Unit-7 Representation and Description.pdf

BSc CSIT and Computer Engineering Image processing uni t 11

1. Representation and
Description

2. Introduction
•Afteranimagehasbeensegmentedintoregions,theresultingaggregateofsegmented
pixelsusuallyisrepresentedanddescribedinaformsuitableforfurtherprocessing.
•Representingaregioninvolvestwochoices:
I.Representregionsintermsofitsexternalcharacteristics(itsboundary),or
II.Representregionsintermsofitsinternalcharacteristics(pixelscomprisingtheregion)
•Anexternalrepresentationischosenwhentheprimaryfocusisonshapecharacteristics.
•Aninternalrepresentationischosenwhentheprimaryfocusisonregionalproperties,
suchascolorandtexture.
•Thenextstepistodescribetheregionbasedonthechosenrepresentation.
•Forexample:aregionmayberepresentedbyitsboundary,anditsboundarydescribedby
itsomefeaturessuchaslength,orientationetc.
•Featuresshouldbeinsensitivetotranslation,rotation,andscaling.
•Bothboundaryandregionaldescriptorsareoftenusedtogether.
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3. Types
•Representationscanbeclassifiedintofollowingtwotypes:
1.ChainCodes
2.Signatures
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4. Chain Codes
•Chaincodesareusedtorepresentaboundarybyaconnectedsequenceofstraight-linesegmentsof
specifiedlengthanddirection.
•Typically,thisrepresentationisbasedon4-or8-connectivityofthesegments.
•Thedirectionofeachsegmentiscodedbyusinganumberingscheme,asshowninfigurebelow.
•AboundarycodeformedasasequenceofsuchdirectionalnumbersisreferredtoasFreemanchain
code.
Figure: Directional numbers for
(a) 4-directional chain code, and
(b) 8-directional chain code
(a) (b)
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5. Chain Codes
•Themethodgenerallyisunacceptablefortwo
principalreasons:
1.Theresultingchainofcodestendstobequite
longand
2.Anysmalldisturbancescausechangesinthe
codethatmaynotberelatedtotheshapeof
theboundary.
•Anapproachfrequentlyusedtocircumventthe
problemjustdiscussedistoresampletheboundary
byselectingalargergridspacing,asshownin
figureaside. Figure: (a) Digital boundary with resampling
grid superimposed. (b) Result of resampling
(c) 4-directional code. (d) 8-directional chain
code
(a) (b)
(d)(c)
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6. Chain code
•Thechaincodeofaboundarydependsonthestartingpoint.However,thecodecanbe
normalizedwithrespecttothestartingpointbytreatingitasacircularsequenceof
directionnumbersandredefiningthestartingpointsothattheresultingsequenceof
numbersisaintegermagnitude.
•Wecannormalizealsoforrotationbyusingthefirstdifferenceofthechaincodeinstead
ofthecodeitself.Thedifferenceisobtainedbycountingthenumberofdirectionchanges.
•Forexample:thefirstdifferenceofthe4-directionchaincode10103322is3133030.
•Ifwetreatthecodeasacircularsequencetonormalizewithrespecttothestartingpoint,
thenfirstelementofthedifferenceiscomputedbyusingthetransitionbetweenthelast
andfirstcomponentsofthechain.
•Heretheresultis33133030.
•Thefirstdifferenceofsmallestmagnitude(i.e.obtainedbytreatingtheresultingarrayasa
circulararrayandrotatingitcyclicallyuntiltheresultingnumericalpatternresultsisthe
smallestpossiblenumber)isknownasshapenumberofthecounter.
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7. Chain code
Figure: Chain code, first difference, and shape number
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8. Signatures
•Signaturesisa1-Dfunctionalrepresentationofaboundaryandmaybegeneratedinvariousways.
•Oneofthesimplestmethodisplotthedistancefromthecentroidtotheboundaryasafunctionof
angle,asillustratedinfigurebelow.
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9. Signatures
•Signaturesgeneratedbytheapproachjustdescribedareinvarianttotranslation,
buttheydodependonrotationandscaling.
•Normalizationwithrespecttorotationcanbeachievedbyfindingawaytoselect
thesamestartingpointtogeneratedthesignature,regardlessoftheshape’s
orientation.
