CE-636 Soft Classification

8/10/2019 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#

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CE-636 Soft Classification