CE-636 Soft Classification
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Transcript of CE-636 Soft Classification
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Soft Classifications Methods
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Mixed Pixel Problem
Depends upon the spatial resolution of the sensor.
Pure
Pure
Pure
Mixed
Mixed
Pure
Pure
MixedMixed
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Both supervised and unsupervised classification may be
applied to perform the hard and soft classification.
Hard classification allocates each pixel of remote sensing
image to a single class.
It results an inherent assumption that all the pixel in the remote
sensing imagery are pure.
However often the images are dominated by mixed pixel they
do not represent one particular land cover but contain two or
more !and Cover "!C# classes in a single pixel.
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Coarser the spatial resolution higher is the chance of
mixed pixels occurring in a single pixel area.
$lthough the chances of two or more class contributing
to a mixed pixel are high with a coarse spatial
resolution but the number of such pixels is small. %n
the other hand with improved spatial resolution the
number of classes within a pixel is reduced but the
number of mixed pixels increases.
&urthermore for improved spatial resolution the
mas'ing due to shadow also results the loss of
information.
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(resence of mixed pixel creates a problem in image classification.
a mixed pixel displays a composite spectral response that may be
dissimilar to the spectral response of each of its component !C
classes and therefore pixel may not be allocated to any of its
component !C classes.
Conventional image classification techni)ues may thus result into
a lot of information loss present in a pixel. *hese techni)ues
therefore tend to over+or under+estimate the actual areal extents of
the !C classes on ground thereby degrading the classificationaccuracy of the image contaminated by mixed pixels.
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Resolution and spectral mixing
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CLASSIFICATION AND TAR!T
ID!NTIFICATION
Spectral analysis methods usually compare pixel spectra with a
reference spectrum "often called a target#. *arget spectra can be
derived from a variety of sources including spectral libraries
regions of interest within a spectral image or individual pixels
within a spectral image.
"#ole Pixel Met#ods
,hole pixel analysis methods attempt to determine whether oneor more target materials are abundant within each pixel in a
multispectral or hyperspectral image on the basis of the spectral
similarity between the pixel and target spectra.
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,hole pixel tools include standard supervisedclassifiers such as Minimum Distance or Maximum
li'elihood as well as tools developed specifically for
hyperspectral imagery such as
Spectral $ngle Mapper
Spectral &eature &itting
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$%Spectral Angle Mapper &SAM'
Scatter plot of pixel values from two bands of a spectral
image. In such a plot pixel spectra and target spectra willplot as points
*he Spectral $ngle Mapper "-uhas et al. //0#
computes a spectral angle between each pixel spectrum
and each target spectrum.
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(% Spectral Feature Fitting
In Spectral &eature &itting the user specifies a range of
wavelengths within which a uni)ue absorption feature
exists for the chosen target. *he pixel spectra are then
compared to the target spectrum using two measurements1
.*he depth of the feature in the pixel is compared to the
depth of the feature in the target and
0.*he shape of the feature in the pixel is compared to the
shape of the feature in the target "using a least+s)uares
techni)ue#.
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)%Complete Linear Spectral *nmixing
It is also 'nown as spectral mixture modeling or spectral
mixture analysis.
Set of spectrally uni)ue surface materials existing within ascene are often referred to as the spectral end members.
reflectance spectrum of any pixel is the result of linear
combinations of the spectra of all end members inside that
pixel. 2nmixing simply solves a set of n linear e)uations for
each pixel where n is the number of bands in the image.
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Matc#ed Filtering
%ften called a 3partial un+mixing4.
5o need to find the spectra of all end members in the
scene to get an accurate analysis.
%riginally developed to compute abundances oftargets that are relatively rare in the scene.
Matched &iltering 6filters7 the input image for good
matches to the chosen target spectrum by maximi8ing
the response of the target spectrum within the dataand suppressing the response of everything else.
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So+t Classi+ication
9ach pixel may represent the multiple and partial classmemberships.
It is an alternative to hard classification because of its
ability to deal with the mixed pixel.
