Towards soft classification of satellite data A case study based ... - KTH

Towards soft classification of satellite data
A case study based upon Resurs MSU-SK satellite data and land
cover classification within the Baltic Sea Region.
Anna Haglund
Master of Science Project no. In Geoinformatics
Royal Institute of Technology
Department of Geodesy and Photogrammetry
Stockholm, Sweden
March 2000

Universitetsservice US AB
Stockholm 2000
08-790 7400

Preface
This master of science project has been performed at the department of geodesy and
photogrammetry, division for geoinformatics by assignment of Satellus, during the autumn
1999. The project comprises 20 credits and is the completion of the education for technical
surveyors at the Surveying Program at the Royal Institute of Technology, KTH, in Stockholm.
I would like to thank my supervisors at KTH: Sindre Langaas, dept.of Civil and
Environmental Engineering and Maria Roslund, dept. of Geodesy and Photogrammetry.
I would also like to thank Satellus in Solna, where I have performed the project.
Especially I want to thank Kjell Wester, who has been my supervisor at Satellus and has
given many technical advises and come up with ideas.
I
Stockholm, mars 2000
Anna Haglund

Sammanfattning
Vid användning av medelupplösande satellitbilder med en pixelstorlek på 150-250 m på
marken kan det vara svårt att välja homogena träningsytor. Pixelstorleken är också större än
många objekt på marken, varför de kanske försvinner i en ”hård klassning”, där varje pixel
bara kan tilldelas en klass. Ibland vill man att varje pixel ska innehålla så många klasser som
det är i verkligheten. För att klara dessa problem har s k. mjuka klassificerare utvecklats.
Syftet med rapporten är att undersöka hur många klasser som kan fås från
medelupplösande satellitdata när man använder högupplösande data som referens för
generering av träningsytor och fastställa hur bra klassificeringen blir.
Undersökningen gjordes med delar av två RESURS-bilder från två olika tidpunkter, med
tre spektrala band, över en del av södra Sverige. Som referens användes svenska
landtäckedata (SLD). För fyra olika samplingsmetoder jämfördes resultatet från IDRISIs
moduler för mjuka klassificerare med varandra. Det skattade medelfelet varierade mellan
klasserna och var minst för de små klasserna och förekomsten för varje klass jämfört med
referensbilden skiljde sig relativt mycket. En orsak till den bristfälliga överensstämmelsen kan
delvis bero på att referensbilden inte är helt korrekt. Referensbilden är baserad på information
från den digitala topografiska kartan, varifrån klassgränser tagits och klassning oftast skett
bara innanför gränsen med maximum-likelihood. Med antagandet att referensbilden är korrekt
kommer felaktigheten i referensdata att skyllas på RESURS-klassningen och därmed försämra
den bedömda noggrannheten. Passningen mellan RESURS-scenerna och referensbilden är
också en felkälla liksom passningen RESURS-scenerna sinsemellan. Så det finns både
tematiska och geometriska fel. En annan orsak är för få träningsytor tillsammans med att
klasserna inte alltid är spektralt separerbara.
En förbättring av mjukvaran måste också göras innan någon användning i produktion kan
bli aktuell.
III

Abstract
When using medium resolution satellite images with a pixel size of 150-250 m on the ground
it can be difficult to collect homogenous training sites. The pixel size is also larger than many
objects on the ground, why they might disappear in a “hard classification”, where every pixel
just can contain one class. The wish is often that every pixel should contain as many classes
as there are in reality. To manage these problems, so called soft classifiers have been
developed.
The purpose of the paper is to examine how many classes that can be extracted from
medium resolution satellite data when using higher resolution satellite data as reference and
how well the classification performs.
This examination was conducted using parts of two RESURS images from two different
dates, with three spectral bands, covering a section of the southern parts of Sweden. As
reference the national land cover classification was used. For four different samplings I
compared the results from the IDRISI modules for soft classification with each other. The
RMS errors varied between the classes and were smallest for the small classes and the
occurrence in the image for each class compared to the reference image differed relatively
much. One reason for the insufficient agreement can partly be due to that the reference image
is not completely correct. The reference image is based on information from the digital
topographical map, from which class boundaries has been taken and the classification mostly
been performed within these, with maximum-likelihood. With the assumption that the
reference image is correct, the errors in this will be blamed on the RESURS classification and
thus worsen the assessed accuracy. The geometric correction between the RESURS images
and the reference image, as well as the geometric correction between the RESURS images
them selves, are also an error source. So there are both thematic and geometric errors. One
other reason is too few training sites along with not always spectrally separable classes.
There need to be done some improvements in the software before any use in production can
be of interest.
IV

Contents
PREFACE...................................................................................................................................................................I
SAMMANFATTNING.......................................................................................................................................... III
ABSTRACT.............................................................................................................................................................IV
CONTENTS ............................................................................................................................................................. V
1. INTRODUCTION ................................................................................................................................................1
1.1BACKGROUND...................................................................................................................................................1
1.2 OBJECTIVES......................................................................................................................................................1
1.3 THE BALANS PROJECT ..................................................................................................................................1
1.4 STRUCTURE OF THE THESIS..............................................................................................................................2
2. MEDIUM RESOLUTION SENSORS...............................................................................................................3
2.1 AVAILABLE SENSORS .......................................................................................................................................3
2.2 FUTURE SENSORS .............................................................................................................................................4
3. A REVIEW OF SOFT CLASSIFIERS..............................................................................................................5
3.1 INTRODUCTION.................................................................................................................................................5
3.2 FUZZY SET THEORY.........................................................................................................................................6
3.2.1 Fuzzy c-means (k-means) ........................................................................................................................7
3.2.2 Applications with Fuzzy c-means classifier............................................................................................7
3.3 SOFTENING MAXIMUM LIKELIHOOD CLASSIFIER (MCL).................................................................................8
3.3.1 Applications with softening MCL ...........................................................................................................8
3.4 LINEAR MIXTURE MODELLING.........................................................................................................................8
3.4.1 Applications with linear mixture modelling ...........................................................................................9
3.5 METHODS BASED ON BAYESIAN PROBABILITY THEORY .................................................................................9
3.5.1 Applications with Bayesian probability theory ....................................................................................10
3.6 METHODS BASED ON DEMPSTER-SHAFER THEORY ......................................................................................10
3.6.1 Applications with Dempster-Shafer theory ..........................................................................................11
3.7 NEURAL NETWORK........................................................................................................................................11
3.7.1 The Multilayer Perceptron Classifier using feed-forward and back-propagation.............................11
3.7.2 Applications with Multilayer Perceptron Classifier ............................................................................13
3.7.2 Neural Network using Cascade-correlation.........................................................................................14
3.7.3 Applications with Cascade-correlation................................................................................................14
3.7.4 Fuzzy ARTMAP......................................................................................................................................14
3.7.5 Applications with Fuzzy ARTMAP........................................................................................................16
4. DATA AND METHODS ...................................................................................................................................17
4.1 INTRODUCTION...............................................................................................................................................17
4.2 DATA ..............................................................................................................................................................17
4.2.1 Satellite data ..........................................................................................................................................17
4.2.2 Reference data .......................................................................................................................................18
4.3 STUDY AREA...................................................................................................................................................19
4.3.1 General description of the Baltic Sea region landscape......................................................................19
4.3.2 Quantitative characterisation ...............................................................................................................20
4.4 TOOLS.............................................................................................................................................................20
4.4.1 IDRISI ....................................................................................................................................................20
4.4.2 ERDAS IMAGINE .................................................................................................................................21
4.5 METHODOLOGY..............................................................................................................................................22
4.5.1 Outline....................................................................................................................................................22
4.5.2 Initial data preprocessing .....................................................................................................................22
4.5.3 Choice of soft classifiers .......................................................................................................................24
V

4.5.4 Application of soft classifiers................................................................................................................24
4.5.4 Evaluation and comparison of soft classifiers .....................................................................................25
5. RESULTS ............................................................................................................................................................27
5.1 INTRODUCTION...............................................................................................................................................27
5.2 FUZZY SIGNATURES .......................................................................................................................................27
5.3 RMS ERRORS .................................................................................................................................................27
5.4 OVER- AND UNDER CLASSIFIED PIXELS .........................................................................................................29
5.5 AVERAGE VALUES..........................................................................................................................................33
6. DISCUSSION......................................................................................................................................................40
7. CONCLUSIONS AND RECOMMENDATIONS..........................................................................................41
REFERENCES.........................................................................................................................................................42
APPENDIX 1: ACTION STEPS FOR SOFT CLASSIFICATION...............................................................................44
APPENDIX 2: MACROFILE- SCHEME ..............................................................................................................47
VI

1. Introduction
1.1 Background
Satellite images have been used for land cover classification ever since the first earth resource
satellites were launched. The most used method for classification has been the maximumlikelihood
algorithm. Recently, medium resolution satellite data (150-250 m) has begun to be
provided. Also then was the maximum-likelihood algorithm used in classification. There have
been several studies done with the maximum-likelihood classifier. One made with medium
resolution satellite data was done by Malmberg and Furberg (1997). The last five years there
has been a progress on the method side. New classifiers have been developed – soft
classifiers. They have been developed as a consequence that coarse- and medium resolution
satellite data often contain mixed pixels, e.g. forests have no sharp boundaries between
coniferous- and deciduous forest.
It is a new and exciting field. These new soft classifiers can extract more information than
the maximum-likelihood classifier.
1.2 Objectives
The main objective is to evaluate and compare the suitability of some soft classifiers to
deduce land cover information in a patchy landscape using medium resolution satellite data,
in particular for a study area in the Baltic Sea region for the purpose of the BALANS project
(Landcover Information for the Baltic Sea Drainage Basin).
Secondary objectives are to provide information about present and future satellites with
sensors that provide medium resolution data and make a review of the available soft
classifiers today and there requirements on input- and reference data.
1.3 The BALANS Project
The Remote Sensing Technology Division at Satellus, a subsidiary to the Swedish Space
Corporation, has in partnership with six organisations in Sweden, Norway, Finland and
Poland, started a project called BALANS. The BALANS project’s aim is to develop a
satellite-based land cover database for the complete Baltic Sea Drainage Basin, see figure 1,
using medium resolution satellites (Olsson 1999). Many organisations in the Baltic Sea region
have a common need for basic geographical data sets. Up to now the main need has been from
the environmental, hydrometeorological and marine sciences, but now there are growing
requirements from the physical planning, political and business communities (Langaas 1996).
Today, there are many growing pressures on the Baltic Sea. There is a critical need for
development that is sustainable, both economically and environmentally.
The database is envisaged to have a maximum resolution in the order of 200 meters.
The project will last for three years, and will be finished sometime in the end of year 2001
or the beginning of year 2002.
1

