sk1 ... sknk
μ
ε
μ(r)
ε(r)
0
s2n2
C1
…
s(t)
s(r)
v(r) 0
w(r)
Ck
sk1 ... sknk
s21
w(r)
0
0
Figure 3. The principle of generating the optimal spectral library. The spectra s of the different
vegetation classes C are used to create a matrix containing the spectral angle values between all
spectra. These spectral angle values are used to create a vector, μ, containing the smallest inter-class
spectral angle values in w. The intra-class spectral angle values in v and μ are used to create a vector
containing the effectiveness value ε which is used to generate an Optimal Spectral Library. A detailed
description of the algorithm is given in the text.
B. The optimized spectral angle mapper classification
In the final step, all image pixel spectra are classified using the reference spectra
stored in the optimal spectral library. Therefore, the spectral angle values are calculated
between each image pixel spectrum and all spectra in the OSL. To make the calculated
spectral angle values comparable, it is necessary to normalize them to values between 0
and 1. This is done by dividing them by their corresponding minimum spectral angle
value μ(l). Finally, the image pixel will be assigned to the class corresponding with the
reference spectrum for which the smallest spectral angle value was calculated.
C. Accuracy Assessment
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
The classification accuracy is calculated by randomly selecting 50% of the ROIs
present for a certain class and using them for training the classification (i.e. building the
OSL). The remaining 50% of the ROIs of a certain class, are used to validate the OSAM
classification result (i.e. they are classified using the OSL).
IV. EXPERIMENTS AND DISCUSSION
A. Data
Dewberry
Roughness
Sparse_vegetation
Wet_sand
Dry_sand
Urbain
Water
35
10
18
12
10
3
6
3
7
4
3
2
Validation
4
8
4
9
10
5
11
5
4
1
4
2
4
2
2
1
Elder
14
Wild_privet
4
Creeping_willow
9
Grey_willow
Grassland
5
Sea_buckthorn
Moss
Training
Dune_slack
Number
of
ROIs
Marram
On July 6 2004, a flight campaign was undertaken with the objective of mapping
the dune vegetation along the entire Belgian coast (about 30 square kilometers).
Hyperspectral data were collected by the British company Infoterra Ltd using the AISA
Eagle sensor which was flown at an altitude of 1500 m. The data was collected in 32
bands in the VIS-NIR region with a pixel resolution of 1 m x 1 m. The total length of
flight lines acquired is about 50 km; however, this study concentrates on a small part of
the imagery collected, i.e. the nature reserve ‘De Westhoek’. Radiometric, geometric and
atmospheric corrections were made to convert the raw data, as collected by the AISA
Eagle sensor, to corrected, calibrated and georeferenced hyperspectral images.
During an extensive field campaign, performed by experienced ecologists from
the Flemish Institute for Nature Conservation (IN), several hundreds of vegetation plots
were inventoried and their geographic locations were measured by using dGPS. Some
targets were measured as polygons, but in case of homogeneous regions with a minimum
diameter of 5m, a point measurement of the central location was performed. The point
measurements were used to define ROIs of 3 by 3 pixels size around the central point’s
location. Finally, the ROIs were used to extract the pixel spectra from the hyperspectral
imagery which are used as references in the classification algorithm. All classification
experiments were performed with the commercial software package ENVI© Version 4.0.
Water
Urbain
Dry_sand
Wet_sand
Sparse_vegetation
Roughness
Dewberry
Elder
Wild_privet
Creeping_willow
Grey_willow
Sea_buckthorn
Dune_slack
Grassland
Moss
Class
Marram
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
SAM
58
76
17
40
63
37
25
35
24
12
15
70
34
100
88
100
OSAM
67
86
14
38
90
64
47
41
11
0
44
47
33
100
100
100
Overall Accuracy
%
Kapa
Coefficient
SAM
53
0.46
OSAM
64
0.59
Class
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
ACKNOWLEDGMENT
This research was financed by the Belgian Science Policy and by the Flemish
Government – Coastal Waterways Division. The authors gratefully thank Dr. Carine
Petit, Dr. Joost Vandenabeel, Ir. Peter De Wolf and Ir. Toon Verwaest for their support.
The 9th International Symposium on Physical Measurements and Signatures in Remote Sensing
(ISPMSRS). Beijing, October 17-19, 2005
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