•Onewaytonormalizeforthisresultistoscaleallfunctionssothattheyalways
spanthesamerangeofvalues,say,[0,1]
•Whateverthemethodused,keepinmindthatthebasicideaistoremove
dependencyonsizewhilepreservingthefundamentalshapeofthewaveforms.
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10. Signatures
Figure:Effectofnoiseonsignaturesfortwodifferentobjects.
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11. Descriptors
•Approachestodescribetheboundaryofaregion.
•Types
▪BoundaryDescriptors
▪RegionalDescriptors
▪RelationalDescriptors
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12. Some simple Descriptors
•Thelengthofaboundaryisoneofitssimplestdescriptors.
•Thenumberofpixelsalongaboundarygivesroughapproximationofitslength.
•Thediameterofaboundaryisdefinedas
Diam(B)=�??????�
�,�
[????????????
�,??????�]whereDisadistancemeasureandp
iandp
j
arepointsonboundary.
•Thelinesegmentconnectingthetwoextremepointsthatcomprisethediameteris
calledthemajoraxisoftheboundaryandthelineperpendiculartothemajoraxis
iscalledminoraxis.
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13. Shape Number
•Theshapenumberofboundarygenerallybasedonfourdirectionalchaincodesis
definedasthefirstdifferenceofsmallestmagnitude.
•Theordernofashapenumberisdefinedasthenumberofdigitsinits
representation.
•
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14. Figure: shape
number of order 4, 6
and 8 along with
their chain-code
representations, first
difference, and
corresponding shape
numbers.
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15. Example: suppose n=18 is
specified for the boundary.
▪To obtain the shape
number of this order,
following steps are done:
1.Find the basic rectangle.
2.The closet rectangle of
order 18 is 3 x 6
rectangle; sub-divide the
rectangle.
3.Align the chain code
directions with the
resulting gird.
4.Obtain the chain code
and use its first difference
to compute the shape
number.
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16. Fourier Descriptors
•TheideabehindFourierDescriptorsistotraverse
thepixelsbelongingstoaboundarystartingfrom
anarbitrarypoint,andrecordtheircoordinates.
•Eachvalueintheresultinglistofcoordinatespairs
(x
0,y
0),(x
1,y
1),…….,(x
k-1,y
k-1)isthen
interpretedasacomplexnumberx
k+jy
k,fork=
0,1,….K-1.
•ThediscreteFouriertransform(DFT)ofthislistof
complexnumbersistheFourierdescriptorofthe
boundary.
•TheinverseDFTrestorestheoriginalboundary.
•FollowingfigureshowsaK-pointdigitalboundary
inthexyplaneandthefirsttwocoordinatespairs
(x
0,y
0)and(x
1,y
1).
Figure: Fourier Descriptor of a boundary
Real Axis
Imaginary Axis
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17. Steps for Fourier Descriptors
•Definethearbitrarypoint(x
0,y
0)andthecoordinatepointorpairs(x
0,y
0),(x
1,y
1),….,(x
k-1,y
k-1)
areencounteredintraversingtheboundaryincounterclockwisedirection.
•Thesecoordinatescanbeexpressedintheformx(k)=x
kady(k)=y
k.Theboundarycanbe
representedasthesequenceofcoordinatesas:
s(k)=[x(k),y(k)]fork=0,1,2,….K-1.
Theeachcoordinatespaircanbetreatedasacomplexnumbersothat:
s(k)=x(k)+jy(k).
•ThediscreteFouriertransformof1-Dsequence,s(k)canbewrittenas:
a(u)=
1
??????
σ
�=0
??????−1
??????(�)??????
−�2????????????�/??????
where,u=0,1,2,……..,K-1
•Thecomplexcoefficienta(u)arecalledtheFourierdescriptorsoftheboundary.
•TheinverseFouriertransformofthesecoefficientis:
s(k)=
1
??????
σ
�=0
??????−1
??????(??????)??????
�2????????????�/??????
where,k=0,1,2,……..,K-1
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18. Pattern Recognition

19. Human Perception
•Humanshavedevelopedhighlysophisticatedskillsforsensingtheirenvironment
andtakingactionsaccordingtowhattheyobserve.Examples:
➢Recognizingaface,
➢Understandingspokenwords,
➢Readinghandwriting,
➢Distinguishingfreshfoodfromitssmell.Etc.
•Wewouldliketogivesimilarcapabilitiestomachines.