Figure 1. The Baltic Drainage Basin and the BALANS study area
(adapted from http://www.grida.no/baltic/htmls/maps.htm).
1.4 Structure of the thesis
In chapter 2, a review of present and future satellites with medium resolution satellite data is
provided. Chapter 3 is a review of available soft classifiers and some applications made with
those. Chapter 4 contains the data and method used in this study, chapter 5 the result and
discussion, followed by chapter 6 with the conclusions.
2

2. Medium Resolution Sensors
2.1 Available sensors
Medium resolution sensors are sensors that have a pixel size covering the ground of about
150-250 meter. They bridge the gap in image extent and spatial resolution between
SPOT/Landsat TM (20-30 m) and NOAA AVHRR (1.1 km) and are appropriate for mapping
of large areas, since not so many images are needed and the images are not too coarse.
Two satellites with medium resolution sensors covering the Nordic area are the Russian
satellite RESURS-O1 and the Indian Remote Sensing satellite, IRS. The satellites have
different sensors. RESURS-O1 has a MSU-SK sensor and IRS has a wide field sensor (WIFS),
see descriptions and data in table 1. The only available MSU-SK data today is archived
RESURS-O1 #3 data (SSC Satellitbild 1999). One orbit period takes 98 minutes and the
repetition cycle for that satellite is 21 days, with a potential coverage of a specific area every
third to fourth day at the equator. Every scene covers 600 x 600 km 2 . It is a wide-angle
instrument with a conical scan where every pixel has the same size and viewing angle. The
data from the curved scanning lines are resampled by cubic convolution from the nominal 170
meters raw pixels to 160 meter pixels to obtain a quadratic image grid.
The WIFS has two spectral bands, the red and the near infrared, with the applications to see
chlorophyll absorption of plants and to survey biomass and see waterbodies, respectively
(euromap 1997). One orbit around the earth takes 101.35 minutes to complete and it takes 341
orbits to cover the entire earth. The repetition cycle for the IRS satellites is 24 days, but IRS
1C/D works as a system so their combined repetition is 12 days. At the Nordic latitudes a
specific area is covered every 1-2 days. Also the WIFS’s scanning lines are resampled by cubic
convolution to obtain a quadratic image grid.
Both satellite types have large swath width. The largest difference between the satellites is
the number of wavelength bands. While RESURS-O1 MSU-SK has five bands: red, green, two
near infrared (NIR) and one thermal infrared (TIR), IRS WIFS only has two: the red and near
infrared. But in practice the TIR band in MSU-SK cannot be acquired in parallel with the
others. Experiences from the data indicates that there are better radiometric dynamics in data
from WIFS on IRS than in the data from MSU-SK on RESURS-O1 #3 (Hyyppä 1999).
3

Table 1. Summary of satellite and sensor data.
Satellites:
RESURS-O1 MSU-SK IRS-1C WiFS IRS-1D WiFS
Orbit sun-synchronous, circular sun-synchronous, circular, near polar
Average altitude 678 km 817 km
Inclination 98.04 deg 98.69 deg
Orbit period 98 min 101.35 min
Orbit repeat cycle 21 days 12 days (24 days for each)
Launch date 4/11 1994 28/12 1995 29/12 1997
Sensors:
Imaging mechanism Conical scan 2048 element linear array CCD
Viewing angle 39 deg ?
Spectralband: Wavelength: pixelsize: Wavelength: pixelsize:
1: Green 0.5-0.6 µm 160 m -
2: Red 0.6-0.7 µm 160 m 0.62-0.68 µm 188 m
3:NIR 0.7-0.8 µm 160 m 0.77-0.86 µm 188 m
4: NIR 0.8-1.1 µm 160 m -
5: TIR 10.4-12.6 µm 600 m -
Swath width 600 km 810 km 728-812 km
Potential coverage of same area 3-4 days at the equator 1-2 days at Nordic latitudes
Overlap ? Ca. 80%
2.2 Future sensors
There are two new medium resolution sensors coming. These are MODIS on the EOS AM-1
and MERIS on the ENVISAT satellite (Hyyppä 1999).
MODIS has a cross-track scan mirror and a set of linear arrays with spectral interference
filters located in four focal planes. It has a viewing swath width of 2330 km and will cover the
earth every 1-2 days. It will have 36 spectral bands in the range of 0.4-14.4 µm optimized for
measuring surface temperature, ocean colour, global vegetation, cloud characteristics, aerosol
concentrations, temperature and moisture soundings, snow cover and ocean currents. The
spatial resolution will be 250 m for band 1-2, 500 m for band 3-7 and 1000 m for band 8-36.
EOS AM-1 MODIS data will be available in spring 2000.
MERIS has radiation-sensitive arrays (CCD’s) that provides spatial sampling in the acrosstrack
direction and the satellite’s motion provides scanning in the along- track direction. It
will have 15 spectral bands in the range of 0.39-1.04 µm, that can be selected by ground
command. The swath width will be 1150 km. The spatial resolution will be 300 m over
coastal zones and land surfaces where communication capabilities exists. Otherwise, the
resolution is reduced to 1200 m to reduce the amount of data that will be recorded onboard.
ENVISAT MERIS data will be available in spring 2001.
4

3. A review of soft classifiers
3.1 Introduction
In conventional classification in remote sensing discrete pixels are used, i.e. the result is only
one class per pixel. Much information about the memberships of the pixel to other classes is
lost. This additional information can increase the accuracy of the classification.
Mixed pixels or ‘mixels’ occur because the pixel size may not be fine enough to capture
detail on the ground necessary for specific applications or where the ground properties, such
as vegetation and soil types, vary continuously, as almost everywhere.
Fuzziness suggests that a given pixel, owing to its spectral reflectance properties, may be
placed into more than one informational/spectral class. The output of a soft classification is a
set of images (one per class) that express for each pixel the degree of membership in the class
in question.
Soft classifiers can be useful in delineating forest boundaries, shorelines and other
continuous classes. They can also bring out objects that cover small areas, which with
conventional classifiers otherwise would have disappeared.
In training and testing in a classification, mixed pixels are usually avoided. But it may be
difficult to acquire a training set of an appropriate size if only pure pixels are selected for
training, since large homogenous regions of each class are needed in the image. The training
statistics defined, may not be fully representative of the classes and so provide a poor base for
the remainder of the analysis.
By recognising that there are various degrees to which fuzziness may be incorporated in
each stage, a continuum of classification fuzziness may be defined (Foody 1999). As
fuzziness may be a characteristic feature of both the remotely sensed data and the ground
data, the use of a fuzzy classification algorithm alone may be insufficient for the resolution of
the mixed-pixel problem.
The continuum ranges from fully fuzzy, where fuzziness is accommodated in all three
stages of the classification (the training-, allocation and testing stages), to completely crisp,
which are the conventional classification.
A modified maximum-likelihood classifier can accommodate fuzziness in any or all three
stages of the analysis and neural networks can provide a classification at any point along the
continuum of classification fuzziness.
In training, the data is hard if the pixels are pure and vary in fuzziness for mixed pixels.
Data on the fuzzy membership properties of training samples may be used to derive refined
class descriptors for use in the class allocation stage. By refining the training statistics where
some or even all of the pixels were mixed, the statistics that would have been derived if the
pixels had in fact been pure can be obtained (Foody 1999).
In the allocation stage for a soft classifier a pixel can be allocated from a single class to all
classes it provide membership in.
This chapter will describe the theory and algorithms behind the existing soft classifiers.
To make the theory more understandable this chapter will also describe some applications that
have been made.
5

3.2 Fuzzy Set Theory
Fuzzy sets are sets without sharp boundaries and they are applied to handle uncertainty in the
process of classification (Palubinskas 1994). The result is often a more detailed and precise
classification. Fuzziness can effectively extend the usefulness of map products developed
from remote sensing imagery. The fuzzy set theory is particularly interesting as the analyst
controls the degree of fuzziness (Foody 1996).
It is the shape of the membership function that defines the ‘fuzziness’ of the phenomenon
represented by the set. There are four membership functions that are usually used: sigmoidal
(s-shaped), J-shaped, linear and user-defined (Eastman 1997). The sigmoidal membership
function is the most commonly used in fuzzy set theory, see figure 2. It can be produced using
a cosine function that requires the positions (along the X-axis) of 4 points governing the shape
of the curve.
The J-Shaped membership function is also quite common, although in most cases the
sigmoidal function would be better. The linear is used extensively in electronic devices
advertising fuzzy set logic and the user-defined is used when the relationships between the
value and fuzzy membership does not follow any of the above three functions. The userdefined
is the most applicable (Eastman 1997). The control points used in this function can be
as many as necessary to define the fuzzy membership curve. The fuzzy membership between
any two control points is linearly interpolated.
Figure 2. The Sigmoidal Membership Function (based on Eastman 1997).
The outputs for each pixel are the different membership values for each class. A high
membership value indicates that the relevant land cover type covers a large area of the pixel
(Bastin 1997). When using summation of memberships for a post-classification of fuzzy
classification results, most of the increase of average classification accuracy is achieved after
the first iteration (Palubinskas 1994).
6

3.2.1 Fuzzy c-means (k-means)
Fuzzy c-means is a clustering algorithm used for either unsupervised or supervised
classification. The algorithm subdivides a data set into c-clusters or classes (Foody 1996). It
begins by randomly assigning pixels to classes and iteratively moves the pixels to other
classes with the aim of minimizing the generalised least-squared error,
J m ( U,
v)
= ∑∑(
u
n
c
k = 1 i=
1
where U is a fuzzy c-partition of the data set Y containing n pixels, c is the number of classes,
|| ||A is an inner product norm, v is a vector of cluster centres, vi is the centre of cluster i and
m is a weighting component that lies within the range 1≤ m ≤ ∞ which determines the degree
of fuzziness. The inner product norm is derived from,
2
7
k
)
m
y
k
− v
T
y − v = ( y − v ) A(
y − v )
k
i
A
k
−1
A number of norms may be selected, for instance the Mahalanobis norm, A = C y , where
Cy is the covariance matrix of the data set Y.
To implement the fuzzy c-means algorithm, additional parameters are required to guide the
partitioning process. These parameters are: selection of a distance measure and choosing a
weighting exponent. The weighting exponent controls the ‘hardness’ or ‘fuzziness’ of the
classification. The range of useful values for m is 1.5 < m < 3.0.
The fuzzy c-means algorithm is particularly useful in circumstances where it is not
reasonable to make assumptions about the statistical distributions of sample data (e.g. where
training sets of pure pixels are small).
For each pixel a fractional value is obtained for each class in the form of a real number
between 0 and 1, and will generally sum up to 1.0 across all candidate classes.
As output one also gets a residual error map showing the RMS error across the image.
The values need to be adjusted (i.e. using the slope from linear regression) for area
predictions to be made.
3.2.2 Applications with Fuzzy c-means classifier
A comparative study between traditional unsupervised classification and the fuzzy c-means
algorithm was done by Manyara and Lein (1994). Landsat MSS subsets were conducted to
detect environmental change. The fuzzy c-means were used since the boundary between forest
and other categories of land cover may be difficult to delineate precisely. Four smaller study
sites depicting different forest environments were extracted from the image. The approach of
the fuzzy c-means proved that a pixel often belongs to more than one class. Of the total 2 500
pixels per site, only 249 were pure in site I, 219 in site II, 29 in site III and 87 in site IV.
Another comparison has been made by Bastin (1997) between the fuzzy c-means and the
linear mixture model in the use for unmixing of coarse pixel signatures to identify four land
cover classes. The Mahalanobis norm was used as a typically measure and after a little
experimentation the weighting exponent, m, was set to 1.5. By this, dominant and minor land
cover classes in each pixel was easily identified, without the classification being overly hard.
The fuzzy c-means classifier performed best overall at locating and quantifying inclusions in
mixed pixels.
i
k
i
i
2
A