Membership functions allocates to each pixel a real
value between : and i.e. membership grade.
Sub+pixel scale information is typically represented in
the output of a soft classification by the strength ofmembership a pixel displays to each class.
It is used to reflect the relative proportion of the classes
in the area represented by the pixel.
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So+t classi+iers
Most common soft classifiers are1
Maximum li'elihood classification
&u88y c+means
(ossibilistic c+means
5oise Clustering
$rtificial neural networ's Decision *rees
&u88y set theory
based approaches
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*hese techni)ues can be applied to resolve a pixel
into various !C class components thus generatingsoft class outputs.
*he output is not a single classified image in soft
classification. Here a number of images are obtainedas the classified output. *he pixel in each image
"generally referred to as fraction image# depicts the
proportion of individual !C classes.
However these proportions do not actually represent
the spatial distribution of !C classes on ground.
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Maximum Li,eli#ood Classi+ier &MLC' -
M!C is one of the most widely used hard classifier.
In a standard M!C each pixel is allocated to the class with which
it has the highest posterior probability of class membership.
M!C has been adapted for the derivation of sub+pixel information.
*his is possible because a by+product of a conventional M!C are
the posterior probabilities of each class for each pixel.
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*he posterior probability of each class provides is a relative
measure of class membership and can therefore be used as an
indicator of sub+pixel proportions.
%ften many author use the term &u88y M!C to discriminate it
from the "hard# M!C.
Conceptually, there is not a direct link between the proportional
coverage of a class and its posterior probability. In fact, posterior
probabilities are an indicator of the uncertainty in making aparticular class allocation. However, many authors have find that
in practice useful sub-pixel information can be derived from this
approach.
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( ) ( )..
ln0
t
m i i i ip N x N x =
m ip p>
Xis a !C class cif and only if
,here
X is a vector of D5 values of unclassified pixels
ip
mpis li'elihood of ith!C class "i;
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a posterior probabilities of a pixel belonging to ith!C class the
can be given by1ap
.
c
a m mj
j
p p p
=
=
*hese a posterior probabilities represent the soft classification
output. &or example the a posterior probabilities of classmemberships for a pixel containing three !C classes= soil water
and vegetation are obtained as :.>? :.:@ and :.00 respectively.
*he M!C in its hard form will assign the pixel to soil= its
probability of occurrence being maximum in that pixel. %n the
other hand a softened output will show the probabilities of each
of the !C classes considered in a pixel.
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Fu../ c-Means &FCM'-
It is an iterative clustering method. may be employed to partition
pixels of a satellite image into different class membership values. 9ach pixel in the satellite image is related with every information
class by a function 'nown as membership function. *he value of
membership function 'nown simply as membership varies between
: and . *he membership value close to implies that the pixel is more
representative of that particular information class while
membership value close to : implies that the pixel has little or no
similarity with the information class. *he net effect of such a function is to produce fu88y c-partition of a
given data "or satellite image in case of remote sensing#.
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*he obAective function for &CM can be given by
( ). ." # " #
c Nm
fcm ki k ii kJ U V D x v= ==
00" # " # " #Tk i ki k i k i k iAD x v d x - v x - v A x - v= = =,here
SubAect to the constraints
.
.c
ki
i
=
= for all k ;.
:
N
ki
k
=
> for all i ; : .ki
for all k,i
,hereU N c= matrix
" #1 cV v v= is the collection of the vectors with the informationclass center iv
ki is a class membership values of a pixel
kid is distance between feature space between kx and iv
kx is vector "feature vector# denoting spectral response of class k
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iv is vector " prototype vector# denoting the information class center
of class i
c Nand are total number of information classes and pixels
respectively.A is a weight matrix.
m is a weighting exponent "or fu88ifier# . m< <
..
.
.
" #
" #
c mk i
kijj k
D x v
D x v
=
=
&rom the obAective function of the &CM the membership value can
calculated as1
.
" # " #c
jk k i
i
D x v D x v=
= where
ki is reali8ation value of class membership ki
( )
( )
.
.