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20. What is pattern?
•Apatternisanentity,vaguelydefined,thatcouldbegivenaname,e.g.,
➢Fingerprintimage
➢Handwrittenword
➢Humanface
➢Speechsignal
➢DNASequence,
➢……..
•Apatterninanarraignmentofdescriptors.Thenamefeatureisoftenusedinto
denoteadescriptor.
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21. What is pattern recognition?
•Apatternclassisafamilypatternthatsharesomecommonproperties.Patternclassesare
denotedbyw
1,w
2,w
3,……,w
WwhereWisthenumberofclasses.
•Apatternrecognition/patternclassificationisthestudyofhowmachinescan
•Observetheenvironment,
•Learntodistinguishpatternsofinterest,
•Makesoundandreasonabledecisionsaboutthecategoriesofthepatterns.
•Patternrecognitionbymachinesinvolvesforassigningpatternstotheirrespectiveclasses
–automaticallyandwithaslittlehumaninterventionaspossible.
•Patternvectorsarerepresentedbyboldlowercaseletters,suchasx,y,andz,andtakethe
form
x=
�
1
�
2
.
.
.
�
�
Equivalently,x=�
1,�
2,�
3
,
....,��
??????
•Whereeachcomponents,x
i,representthei
th
descriptorandnisthetotalnumberofsuch
descriptorsassociatedwiththepattern.
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22. Goal of Pattern Recognition
•Toassignaclasstoeachimage(orobjectwithinanimage)basedonanumerical
representationoftheimage’s(orobject’sproperties).
Techniques:
•Patternclassificationtechniquesareusuallyclassifiedintotwomaingroups:
1.Statistical,and
2.Structural(orsyntactical)
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23. Pattern Recognition Application
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24. An Example
•Problem:Sortingincoming
fishonconveyorbelt
accordingtospecies.
•Assumethatwehaveonlytwo
kindsoffish:
•Seabass,
•salmon
Figure: Picture Taken from a camera
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25. An Example: Decision Process
•Whatkindofinformationcandistinguishonespeciesfromtheother?
➢Length,width,numberandshapeoffins,tailshapeetc.
•Whatcancauseproblemsduringsensing?
➢Lightingconditions,positionoffishontheconveyorbelt,cameranoise,etc.
•Whatarethestepsintheprocess?
➢Captureimage→isolatefish→takemeasurement→makedecision
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26. An Example : Selecting Features
•Assumeafishermantoldusthataseabassisgenerallylongerthana
salmon.
•Wecanuselengthasafeatureanddecidebetweenseabassadsalmon
accordingtoathresholdonlength.
•Howcanwechoosethisthreshold?
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27. An Example : Selecting Features
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28. An Example : Selecting Features
•Eventhoughseabassislongerthansalmonontheaverage,thereare
manyexamplesoffishwherethisobservationdoesnothold.
•Tryanotherfeature,averagelightnessofthefishscales.
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29. An Example : Selecting Features
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30. An Example: Cost of Error
•Weshouldalsoconsidercostsofdifferenterrorswemakeinour
decisions.
•Forexample,ifthefishpackingcompanyknowsthat:
•Customerswhobuysalmonwillobjectvigorouslyiftheyseesea
bassintheircans.
•Customerswhobuyseabasswillnotbeunhappy,ifthey
occasionallyseesomeexpensivesalmonintheircans.
•Howdoesthisknowledgeaffectourdecision?
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31. An Example: Cost of Error
•Assumewealsoobservedthatseabassaretypicallywiderthansalmon.
•Wecanusetwofeaturesinourdecision:
➢Lightness:x
1
➢Width:x
2
•Eachfishimageisnowrepresentedasapoint(featurevector)
x=
�
1
�
2
inatwo-dimensionalfeaturespace.
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32. An Example: Multiple Features
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33. An Example: Multiple Features
•Doesaddingmorefeaturesalwaysimprovetheresults?
➢Avoidunreliablefeatures.
➢Becarefulaboutcorrelationwithexistingfeatures.
➢Becarefulaboutmeasurementcosts.
➢Becarefulaboutnoiseinthemeasurements.
•Istheresomecurseforworkinginveryhighdimensions?
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34. Pattern Recognitions Systems
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35. Pattern Recognitions Systems
•Dataacquisitionandsensing
•Measurementsofphysicalvariables.