3.3 Softening maximum likelihood classifier (MCL)
MCL operate by using band means and standard deviations from training data to model land
cover classes as centroids in feature space, surrounded by probability contours. The
probability density function assumes that the sample values for each class are normally
distributed. The unclassified pixels are plotted in the same feature space and get a posteriori
probability. Usually the pixels are then assigned to the class for which they have highest
membership probability. But it is possible to soften the maximum likelihood classification by
using the a posteriori membership probability values as indices of class membership (Bastin
1997).
The data must still satisfy the assumptions and requirements of the classification technique
used, which is often unlikely with the probability-based classifiers.
3.3.1 Applications with softening MCL
In the comparison made by Bastin (1997) described above, a shell script was used to combine
each set of eight maximum likelihood classification output maps, and to produce a map
showing the a posteriori probabilities for each class. The result was mostly extremely
classified pixels, i.e. most of them were classified as pure pixels or as habitats being entirely
absent. To avoid an incorrect evaluation of this method, the classification should be softened,
by broadening the spread of the normal distribution functions, which represent the land cover
classes.
3.4 Linear mixture modelling
For linear unmixing of the spectral data, a ‘pure’ spectral signature needs to be obtained from
the training data, for each of the defined land cover types (Bastin 1997). The model views
mixed pixel signatures as being made up of a simple weighted linear sum of the component
land cover signatures in that pixel. The weights are directly determined by the relative
proportions of ground covered by each different land cover class by,
x = Mf + e
where x is the set of digital values measured by the sensor in each of n measurement
wavelengths, f is a vector of ground cover proportions, for each of c land covers.
M is a matrix of n x c coefficients, in which the columns are the vectors µ1…µc, which
represent the pure spectral signatures given by the c cover classes in the absence of noise, e is
a terments noise, which is minimized in some way in order to obtain a measure of the
proportion vector f.
The expected signature for a mixed pixel is the sum,
f1µ 1 + f 2µ
2 + ... + f c µ c = Mf
where for class c, fc is the proportion of the pixel covered, and µc is the characteristic
signature.
The noise caused by the sensor and by natural variability within a scene is quantified as
the vector of errors, e, which can be quantified as the sum of squares of its elements or as the
variance of the training data.
The linear mixture model assumes that each photon on the ground is interacting with only
one land cover type before being reflected back to the sensor. In a complex and non-random
landscape the linear mixture model is a reasonable approximation.
The model is trained using the matrix of values M generated from ground truth
8

information on ground cover proportions within selected pixels or from selected ‘purest’
pixels for each component. The effectiveness of the model is dependent on the degree of
separation of the different signatures and the level of noise present in the scene.
Rather than incorporating the noise and variability of the sample data into statistical or
fuzzy limits around each cluster centriod, the linear mixture model uses the centroid vectors
to define the spectral signatures of the pure land cover classes, and separates out scene/sensor
noise into a separate error term.
The number of distinguishable land cover types is strictly limited by the number of spectral
bands in the data.
3.4.1 Applications with linear mixture modelling
The comparison, mentioned above in the fuzzy c-means algorithm application and in the
softening of MCL, showed that the linear mixture model assigned extreme values to most of
the pixels (Bastin 1997). One of the reasons for that is that there were pixels outside the range
from zero to one in the classification, so called outliers. These outliers were reclassified to
minimum or maximum values respectively. The result from the linear mixture model was
fairly successful at picking up the general spatial patterns and gradations of the different cover
classes, but it had problems with specific land cover signatures, because of poor spectral
separability (Bastin 1997).
3.5 Methods based on Bayesian probability theory
The prime use for methods based on Bayesian probability theory is to determine the extent to
which mixed pixels exist in the image, and their relative proportions. The methods can only
be used when complete information is available or assumed (Eastman 1997). They are based
on the bayesian probability theory, which is the primary tool for the evaluation of the
relationship between the indirect evidence and the decision set. The bayesian probability
theory allows us to combine new evidence about a hypothesis along with prior knowledge to
arrive at an estimate of the likelihood that the hypothesis is true. The basis for this is
Bayes´theorem, which states that,
p(
h e)
=
where:
p(h⏐e) = the probability of the hypothesis being true, given the evidence (posterior
probability)
p(e⏐h) = the probability of finding that evidence, given the hypothesis, being true
p(h) = the probability of the hypothesis being true regardless of the evidence (prior
probability)
∑
i
p(
e h)
⋅ p(
h)
p(
e h ) ⋅ p(
h )
The variance/covariance matrix derived from training site data is the matrix that allows one
to assess the multivariate conditional probability p(e⏐h). This quantity is then modified by the
prior probability of the hypothesis being true and then normalized by the sum of such
considerations over all classes. This modification- and normalization step is important
because it assumes that the only possible interpretation of a pixel is one of those classes for
which training site data have been provided. Thus even weak support for a specific
interpretation may appear to be strong if it is the strongest of the possible choices given. So
even if the reflectance data for a certain class in a pixel is very weak it is treated as
unequivocally belonging to that class (p=1.0) if no support exists for other classes. It therefore
admits no ignorance and is a confident classifier.
9
i
i

The posterior probability p(h⏐e) is the same quantity that the maximum-likelihood module
evaluates to determine the most likely class.
If a pixel has posterior probabilities of belonging to certain classes of 0.72 and 0.28
respectively, this would be interpreted as evidence that the pixel contains 72 % of the first
class and 28 % of the second. But this requires that the classes for which training site data
have been provided are the only one existing and that the conditional probability distribution
p(e⏐h) do not overlap in the case of pure pixels. These requirements may in practice be very
difficult to meet.
3.5.1 Applications with Bayesian probability theory
No reports on studies using Bayesian probability theory have been found.
3.6 Methods based on Dempster-Shafer Theory
The methods based on Dempster-Shafer theory are the most important of the soft classifiers.
It allows for the expression of ignorance in uncertainty management (Eastman 1997). The
prime use of these methods is to check for the quality of one’s training site data and the
possible presence of unknown classes.
The basic assumptions of Dempster-Shafer theory are that ignorance exists in the body of
knowledge, and that belief for a hypothesis is not necessarily the complement of belief of its
negation.
The degree to which evidence provides concrete support for a hypothesis is known as
belief, and the degree to which the evidence does not refute that hypothesis is known as
plausibility. The difference between these two is the belief interval, which acts as a measure
of uncertainty about a specific hypothesis.
If the evidence supports one class to the degree of 0.3 and all other to 0.0, the Dempster-
Shafer theory would assign a belief of 0.3 to that class and a plausibility of 1.0, yielding a
belief interval of 0.7. Furthermore, it would assign a belief of 0.0 to all other classes and a
plausibility of 0.7.
Dempster-Shafer theory defines hypotheses in a hierarchical structure and will accept all
possible combinations of hypotheses, see figure 3. The combinations of hypotheses
acceptance is because it often happens that the evidence we have, supports some
combinations of hypotheses without the ability to further distinguish the subsets. The basic
classes are called singletons and the combinations non-singletons.
[A,B,C]
[A,B] [A,C] [B,C]
[A] [B] [C]
Figure 3. The Hierarchical Structure of the Subsets in the Whole Set [A,B,C] (based on
Eastman 1997).
10

When evidence provides some degree of commitment to one of these non-singleton
classes and not to any of its constituents separately, this commitment is called Basic
Probability Assignment (BPA). Thus, belief in a non-singleton class is the sum of BPA’s for
that class and all sub-classes. Belief represents the total commitment to all members of a set
combined.
These non-singletons represents mixtures and might be used for more detailed examination of
sub-pixel classification.
3.6.1 Applications with Dempster-Shafer theory
In a study of fire scars in Indonesia by Fuller and Fulky (1998), Dempster-Shafer theory was
used. That algorithm was used because each AVHRR pixel had a resolution of 1.1 km and
could have contained several patches of fire scars. The only training sites used was for fire
scars, all other classes were to be ‘other’ in the classification. As input some surface
temperature layers and vegetation change detection layers were used. No rigorous ground
validation could be done, due to lack of ground data at a scale meaningful to the AVHRR
analysis. But compared to the other method used in the study, multiple threshold approach,
the Dempster-Shafer method managed to extract more fire scars and came closer to the result
done by the the Center for Remote Sensing, Imaging and Processing (CRISP) of the National
University of Singapore. The CRISP analysis relied on visual interpretation of 766 SPOT
quicklook images mapped to 100 m spatial resolution.
3.7 Neural Network
Neural networks learn by example (Kanellopoulos 1997). From the training set the network
can learn the values of the samples internal parameters. Usually neural networks deal with
large amounts of training data (i.e. thousands of samples) whereas statistical methods use
much smaller training sets. The goal is the representation of complicated phenomena. The
neural network does not make any explicit a priori assumptions about the data.
3.7.1 The Multilayer Perceptron Classifier using feed-forward and back-propagation
The multilayer perceptron classifier (MLP) are the most widely used neural classifier today.
These networks are general-purpose, flexible, non-linear models consisting of a number of
units organised into multiple layers (Kanellopoulos 1997). Varying of the number of layers
and the number of units in each layer can change the complexity of the MLP. These networks
are valuable tools in problems when one has little or no knowledge about the form of the
relationship between input vectors and their corresponding outputs. The principle for the
multi-layer perceptron neural network is that processing elements or nodes divided into layers
perform calculations until an output value is computed at each of the output nodes (Foody
1996). Data to the input layer are the satellite channel values used in the classification
procedure. Then one or more hidden layers perform the calculations and send the result to the
output layer, which has one node for each class. Every node in a layer is connected to every
node in the layer above and below, see figure 4. The connections carry weights, which
encapsulate the behaviour of the network and are adjusted during training.
11