N m
ki k
ki N m
ki
k
x
v
=
=
=
*he center of information class can be computed as1
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Possibilistic c-Means &PCM'-
( ). . . .
" # " # ". #c N c N
m m
pcm ki k i i ki
i k i k
J U V D x v = = = =
= +
*he obAective function for (CM can be given by1
*he specificity of this new term is that it emphasi8es "orassigns high membership value# the representative feature
point and de+emphasi8es "or assigns low membership value#
the unrepresentative feature point present in the data.
SubAect to the constraints
max :kii
> for all k;.
:
N
ki
k
=
> for all i ; : .ki for all k,i
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( )( )..
.
. " #ki
mk i iD x v
= +
&rom the obAective function of the (CM the membership value can calculated as1
. .
" #N N
m m
i ki k i ki
k k
! D x v = =
=
where
i is 'nown as bandwidth parameter
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Noise Clustering &NC'-
In &CM noisy points "i.e. outliers# are grouped with
information classes with same overall membership value of one.
5oise classes "or outliers# can be segregated from the core
information class "or cluster#. *hey do not degrade the )uality
of clustering analysis.
*he main concept of the 5C algorithm is the introduction of a
single noise information class "c# that will contain all noise
data points.
*he obAective function for 5C can be given by1
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( ) ( ) .. . .
" # " #c N N
mm
nc ki k i k c
i k k
J U V D x v += = =
= +
" # " #
" #
c m mk i k i
kijj k
D x v D x vi c
D x v
=
= +
( )
..
.
.
.
.
mc
k c
j jkD x v
+=
= +
(erformance of the 5C classifier is dependent on the Resolution parameter
&0'.
%ptimi8ed value of resolution parameter is re)uired.
*he obAective function for 5C can be given by1
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Arti+icial Neural Net1or, &ANN'-
$n $55 is a form of artificial intelligence that imitates somefunctions of the human brain.
$n $55 consists of a series of layers each containing a set of
processing units "i.e. neurones#.
$ll neurones on a given layers are lin'ed by weighted connections
to all neurones on the previous and subse)uent layers.
During the training phase the $55 learns about the regularities
present in the training data and based on these regularities
constructs rules that can be extended to the un'nown data.
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Ad2antages o+ ANN It is a non+parametric classifier i.e. it does not re)uire any assumption about the
statistical distribution of the data.
High computation rate achieved by their massive parallelism resulting from a dense
arrangement of interconnections "weights# and simple processors "neurones# which
permits real+time processing of very large datasets.
Disad2antages o+ ANN
$55 are semantically poor. It is difficult to gain any understanding about how the
result was achieved.
*he training of an $55 can be computationally demanding and slow.
$55 are perceived to be difficult to apply successfully. It is difficult to select the type
of networ' architecture the initial values of parameters such as learning rate and
momentum the number of iterations re)uired to train the networ' and the choice of
initial weights.
i i & '
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Decision Trees &DT'-
Can be used as both the 3ard or so+t classi+ierAd2antage-
$bility to handle non+parametric training data i.e. D* are not based on anyassumption on training data distribution.
D* can reveal nonlinear and hierarchical relationships between input variables
and use these to predict class membership.
D* yields a set of rules which are easy to interpret and suitable for deriving a
physical understanding of the classification process.
ood computational efficiency.
D* unli'e $55 do not need an extensive design and training.
Disad2antage- *he use of hyperplane decision boundaries parallel to the feature axes may
restrict their use in which classes are clearly distinguishable.
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$lthough the soft classification is informative andmeaningful it fails to account for the actual spatial
distribution of class proportions 1it#in t#e pixel%
Super+resolution mapping "or sub+pixel mapping# is a
step forward.
Super+resolution mapping considers the spatialdistribution within and between pixels in order to
produce maps at sub+pixel scale.
Super4resolution Mapping -
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Several approaches of super+resolution mapping havebeen developed1
Mar'ov random fields
Hopfield neural networ's
!inear optimi8ation
(ixel+swapping solution "based on geostatistics#