Level
k
j
i
Connection
weights
Output Classes
1 2
Input Pattern Feature Values
Figure 4. The Architecture of Multi-Layer Perceptron (based on Kanellopoulos 1997).
For the hidden layers the input to each node is the sum of the scalar products of the
incoming vector components with their respective weights,
input
∑
= i
where wji is the weight connecting node i to node j and outi is the output from node i.
The output of a node j is,
The function f denotes the activation function of each node. The most frequently used is the
sigmoid activation function,
where x =inputj. This ensures that the node acts like a thresholding device.
The network learns using the back-propagation algorithm iteratively. This algorithm
minimizes the mean square error between the network's output and the desired output,
where P are all input patterns and dk is the desired output.
j
12
w
ji
out
out j = f ( input j )
1
f ( x)
=
1+
exp( −x)
1
E = ∑∑( d k − out k )
2P
P k
i
2
Output layer
Hidden layer
Input layer

It compares the calculated output with the desired one, and adjust the weights attached to
the connections, until the difference between the outputs is reduced to an acceptable level and
the set of weights is stable.
The weights are from the beginning small and random and then adjusted by the
generalised delta rule,
where wkj (t+1) and wkj (t) are the weights connecting nodes k and j at iteration (t+1) and t
respectively, η is a learning rate parameter.
For nodes in the output layer,
and for nodes in the hidden layers,
wkj ( t + 1)
= wkj
( t)
+ η(
δ koutk
)
δ
k
= ( d k − outk
) f ′ ( inputk
)
To measure the generalisation ability it is common to have a set of data to train the network
and a separate set to assess the performance. Once the neural network has been trained, the
weights are saved to be used in the classification phase.
The activation level of an output unit is positively related to the strength of membership to
the class associated with the unit and lies on a 0-1 scale. These levels are significantly
correlated with the sub-pixel land cover composition and may be mapped as fraction images.
The classifier encounters lot of problems to separate the classes when the classes have lot
of similarities. A-priori knowledge of the relative class distribution could be used to apply
non-random weights to the network inputs to further distinguish similar classes.
Another disadvantage is that the back-propagation method is extremely slow. About
thousand iterations need to be done before the network converges to a solution. Sometimes no
solution is found (Augusteijn and Warrender 1998).
3.7.2 Applications with Multilayer Perceptron Classifier
Several applications have been performed with the multilayer perceptron classifier. Howald
classified Landsat TM data into seven land cover classes using a three layer network, with a
slightly better overall classification accuracy than a maximum likelihood classifier (1989).
Kanellopoulos et al. used a four-layer neural network for classifying multi-temporal SPOT
multi-spectral imagery into twenty land cover classes (1991). Owing to the complexity of the
classification, a relatively large neural network architecture was required and therefore the
computation time was quite long. Gualtieri and Withers used clustering of multispectral data
(1988). Ryan et al. (1991) reported the use of a neural network to categorise small blocks of
pixels to extract shoreline features from images.
Foody and Boyd (1999) used a neural network to derive fuzzy classifications of land cover
along a transect crossing the transition from moist semi-deciduous forest to savannah in West
Africa in February and December 1990. They used NOAA AVHRR for the study. The
training data was acquired from core regions of each class. The AVHRR provides five
spectral channels, so the network had five input units. The architecture also consisted of five
hidden units in a single layer and four output units and a logistic sigmoid transfer function
was used. The initial network weights were set randomly between the limits of ± 0.5 and the
learning rate and momentum were set to 0.1 and 0.9 respectively. When 1000 iterations of
13
∑
δ f ′ (
input ) δ w
j = k k kj

stochastic backpropagation learning algorithm had been performed, the RMS error was 0.096
and 0.117 for the February and December data sets respectively. The method was able to
represent both gradual and sharp changes in land cover, as those associated with the forestsavannah
and savannah-water boundaries respectively. It also enabled important properties of
the boundaries to be inferred, such as that the width of the forest-savannah transitional zone
remained relatively constant, but had migrated significantly, between the two time periods.
3.7.2 Neural Network using Cascade-correlation
Improvements have been made on back-propagation, since it is so slow. One of these
improved architectures is the cascade-correlation (Augusteijn and Warrender 1998). Cascadecorrelation
is a feed-forward neural network. The network builds its internal structure
incrementally, during training. The initial network consists of only two layers: an input layer
and an output layer, which are completely connected. These connections are trained until no
more significant changes occur between iterations. If the total training error still is too high, a
hidden node will be allocated and trained to further reduce this error. This goes on until the
termination criterion is reached or until a maximum number of hidden nodes are reached and
the conclusion is made that the network cannot learn the problem.
3.7.3 Applications with Cascade-correlation
A study made of Augusteijn and Warrender (1998) was conducted to investigate the ability of
a cascade-correlation neural network to delineate upland and forested wetland areas and to
distinguish between different levels of wetness in a forested wetland. They used NASA’s
Airborne Terrestrial Applications Sensor (ATLAS) multispectral data and Airborne Imaging
Radar Synthetic Aperture Radar (AIRSAR) data. The input values used for training and
testing of the neural network classifier were not simply digital number (DN) values indicating
the reflectance of each pixel in a given band, but averages of DN values calculated over 3
pixel by 3 pixel neighbourhoods inside the training and test polygons. The same sample size
had to be used in each category for the network to learn all categories equally well. First a five
class categorization was tried. But three of the five classes were too similar to be
distinguishable, so they were merged together. Several networks were trained using different
band combinations. Every network were always trained five times on the same data set, each
time using a different selection of random initial values for the connection strengths, to reduce
the influence of a specific set of initial values on network performance. Test sample
agreement scored well over 80 per cent in most cases.
3.7.4 Fuzzy ARTMAP
ARTMAP achieves a synthesis of fuzzy logic and ART networks (Mannan et al. 1998). ART
stands for Adaptive Resonance Theory. The architecture of fuzzy ARTMAP consists of four
layers of neurons: the input-, category-, mapfield-, and output layer. The values of the spectral
bands and their complement, of dimension n, are the input to the first layer, which consists of
2n neurons. The category layer starts with one neuron, but grows in number as the learning
proceeds. The output and mapfield layers consist of as many neurons as there are classes.
Two vigilance parameters ρ1 and ρ2 control the operation during learning and operational
phases of the network.
14

The learning phase is an iteratively process where for each input a category choice is
calculated according to,
A ∧W
S =
α + W
where A is the input feature vector and W1 is the weight vector between the input layer and a
node in the category layer.
For the node which has the largest value of S the match ratio at mapfield is calculated by,
where B is the output class vector and W2 is the weight vector between a chosen node of
category layer and the mapfield layer.
If the Rm value is larger than ρ2 the weights are changed and a new input value is managed.
The learning process of mapfield- and category layer weights is called resonance, and the
weights are calculated by,
( new)
1
If not, ρ1 = Rc for that input, where Rc is calculated by,
1
R m
For the nodes which has Rc ≥ ρ1 it is checked if any has Rm ≥ ρ2, if so is the case the
weights are changed and a new input is managed, otherwise a new nodes committed, the
weights are changed and a new input managed. This goes on until all training samples are
exhausted and the category layer nodes stop growing or the number of iterations exceeds T, a
chosen positive constant.
After this process a score S is calculated for each of the committed nodes. The node in the
output layer, which corresponds to the node with the largest value of S, indicates the category
of the input pixel.
α can be chosen around 0.01, β can be set to 1.0 in the beginning of the learning phase and
to a smaller value later. ρ1 and ρ2 are set to 1.0 for the most accurate results.
There is an advantage compared to maximum-likelihood and the multilayer perceptron
classifier (MLP) of about 5 % in the overall accuracy (Mannan et al. 1998). The method is
stable, easy to use, with a smaller number of parameters to manage and faster than MLP.
15
1
1
B ∧W
=
B
( old )
1
∗
2
W = β ( A ∧W
) + ( 1−
β ) W
W = β ( A ∧W
) + ( 1−
β ) W
( new)
2
2
R c
( old )
2
A ∧W1
=
A
1
2
( old )
1
( old )
2

3.7.5 Applications with Fuzzy ARTMAP
Six multispectral images acquired by Linear Imaging Self-scanning Sensor (LISS-II) camera
of Indian Remote Sensing Satellite (IRS-1B) have been used in an experiment in using fuzzy
ARTMAP in classification by Mannan et al. (1998). The training samples were selected by
visual interpretation of the scenes. In order to preserve the samples relative values, the grey
levels were normalized. 40 per cent of the samples were used in the training phase and the rest
were applied in the operational phase to assess the accuracy. The four spectral band pixel grey
values and their complements were input to the network. In the output binary vector, the bit,
which belongs to the input’s class, was set to 1 and the rest to 0:s.
All weights were initially set to 1, but decreased as the learning progressed. The result was
about 5 per cent better in the overall accuracy compared to multilayer perceptron- and
maximum likelihood classifier. In this experiment 7483 pixels were correctly classified and
397 misclassified.
16

4. Data and methods
4.1 Introduction
This chapter describes the study area and the data that has been used in the classification.
Two different softwares have been used to manage the problem and the method to do this, is
described.
4.2 Data
4.2.1 Satellite data
For the case area, only one Indian IRS-1C image is available and that one is very cloudy.
Since IRS-1C Wifs only have two spectral bands, at least two images are needed to get a
reliable classification. So the choice has fallen on the Russian RESURS-O1 #3 with MSU-SK
sensored images. Several RESURS images are available for the study area, but only three are
more or less cloud-free. These are from July and August 1995 and September 1996. These
RESURS images have five spectral bands, but only four can be acquired in parallell. Of these
four spectral bands, only three are acceptably noise free to be used, these are the red band and
the two near infrared bands, see figure 5. Only seven bands are allowed in the software, so the
image from August 1995 is excluded.
The study area constituted only a small part of each image and was therefore extracted to
reduce the amount of data. The area was 22 km × 44 km.
17
Figure 5. RESURS multitemporal colour
composite of the first near-infrared band,
red band and the second near infrared
band from July 1995 (RGB) over the study
area.

4.2.2 Reference data
As reference data for training and
evaluation the existing land cover data
from the pilot production of the Swedish
CORINE land cover over the Gripen area
was used, see figure 6.
CORINE stands for ‘Co-ordinating
Information on the Environment’ and was
a EU programme beginning 1985. This
land cover is mainly based on information
from digital topographical maps
interpretation and classification of Landsat
TM images with 30 m resolution,
resampled to a pixelsize of 25 m.
In most of Europe the CORINE land
cover contains 44 classes, but Sweden has
added 11 classes to better fulfil the needs
(SSC 1998).
The main classes are produced by: Figure 6. The reference image,
Swedish CORINE land cover.
♦ The wetland classes are mapped using masks from the digital topographic map and by
classifying satellite data. The map provides the spatial limits and the satellite data is used
to update the masks for wet mires and dry mires and for division of those classes. The
mires near a lake or sea is by a GIS-operation named inland- or coastal marshes.
♦ The water bodies are classified by thresholding in TM band 5, where that class has low
digital values. Then the water is classified and subtracted from the water mask in the
topographic map. The reason for this is that floating vegetation or lakes overgrown with
reeds are obtained, and can be candidates for the inland marshes.
♦ Forest is classified using codes from National Forest Survey field data. For given
coordinates, these codes say what kind of forest that grows there. For the same
coordinates, spectral signatures are extracted. By this the signatures for different kinds of
forest are known and the image can be classified under the forest mask. Filtered signatures
are used.
♦ Clear-cut forest is extracted from an image showing change, which is produced using
histogram matching between the same channel in each scene. Filtered signatures are used
for classification (nearest-neighbour).
♦ Urban boundaries are interpreted on screen using the Statistics Sweden urban database
and satellite images as background. Buildings within 200 m are included.
♦ Agricultural areas are taken from the digital topographical map, when it exists, as in my
study area.
The forest mask also contains the roads. These roads are mostly classified as forest
regeneration or clear-cut forest. Narrow and long areas of these classes which coincides with
18

oads narrower than 7 meters are alloted to the surrounding class. Then all areas in the image
that were smaller than 2 pixels were removed.
The received image was again resampled, now to 12.5 m.
4.3 Study area
4.3.1 General description of the Baltic Sea region landscape
The Baltic Sea region is the area (i.e. countries) surrounding the Baltic Sea. From the
vegetation’s point of view the countries are very young, in particularly Sweden, because of
the glaciation. The immigration of plants has occurred in several steps and from different
directions (Bråkenhielm et al. 1998). The spreading of the plants is strongly dependent of the
climate and their ability to compete with other species. The human activities, like agricultural
and forestry have also affected the vegetation. Where a species chooses to grow is for
example a matter of the bedrock, i.e. the content of nutrition in the mineral and rock and their
ability to disintegrate and contain water. The disintegration give rise to the foundation of fine
granular soils, which in turn helps keeping water, which in turn makes the chemical
disintegration easier and results in more nutrition. The bedrock has developed from magmatic,
sedimentary and metamorphic processes during billions of years. Different phases have
contributed to bedrock of varying composition. This, along with agricultural fields with
groups of trees and the variations in the terrain, makes the landscape patchy. How patchy a
person or animal experience the landscape is due to the person’s references or the animals
field of view or habitat. For example, doesn’t a hawk think the same area is patchy as do the
mouse.
This patchy landscape makes it difficult to generate a good and reliable hard classification,
from medium resolution satellite images, since they consists of pixels with sizes between 150-
250 m. It is not often such pixels contain just one class. Therefore, the main task for this
project is to analyze if soft classifiers can better show the real situation for such satellite
images.
The study area is very suitable for this task, since it contains all kinds of land covers, from
large agricultural fields with groves of trees, to large forests with patches of agricultural
fields. In figure 7, it can be seen that there are several classes in a 150 m- pixel and therefore a
hard classifier is not suitable.
The study area, called Gripen, is situated between lake Hjälmaren and the southern part of
the Baltic Sea bay – Bråviken, in the southern part of Sweden. The area contains two big
cities – Örebro and Norrköping. Around these cities, the landscape is very flat with large areas
of arable land. The forested area between these cities is very patchy with many smaller lakes
and hills. The forest contains both deciduous and coniferous forest and a mixture of both with
no sharp boundaries.
There are also different kinds of wetlands, which are of special interest in the BALANS
project, since they act as filters of nutrients before the water runs into the Baltic Sea.
19

Figure 7. A part of the study area in Gripen showing the reference image with 12.5 m pixel
size and a 150 m grid to elicit the fuzziness in the medium resolution satellite image pixels
(adapted from http://www.grida.no/baltic/htmls/maps.htm).
4.3.2 Quantitative characterisation
The area distribution of each class in the reference image are: water 5.19%, urban 1.82%,
agricultural areas 20.08%, marsh 0.71%, deciduous forest 11.79%, coniferous forest 36.80%,
mire 2.42%, clear-cut forest 7.35%, rock 0.82%, barren land 0.63%, peat 0.44% and grass
3.51%. This result in 13% unknown classes when using eight classes and 9% unknown
classes when using twelve classes.
4.4 Tools
4.4.1 IDRISI
IDRISI is a geographic information and image processing software system developed by the
Graduate School of Geography at Clark University, Worcester, U.S.A. It covers the full
spectrum of GIS and remote sensing needs. The software has over 150 modules that provide
facilities for the input, display and analysis of geographic data. For this project the fuzzy
signature development and soft classifier modules has been especially important. But at least
this version, version 2.0 for Windows, has its limitations, which force the users to find other
20

solutions to their problems, and sometimes import data from other systems, for example
already radiometric- and geometric corrected images.
The module based on the logic of Fuzzy Sets in IDRISI is FUZCLASS. In that module fuzzy
set membership is determined from the distance of pixels from signature means. To use this
module two parameters has to be set. The first is the z-score distance where fuzzy
membership becomes zero. If a pixel has the same location as the class mean the membership
grade is 1.0, and away from this point the grade decreases until it reaches zero. The second
parameter is whether or not the membership values should be normalized. Normalization
makes the assumption that the classes are the only one existing, and thus the membership
values for all classes for a single pixel must sum to 1.0.
The module using the Dempster-Shafer theory in IDRISI is BELCLASS. In normal use,
Dempster-Shafer theory requires the classes under consideration to be mutually exclusive and
exhaustive. But in BELCLASS the pixel may belong to some unknown class, for which a
training site has not been provided. An additional category is added to every analysis called
[other]. The result is consistent with Dempster-Shafer theory, but recognizes the possibility
that there may be classes present about which we have no knowledge. The uncertainty is
almost identical to that of Dempster-Shafer ignorance.
In BELCLASS you have two choices of output: beliefs or plausibilities. In either case, one
image of belief or plausibility is produced for each class. A classification uncertainty image is
also produced.
4.4.2 ERDAS IMAGINE
ERDAS Imagine is a complete GIS and image processing software produced by the
Engineering department of ERDAS, Inc., Atlanta, U.S.A. It is easy to use and has modules for
most problems. The limitation in this case is that it only has one fuzzy module. For this
project it has been used for preparation of the images and extraction of pixel information in
the resulting images.
21

4.5 Methodology
The outline of the used method is shown in figure 8. A scheme showing the main action
steps is included as appendix 1. The produced macro files are listed by name in a scheme in
appendix 2.
4.5.1 Outline
Figure 8. The used methodology.
4.5.2 Initial data preprocessing
4.5.2.1 Reference data
Preprocessing
reference image
Binarisation,
Thematic aggregation
Spatial aggregation
Sampling of training
sites
Preparation of training statistics
Running the modules
Evaluation and
comparison of soft
classifiers
4.5.2.1.1 Binarisation
The preprocessing of the reference image began with extraction of clouds that were in the
RESURS images. This was done by using the mask made from the satellite images. To m
make one image layer for each class a reclassification was made. The result was a binary
image for each class.
22
Preprocessing
satellite images
Radiometric correction
Geometric correction

4.5.2.1.2 Thematic aggregation
The reference image was reclassified to contain eight or twelve classes. These classes were
water, urban, agricultural field (agri), marshes (marsh), deciduous forest (decid), coniferous
forest (conif), wet/other mires (mire) and clear-cut forest (clear). The urban class consisted
of the classes coarse- and dense city structures and smaller communities from the Swedish
CORINE land cover. The coniferous and deciduous class consisted of conifers/decids with
different age and height. When 12 classes were used, rock, barren land (barr), peat and
grass were added.
The choices were made based on the more detailed classes that the BALANS project
wants to extract.
The BALANS project has envisaged at least five broad classes.
These are,
• Artificial surfaces
• Agricultural areas
• Forests and semi-natural areas
• Wetlands
• Water bodies
More detailed classes envisaged if possible is urban fabric, arable land, inland wetlands,
coniferous- and deciduous forest. Therefore, a classification of these more detailed classes
was tried out to.
4.5.2.1.3 Spatial aggregation
The reference image contained pixels with a size of 12.5 meter. To be able to compare the
reference image with the RESURS images, which have a pixel size of 150 meter, an
aggregation was made in IDRISI. In the process an average of twelve 12.5 m pixels in
both the X- and Y-direction was calculated and was output as a 150 m pixel. That made
the border pixels of each class patch fuzzy, i.e. they didn’t contain 100% of that class any
more. One such layer were made for each class and these were seen as the ‘true’ fuzzy
classes, since now the percent of fuzziness in each pixel was known.
4.5.2.2 Satellite data
4.5.2.2.1 Radiometric correction
Since RESURS images from two different dates were used they had different illumination.
Therefore the image which visually seemed to be the best was set as reference in this case.
Each band in the other image was histogram-matched against respectively band in the
’reference’ image.
4.5.2.2.2 Geometric correction
The RESURS images didn’t have any known projection and didn’t lay above each other. In
one image there was one band that didn’t lay above the other bands either. So the images
were geometrically corrected image to image by taking ground control points (GCPs). The
RMS error were about 25 m as maximum, that is about one sixth of a pixel. The images
were then resampled with cubic convolution and then corrected against the reference image.
The reference image was projected with Transverse Mercator and had datum and spheroid
WGS 84, so after the correction against the reference image, the RESURS images received
the same projection.
A cloud mask was created by taken training sites in the clouds and other ‘close’ classes.
A supervised classification with maximum-likelihood was performed and the output classes
were tested to see which were actually clouds. These clouds were marked in an ‘area-ofinterest’-layer
and cut out in all images.
23

4.5.3 Choice of soft classifiers
The software available for soft classification was IDRISI. This software included soft
classifiers using Bayesian probability theory and Dempster-Shafer theory reviewed earlier. It
also included one method where the distance from a class mean were set where the fuzzy
membership of that class should be zero.
4.5.4 Application of soft classifiers
4.5.4.1 Sampling of ’training data’ from reference data
Different training data samplings were examined.
♦ The first sampling was to take random sample points in the aggregated masks, as training
sites. In this sampling as well as in sampling two and three, different points were sampled
for each class.
♦ The second sampling was to make majority masks from the aggregated ones, were only
the pixels with class values of 75-100 % (90-100% for water) were included, to receive
purer sample points to see if there were any improvement.
♦ The third sampling was to, first (in ERDAS Imagine) manually take training sites within
the wetland mask to see where the wetland had a separable signature from the other
classes. Then a mask from these wetland areas were made under the whole wetland layer
and used as input to the aggregation in IDRISI. The sample points were taken in the
majority masks.
♦ The fourth sampling was to take random sample points in the whole image and divide
them into eight equally quantified classes. In this case the points for a specific class could
be sampled where that class didn’t have any pixel values. Most of the time the training
samples for a specific class did not contain a majority of that class. All training samples
were quite equal.
4.5.4.2 Preparation of training statistics
Each class’ training sites were seen as one training site group. After the sampling step, every
training site group was compared to the aggregated masks to see how much of each class
there was in every training site group. An average value was calculated for each class for each
training site group, e.g. the output is an average value of content of water in the urban training
site group and the content of water in the agricutural training site group etc. These average
values were imported to the fuzzy partition matrix and linked to the image with the training
site groups. The fuzzy partition matrix indicates the membership grades of each training site
group in each class (Eastman 1997). After the linking to the training site groups image, one
image for each class is created showing the membership grade in each training site group. The
fuzzy signatures are created by giving each training site group a weight proportional to its
membership grade when determining the mean, variance and covariance of each satellite
spectral band for each class.
4.5.4.3 Running the modules
After the creation of fuzzy signatures the different modules were tested. When the proportion
of each class in the reference image is known, a prior probability can be input as a weight and
improve the result.
24

4.5.4 Evaluation and comparison of soft classifiers
4.5.4.1 Introduction to thematic accuracy assessment of soft classifiers
The ground data can rarely be assumed to be error free. So testing a classification is an
evaluation of the level of agreement or correspondence between two sets of class allocations,
both of which have their own error characteristics, rather than quantifying the accuracy.
In hard classification, accuracy assessment is generally made with the use of an error
matrix. Error matrices compare, on a class-by-class basis, the relationship between known
reference data and the result of a classification. Such matrices are square, with as many rows
and columns as there are classes to be assessed. Several characteristics are expressed by the
error matrix, for example the error of omission (exclusion) and error of commission
(inclusion). Then the producer’s accuracy, user’s accuracy and overall accuracy can be
calculated. The producer’s- and user’s accuracy tells how much of, for example the
coniferous class, that is correctly classified and how much of the classified category
coniferous that is truly that in reality, respectively.
Another measure to extract from the error matrix is the kappa statistic, which is a measure
of the difference between the observed accuracy and a chance agreement between the
reference data and a random classifier.
The problem is that the error matrix is only appropriate for use with hard classification
(Foody 1996). In soft classification you receive one matrix for each class, i.e. each pixel
would be compared. But each pixel is just allowed to consist of one class, consequently to be
correct or incorrect.
A number of approaches have been suggested to assess the accuracy of soft classification.
For example, entropy can be used (Zhang and Foody 1998). Entropy describes the variations
in class membership probabilities associated with each pixel.
The entropy is calculated by,
∑
H ( p)
= − p(
x)
log 2 p(
x)
where p(x) is the class membership probabilities.
But entropy is only suitable when ground data are hard. When both classified data and
ground data are fuzzy, cross-entropy are more appropriate (Zhang and Foody 1998). Other
possible indices of classification accuracy may be based on correlation analysis and distance
measures between the representations of the land cover in the image classification and ground
data.
One other alternative is to degrade the data to just contain one or two classes in each pixel
and use conventional methods, but the result is not an evaluation of the fuzzy classification.
There are a number of points to note. Firstly, the predictive accuracy of partial values tends
to vary between the land cover classes being considered (Bastin 1997). Secondly, the
estimates of pixel composition give no reliable estimate of where in the pixel objects or
features are likely to be.
To deal with the second point, there are methods for sharpening the fuzzy classification
output (Foody 1998). This is made by fusion between a fine spatial resolution image and the
fuzzy classification derived at a coarser resolution.
There is a difficulty in evaluating soft classifications, and there need to be done more
research for better methods. There is no general measure that says when the classification is
good or bad.
25

4.5.4.2 Criteria and methods available
One method that can be used along the whole continuum of classification fuzziness, from the
case where every stage is hard to the case where every stage is fuzzy, is the RMS error (rootmean-square
error) between the estimated and actual class composition of the pixels (Foody
1999),
where xi is a measurement, t is the true value and n is the number of data to be assessed.
4.5.4.3 A suggested new approach
One new measure can be to calculate how many pixels that are under- or overclassified a
certain percent, in 10%- intervals, for each module.
4.5.4.4 Implementation
RMS =
4.5.4.4.1 Validation data from reference data
In the evaluation RMS errors were calculated for all samplings and modules to see
how well the classification performed in the classes. The training site pixels and
the ‘unknown’ areas in the reference image, i.e. classes that had not
been used, were excluded and then the whole images were used in the validation. To be
able to compare the modules and samplings, a weighted total average RMS error was
calculated. Each class’ RMS error was weighted with the reference area of the same class,
Average_RMS_error =Σ RMS_error⋅ percentuel area in the reference image
Also the average value for each class, in percent was calculated. This was been done in
two ways, one compared to the reference image and one compared to the classified pixels.
This to be able to compare BELclass with BAYclass and the reference image. BELclass
underclassifies and may just classify 10% of the image.
An analysis were made to see if the classification improved when more training pixels
were used, in the sampling where the pixels were randomly taken, using BELclass, and
how many classes that could be extracted in the same sampling.
4.5.4.4.2 Statistical analysis
I used Microsoft Excel for the calculations.
( x t)
∑ i −
i
n
26
2

5. Results
5.1 Introduction
This chapter contains the results in terms of RMS errors, over- and underclassified pixels and
average values.
5.2 Fuzzy signatures
Some of the eight chosen classes extracted have very similar spectral signatures, when using
two near-infrared bands and one red band. That is why the soft classifiers classify so many
pixels, with different percentage of probability, to wrong classes. The mean values for each
spectral band for each class, for the sampling in majority masks, is shown in figure 9. There it
can be seen that coniferous, clear-cut forest, deciduous forest, mire and urban have mean
values close to each other and therefore the training pixels can be mixed.
Mean value
120
100
80
60
40
20
0
-20
Fuzzy signatures for the six spectral bands in the majority sampling
1 2 3 4 5 6
Spectral bands (NIR,NIR,NIR,NIR,red,red)
Figure 9. The mean values for the fuzzy signatures in the six spectral bands used ( 1-2 near
infrared from September 1996, 3-4 near infrared from July 1995, 5 red from July 1995 and 6
red from September 1996).
5.3 RMS errors
To be able to compare the different modules and samplings, each class’ RMS error were
weighted with the percentage area of the reference image for respective class, to retrieve an
overall RMS error, see table 2 below. This table shows that BAYclass performs best
classification result before FUZclass. BELclass is not that far behind. They differ just a little
between the modules and samplings but the result improves when the training pixels get purer
27
agri
clear
conif
decid
marsh
mire
urban
water

and separable signatures are used. The modules classified differently well for the different
classes, as seen in the more detailed tables, 3-5, showing the RMS errors for each class,
sampling and module. In table 3 and 4, it can be seen that the RMS errors are reduced for the
wetland classes when using a mask with areas that manually had been tried out to be
separable. A thematic class can not often be assembled in one spectral class. This is why
clustering or supervised classification need to be done to achieve separable classes within the
masks.
The number of classes you try to extract in BELclass makes no difference in the RMS
errors. This is because BELclass uses unknown classes. It is only the spectral signature that
counts. In that way one class is independent to another class, see table 4. More classes in
BAYclass on the other hand improves the RMS errors for most classes.
Table 2. Overall RMS errors for eight classes, weighted with the area of each class in the
reference image, for the different modules and methods (×100 for percent).
Overall RMS for the different samplings, named 1-4:
1. training sites within 2. within majority 3. in majority mask and with 4. randomly taken
module aggregated mask masks wetland signatures trainingsites
BAYclass 0.299 0.259 0.244 0.362
BELclass 0.404 0.400 0.398 0.436
FUZclass 0.304 0.283 0.258 0.373
Table 3. RMS errors for BAYclass.
RMS for 8 classes classified with BAYclass RMS for 12
classes trainingsites
within
aggregated
mask
within majority
masks
28
in majority mask randomly taken
classes,
BAYclass
randomly
and with
training sites taken training
wetland signatures sites
water 0.13 0.11 0.11 0.23 0.18
urban 0.16 0.15 0.15 0.19 0.13
agri 0.23 0.23 0.22 0.35 0.4
marsh 0.15 0.16 0.07 0.13 0.11
decid 0.21 0.21 0.22 0.24 0.24
conif 0.42 0.33 0.3 0.48 0.5
mire 0.21 0.2 0.12 0.2 0.19
clear 0.22 0.22 0.24 0.21 0.2
rock 0.16
barr 0.13
peat 0.07
grass 0.08

Table 4. RMS errors for BELclass.
RMS for 8 classes classified with BELclass RMS for 12
29
classes
classes training sites within majority in majority mask randomly randomly
within aggregatedmasks and with wetlandtaken taken
masks signatures training sites training sites
water 0.19 0.20 0.20 0.23 0.22
urban 0.11 0.11 0.11 0.13 0.13
agri 0.41 0.41 0.41 0.46 0.46
marsh 0.08 0.08 0.03 0.08 0.08
decid 0.24 0.24 0.24 0.27 0.27
conif 0.56 0.55 0.55 0.59 0.59
mire 0.12 0.12 0.06 0.13 0.13
clear 0.22 0.22 0.22 0.22 0.22
rock 0.03
barr 0.06
peat 0.04
grass 0.06
Table 5. RMS errors for FUZclass.
RMS for 8 classes classified with FUZclass
classes training sites within within majority in majority mask and with randomly taken
aggregated masks masks wetland signatures training sites
water 0.13 0.11 0.11 0.22
urban 0.13 0.13 0.15 0.18
agri 0.22 0.21 0.18 0.37
marsh 0.16 0.15 0.04 0.16
decid 0.22 0.21 0.21 0.24
conif 0.44 0.40 0.36 0.50
mire 0.16 0.18 0.09 0.15
clear 0.21 0.22 0.24 0.21
5.4 Over- and under classified pixels
When looking at the number of correct classified pixels (± 5% ) in the summaries of table 6
and 7, it can be seen that BELclass is superior with an average of 80%, compared to
BAYclass’ 63%. But in these tables, the values are not weighted with the area, and the small
classes that don’t contain so many pixels therefore brings up the average value, since they are
so well classified with BELclass. The under- and overestimated values for each class in the
sum-up tables 6 and 7, is the percent in pixels, not the total RMS error. The detailed tables for
each 10% interval are shown as tables 8 and 9.

Table 6. Percent pixels over- and underestimated, for BELclass (×100 for percent).
Over-, correct- or underestimated for BELclass, method 2
water urban agri marsh decid conif mire clear
underestimated: 0.082 0.027 0.285 0.011 0.255 0.585 0.044 0.161
correct +-5%: 0.918 0.968 0.708 0.970 0.702 0.409 0.929 0.808
overestimated: 0.001 0.005 0.006 0.019 0.042 0.007 0.027 0.030
average:
underest. 0.181
correct 0.802
overest. 0.017
Table 7. Percent pixels over- and underestimated pixels for BAYclass (×100 for percent).
Over-, correct- or underestimated for BAYclass, method 2
water urban agri marsh decid conif mire clear
underestimated: 0.026 0.014 0.140 0.009 0.187 0.486 0.029 0.109
correct +- 5%: 0.907 0.848 0.820 0.823 0.522 0.354 0.423 0.341
overestimated: 0.067 0.139 0.040 0.169 0.291 0.160 0.548 0.550
average:
underest. 0.125
correct 0.630
overest. 0.245
BELclass systematically underclassifies, as seen in table 8 or sum-up table 6. Figure 10 and
11 visualizes the clear-cut forest class from table 8 and 9 to easier see how many pixels that
are over- and underclassifed for BAYclass and BELclass and how much.
30

Table 8. Percent pixels over- and underclassified for BELclass. For example 5.1% of
agricultural areas are underestimated between 84-95%.
RMS in 10 % intervals for BELclass, method 2
water urban agri marsh decid Conif mire clear
100-94% underestimated 0.012 0.004 0.070 0.002 0.004 0.099 0.004 0.010
95-84% 0.0130.0030.051 0.001 0.008 0.096 0.003 0.009
85-74% 0.009 0.002 0.036 0.001 0.013 0.077 0.002 0.011
75-64% 0.008 0.0030.030 0.001 0.020 0.067 0.004 0.013
65-54% 0.009 0.0030.025 0.001 0.027 0.064 0.004 0.017
55-44% 0.007 0.002 0.020 0.001 0.027 0.047 0.004 0.014
45-34% 0.006 0.002 0.013 0.001 0.024 0.030 0.003 0.012
35-24% 0.004 0.002 0.012 0.001 0.031 0.032 0.004 0.017
25-14% 0.005 0.002 0.012 0.001 0.040 0.031 0.006 0.022
15-4% 0.009 0.002 0.016 0.002 0.060 0.0430.010 0.037
5% underest. - 5% overest. 0.918 0.968 0.708 0.970 0.702 0.409 0.929 0.808
6-15% overestimated 0 0.0030.004 0.009 0.025 0.004 0.021 0.016
16-25% 0 0.001 0.001 0.004 0.010 0.002 0.005 0.007
26-35% 0 0 0 0.003 0.004 0 0.001 0.003
36-45% 0 0 0 0.001 0.002 0 0 0.001
46-55% 0 0 0 0.001 0.001 0 0 0.001
56-65% 0 0 0 0 0 0 0 0.001
66-75% 0 0 0 0 0 0 0 0
76-85% 0 0 0 0 0 0 0 0
86-95% 0 0 0 0 0 0 0 0
96-100% 0 0 0 0 0 0 0 0
Procent pixlar
Procent över- eller underklassade pixlar i hyggesklassen, klassad med BELclass
0,900
0,800
0,700
0,600
0,500
0,400
0,300
0,200
0,100
0,000
100-94% underestimated
95-84%
85-74%
75-64%
65-54%
55-44%
45-34%
35-24%
25-14%
15-4%
5% underest. - 5% overest.
6-15% overestimated
16-25%
26-35%
36-45%
46-55%
56-65%
66-75%
76-85%
86-95%
96-100%
10 % - intervall för över- och underklassat
Figure 10. Percent under- and overclassified pixels for the clear-cut forest class with
BELclass.
31
hyggen

Percent pixels
Table 9. Percent pixels over- and underclassified for BAYclass. For example 1.4 % of
agricultural areas are underestimated between 84-95%.
Over- or underclassified, in 10 % intervals for BAYclass, sampling 2
water urban agri marsh decid conif mire clear
100-94% underestimated 0.001 0 0.012 0 0 0.001 0 0
95-84% 0.001 0.001 0.014 0 0.002 0.005 0.001 0.002
85-74% 0.001 0.001 0.012 0 0.004 0.014 0.001 0.005
75-64% 0.002 0.001 0.0130 0.009 0.035 0.0030.010
65-54% 0.0030.002 0.014 0.001 0.015 0.060 0.003 0.012
55-44% 0.0030.001 0.013 0.001 0.022 0.081 0.004 0.015
45-34% 0.002 0.001 0.011 0.001 0.025 0.083 0.004 0.015
35-24% 0.003 0.002 0.013 0.001 0.031 0.080 0.004 0.015
25-14% 0.004 0.002 0.015 0.001 0.036 0.069 0.004 0.016
15-4% 0.007 0.0030.023 0.0030.044 0.058 0.005 0.019
5% underest. - 5% overest. 0.907 0.848 0.820 0.823 0.522 0.354 0.423 0.341
6-15% overestimated 0.036 0.081 0.014 0.087 0.152 0.074 0.217 0.172
16-25% 0.011 0.018 0.009 0.025 0.070 0.0430.1730.226
26-35% 0.008 0.009 0.006 0.013 0.038 0.022 0.094 0.121
36-45% 0.005 0.006 0.005 0.009 0.018 0.011 0.036 0.026
46-55% 0.002 0.005 0.002 0.008 0.009 0.005 0.014 0.004
56-65% 0.002 0.004 0.002 0.005 0.004 0.0030.006 0
66-75% 0.001 0.0030.001 0.005 0.001 0 0.003 0
76-85% 0.001 0.0030.001 0.006 0 0 0 0
86-95% 0 0.005 0.001 0.007 0 0 0 0
96-100% 0 0.005 0 0.004 0 0 0 0
1.000
0.900
0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
Percent pixels under- or overclassified in the 'clear' class with BAYclass
100-94% underestimated
95-84%
85-74%
75-64%
65-54%
55-44%
45-34%
35-24%
25-14%
15-4%
5% underest. - 5% overest.
6-15% overestimated
16-25%
26-35%
36-45%
46-55%
56-65%
66-75%
76-85%
86-95%
96-100%
Percent under- or overclassified intervals
Figure 11. Percent under- and overclassified pixels for the clear-cut forest class with
BAYclass.
32
clear

5.5 Average values
If you look at the average value, in percent of the reference image, for each class classified
with BELclass, in table 10, you see that no sampling performs very well. This can be due to a
low amount of training sites. It is a limitation in the software that only allow 10 000 random
points. The small classes need of up to 40 000 points to get about 100 training pixels for each
class in the aggregated mask. So probably the result improves if the training sites are collected
manually and separable signatures are extracted. BAYclass have some higher occurence and
comes therefore closer to the true average value for some classes, but overclassifies for many
classes as well. It is not so strange that BAYclass have higher occurence, since this module
think that the trained classes are the only one existing. If there are other classes in the image,
it puts them to the most look-alike class. BELclass on the other hand treats the pixel as
belonging to an unknown class if the pixel doesn’t support any of the given classes.
As seen in average table 11, BELclass classifies more of the image when more classes are
added, 13% compared to 0.90% for eight classes. But it is in wrong classes the increase is
done.
33

Table 10. Average values for 8 classes in percent of reference image and percent of classified
image.
Average values for 8 classes (in %) Average values for
classified with BELclass for the different samplings BAYclass and FUZclass
for one sampling
class reference training sites within in majority mask randomly BAYclass FUZclass
image within % of majority % of and with wetland % of taken % of in majority in majority
aggregated classified mask, classified signatures, classified training classified mask, mask,
mask, area % of ref. area % of ref. area sites area % of ref. % of ref.
% of ref.
% of ref.
water 6.03 0.98 7.88 0.78 6.90 0.75 6.44 0.03 2.8 5.81 6.16
urban 2.11 0.37 2.95 0.35 3.10 0.35 3.03 0.38 42.6 5.71 9.23
agri 23.3 4.04 32.57 2.98 26.46 3.15 27.21 0.00 0.4 15.47 17.03
marsh 0.82 0.82 6.65 0.46 4.12 0.01 0.08 0.36 39.9 6.35 7.40
decid 13.68 2.37 19.11 2.23 19.77 2.47 21.33 0.00 0.3 12.74 12.35
conif 42.71 2.84 22.93 3.07 27.23 3.18 27.47 0.00 0.0 25.18 18.30
mire 2.81 0.46 3.75 0.46 4.13 0.06 0.51 0.06 6.9 13.54 14.25
clear 8.53 0.52 4.16 0.93 8.29 1.61 13.94 0.06 7.1 15.20 15.28
Sum %: 100.00 12.40 100.00 11.26 100.00 11.58 100.00 0.90 100.0 100.00 100.00
35

Table 11. Average values for 12 classes in percent of reference image and percent of
classified image.
Average values (in %) for 12 classes
classified with BELclass and BAYclass for sampling 4
class reference BELclass,
BAYclass,
image random training sites
random training sites
% of ref. % of classified % of classified area
area
water 5.67 0.16 1.16 12.07
urban 1.99 0.01 0.04 5.98
agri 21.93 0.00 0.00 5.68
marsh 0.77 7.81 56.84 5.23
decid 12.87 0.00 0.00 7.09
conif 40.19 0.00 0.01 10.39
mire 2.65 0.00 0.02 13.86
clear 8.03 0.01 0.08 8.72
rock 0.89 0.02 0.12 13.61
barr 0.69 3.47 25.22 6.62
peat 0.48 1.43 10.42 4.97
grass 3.83 0.84 6.08 5.80
Sum %: 100.00 13.74 100.00 100.00
As can be seen in table 12, the number of training pixels does not matter when they are
taken randomly. That is because the fuzzy partitioning matrix in the software doesn’t allow
a not-square matrix and therefore an average value is calculated for each class.
Table 12. Comparison of RMS errors with 3000
training sample points and 10 000.
RMS for 8 classes classified with BELclass
classes randomly taken randomly taken
trainingsites trainingsites
RESURS 3000 RESURS 10000
water 0.23 0.23
urban 0.13 0.13
agri 0.46 0.46
marsh 0.08 0.08
decid 0.27 0.27
conif 0.59 0.59
mire 0.13 0.13
clear 0.22 0.22
In figure 12-37 the reference images for all classes along with the result for each class for
BAYclass and BELclass are shown for visual comparison. The agricultural class, the
deciduous-, coniferous and clear-cut forest classes are labelled with shortenings in the figure
texts.
36

Figure 12. The agri.class
from the reference image.
Figure 15. The water class
from the reference image.
Figure 18. The urban class
from the reference image.
Figure 13. The agri.class
classified with BAYclass.
Figure 16. The water class
classified with BAYclass.
Figure 19. The urban class
classified with BAYclass.
37
Figure 14. The agri.class
classified with BELclass.
Figure 17. The water class
classified with BELclass.
Figure 20. The urban class
classified with BELclass.

Figure 21. The mire class
from the reference image.
Figure 24. The decid class
from the reference image.
Figure 27. The clear class
from the reference image.
Figure 22. The mire class
classified with BAYclass.
Figure 25. The decid class
classified with BAYclass.
Figure 28. The clear class
classified with BAYclass.
38
Figure 23. The mire class
classified with BELclass.
Figure 26. The decid class
classified with BELclass.
Figure 29. The clear class
classified with BELclass.

Figure 30. The conif class
form the reference image.
Figure 33. The marsh class
from the reference image.
Figure 31. The conif class
classified with BAYclass.
Figure 34. The marsh class
classified with BAYclass.
Figure 36. Uncertainty
image for BAYclass.
39
Figure 32. The conif class
classified with BELclass.
Figure 35. The marsh class
classified with BELclass.
Figure 37. Uncertainty
image for BELclass.

6. Discussion
The reason why the water is surprisingly bad classified in all tryouts, can be due to error in
the reference image. One lake in the reference image is practically covered with reed in the
RESURS images. Training pixels in that lake can reduce the training site average for the
class, and make at least BELclass to not classify water pixels if to far away from the mean
value. BAYclass handles the problem a bit better since it only chooses among the classes
given. Coniferous forest and agricultural areas have the highest RMS errors. This can be due
to the fact that these classes are not spectrally homogenous. Coniferous pixels can also have
been classified as water, since water and coniferous are the darkest pixels in the image. One
class that is surprisingly well classified is the urban class. This can be due to that time series
are used.
There are many reasons why the classifiers perform unsatisfactory. The major reason is
the input data. The RESURS images only had three, or actually only two spectral bands with
good enough radiometric quality. These were the two near infrared and the red bands.
Therefore, two images from different times were used, to at least have six bands. But in one
of these images the spectral bands did not fit the other so a geometric correction had to be
done. All images were then geometrically corrected to each other and to the reference image.
There can still be small errors in the geometry, which affects the classification and the
evaluation.
The reference data is not really true either. It has been developed using topographic maps to
get the boundaries of the classes and then for some classes just classified within the mask.
Some other classes have been extracted using GIS-operations.
The reference image is based on interpretation, GIS-operations and maximum-likelihood
classification, why the true percentage distribution is not really known. What is really
between 50-100% is set to be 100%. So the assumptions about what really is 100% may not
be true. The classes, which are mixed in the reference image, as for example mixed forest, are
not considered in the validation. The content of each forest kind in a pixel is unknown. But
they have not participated in the training phase either.
40

7. Conclusions and recommendations
The advantages of soft classifiers are that small classes will not vanish as with maximumlikelihood
classification and they gives a measure, not in whole pixels, of the occurrence of
the classes.
To receive an acceptable classification result, the training areas need to be spectrally
separable. This can be done with clustering or expert knowledge. There is also needed to be
collected enough number of training areas to get the spectral variation of each class.
If only red and near infrared bands are available, a time series is required to get enough
information. The images can be chosen close in time to get rid of clouds and more important
from different vegetation periods for a better classification. The satellite images also needs to
have good geometric and radiometric quality.
Forest and agricultural areas are hardest to classify because of the heterogeneous spectral
signatures. Urban on the other hand is surprisingly well classified. This can be due to the time
series. BAYclass is the soft classifier that gives the best result.
There need to be done some improvements in the software to be able to use any of these
soft classifiers in production. The main drawback is that the fuzzy partition matrix has to be
square. So even if you take training sites with separable signatures manually, you have to
calculate an average value for all your training sites for a certain class. This reduces the value
of many training sites.
The second drawback, if still wanting the computer to take training sites, is that not enough
training sites can be taken for small classes. Not enough randomly spread out pixels will hit
the areas where a member of a small class is situated.
The third drawback if wanting to use images from different dates, is that the maximum
number of spectral bands allowed is seven when using IDRISI.
When these improvements are done, these soft classifiers can be a valuable tool when using
medium- or coarse resolution satellite data to extract more information from the images.
41

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Augusteijn, M.F. and Warrender, C.E. 1998, Wetland classification using optical and radar
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Bastin, L. 1997, Comparison of fuzzy c-means classification, linear mixture modelling and
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Bråkenhielm, S., Drakenberg, B., Hellgren, M., Holmgren, P., Karltun, E., Melkerud, P-A.
and Olsson, M. 1998, Markinfo. Institutionen för skoglig marklära, SLU http://wwwmarkinfo.slu.se
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43

Appendix 1: Action steps for soft classification
This is an example for water.
Actions Input Module Output
Make a water mask reference_gripen RECLASS rcwater
in 12.5 m pixelsize
Aggregate to a pixel rcwater CONTRACT aggwater
size of 150 m
Scale the pixel values aggwater SCALAR scwater
to be in range 1-100,
but still real values
Convert the pixel values scwater CONVERT cvwater
to byte binary
For method 2 and 3:
Mask out 75-100 % of cvwater RECLASS majwater
a class, 90-100% for cvdecid… majdecid…
water
Convert the majority majwater CONVERT cv2water
masks to integer binary majdecid… cv2decid…
Take out sample points majwater SAMPLE vecwater
randomly to be majdecid… vecdecid…
training sites from the
mask.
Initialize images with aggwater INITIAL trswater
the same parameters as trsdecid…
an aggregated image
The initialized image vecwater POINTRAS trswater
updated with rasterized vecdecid… trsdecid…
sample points
Reclass the sample trswater RECLASS rc2water
points to 1 and 0 trsdecid… rc2decid…
Overlay to extract just majwater, rc2water OVERLAY ovwater
the sample points which majdecid, rc2decid… ovdecid…
are within the mask
44

Numbering the sample ovwater GROUP grwater
points ovdecid… grdecid…
Reclass the sample grwater RECLASS grwater1
points for one class to grdecid… grdecid1…
only one classnumber
Make an 8-layer image, grwater1 OVERLAY gr1_8
(if you have 8 classes), grdecid1…
with the classes (sample
point groups).
Extract an average value grwater1, aggwater, EXTRACT valwater
for each class in each grdecid1, aggdecid… valurban…
class mask.
Create a fuzzy partitioning matrix. In Database Workshop
Number 8 rows for the use of 8 classes. -Number the rows. One more
Name 8 columns with class names, row comes up with the down
e.g water, decidious. arrow. To create one more
column:
-Modify
-Add field
Real (4 byte) and class name
Put in the values in the valwater In Database Workshop
matrix valurban… -File
-import/export Idridi values file
free format ASCII (VAL file)
valwater… and corresponding
class
Link the matrix to the gr1_8, water In Database Workshop fzwater
training sites (sample gr1_8, decid… -Assign field values to fzdecid….
points groups) image gr1_8 fzwater..
and corresponding class
Create the fuzzy gr1_8, sig.names, FUZSIG water.sig
signatures satellitebands decid.sig….
Classify with different signature names MAXLIKE mlclass
hard/soft classifiers BAYCLASS baywater…
BELCLASS belwater…
FUZCLASS fuzwater…
45

Calculate the over- baywater, aggwater OVERLAY errwater
and underclassified baydecid, aggdecid… errdecid…
pixel values
Add 1 to the extracted errwater SCALAR sc2water
error-values and errdecid… sc2decid…
multiply with 100 to
have positive values
between 1 and 200
Convert the pixel values sc2water CONVERT cv3water
to byte binary sc2decid… cv3decid…
Export the error images and classification images to Imagine to receive pixel information:
Export the images to cv3water, baywater -File expwater.img
ERDAS Imagine cv3decid… - Export ex2water.img
-Export
-Software-Specific Formats
-ERDIDRIS
-IDRISI to ERDAS 7.4
name of file to export and name in
Imagine with extension .img
In Imagine:
-Open the image
-info i
-compute statistics
In the viewer:
-Raster
-Attributes
-Edit
Mark the column
-Copy
Copy the pixel information into excel to calculate RMS and average values for each class
and each module.
In Excel:
-Paste the number of pixels in the excel-file “mall_RMS.xls” and “mall_medeltal.xls”
46

Appendix 2: Macrofile- scheme
8 classes, aggregated mask
NEWMASK
8 classes, majority mask
MACMAJ_3
MACMAJ_5
MACR_8_2
TRSITES3
MACR8_4
MCAGG8_5
8 classes, miresig, aggregated mask
NEWMASK2
MACR8_6 , create matrix
FUZSIG (FUZSIG4 if Landsat TM)
MAC8_BAY MAC8_BEL MAC8_FUZ MAC8_ML
Export to Imagine and Excel. eval.. for RMS for random
cv10.. for average for random
cv4.. for RMS other methods
cv3.. for average other methods
47
8 classes, random
MAC_RD_2 , create matrix
FUZSIG2 (FUZSIG3 IF Landsat TM)

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March 1999. (Examensarbete i geodesi nr 3061. Handledare: Horemuz)
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1999:6 Krzysztof Gajdamowicz. Automated Processing of Georeferenced Colour Stereo Images
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1999:8 Stefan Wulcan. Samlingskarta - En förstudie avseende samordning av ledningar inom
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1999:16 Rannala, Marek. Surveying of road geometry with Real Time Kinematics GPS. Oktober
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2000:5 Malin Skagerström och Karin Wiklander. Extension of a control network in dar es salaam
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Slussen-konstruktionen. Mars 2000. (Examensarbete i geodesi nr 3067. Handledare: Horemuz
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2000:9 Anna Haglund. Towards soft classification of satellite data - A case study based upon Resurs
MSU-SK satellite data and land cover classification within the Baltic Sea Region. Mars 2000.
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