•Importantissues:bandwidth,resolution,sensitivity,distortion,SNR,latency,
etc.
•Pre-processing
•Removalofnoiseindata
•Isolationofpatternsofinterestfromthebackground
•Featureextraction
•Findinganewrepresentationintermsoffeatures
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36. Pattern Recognitions Systems
•Modellearningandestimation
•Learningamappingbetweenfeaturesandpatternsgroupsandcategories
•Classification
•Usingfeaturesandlearnedmodelstoassignapatterntoacategory.
•Postprocessing
•Evaluationofconfidenceindecisions
•Exploitationofcontexttoimproveperformance
•Combinationofexperts
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37. The Design Cycle
DataCollection
•Collectingtrainingandtestingdata
•Howcanweknowwhenwehaveadequentlylargeandrepresentativesetof
samples?
Collect Data
Select
Feature
Select
Model
Train
Classifier
Evaluate
Classifier
Figure 8: The Design Cycle
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38. The Design Cycle
FeatureSelection
•Domaindependenceandpriorinformation
•Computationalcostandfeasibility
•Discriminativefeatures
•Similarvaluesforsimilarpatterns
•Differentvaluesfordifferentpatterns
•Invariantfeatureswithrespecttotranslation,rotationandscale
•Robustfeatureswithrespecttoocclusion,distortion,deformation,and
variationsinenvironment
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39. The Design Cycle
ModelSelection
•Domaindependenceandpriorinformation
•Definitionofdesigncriteria
•Parametricvs.non-parametricmodels.
•Handlingofmissingfeatures
•Computationalcomplexity
•Typesofmodels:templates,decision-theoreticorstatistical,syntacticalor
structural,neural,andhybrid
•Howcanweknowhowclosewearetothetruemodelunderlyingthepatterns?
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40. The Design Cycle
Training
•Howcanwelearntherulefromdata?
•Supervisedlearning:
•Ateacherprovidesacategorylabelorcostforeachpatterninthetrainingset.
•Unsupervisedlearning:
•Thesystemformsclustersornaturalgroupingoftheinputspatterns.
•Reinforcementlearning:
•Nodesiredcategoryisgivenbuttheteacherprovidesfeedbacktothesystemsuchasdecisionis
rightorwrong.
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41. The Design Cycle
Evaluation
•Howcanweestimatetheperformancewithtrainingsamples?
•Howcanwepredicttheperformancewithfuturedata?
•Problemsofover-fittingandgeneralization.
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42. Statistical Pattern Classification Techniques
•Wehavemanystatisticalpatternclassificationtechniques.Inthissection,we
discussthreebasictechniques:
•Theminimumdistanceclassifier
•Thek-nearestneighbors(KNN)classifier,and
•Themaximumlikelihood(orBayesian)classifier.
•Weknowthatobjects’propertiescanberepresentedusingfeaturevectorsthatare
projectedontoafeaturespace.
•Featurevectorsassociatedwithobjectsfromthesameclasswillappearclose
togetherasclustersinthefeaturespace.
•Thejobofastatisticalpatternclassificationtechniquesistofindadiscrimination
curve(orahypersurface,inthecaseofann-dimensionalfeaturespace)thatcan
telltheclustersapart.
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43. Classifier concept
Figure: Discrimination functions for a
three-class classifier in a 2D feature
space
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44. Statistical Pattern Classification Techniques
Figure: Diagram of a Statistical pattern Classifier
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45. Statistical Pattern Classification Techniques
•Astatisticalpatternclassifierhasninputs(thefeaturesoftheobjecttobe
classifiedencodedintofeaturevector,x=�
1,�
2,�
3
,
....,��
??????
andoneoutput(
theclasstowhichtheobjectbelongs,C(x),arerepresentedbyoneofthesymbols
byw
1,w
2,w
3,……,w
WwhereWisthenumberofclasses).Thesymbolsw
Ware
classidentifiers.
•Classifiersmakecomparisonsamongtherepresentationsoftheunknownobject
andtheknowclasses.Thesecomparisonsprovideinformationtomakedecision
aboutwhichclasstoassigntotheunknownpattern.
•Mathematically,thejoboftheclassifieristoapplyaseriesofdecisionrulesthat
dividethefeaturespaceintoWdisjointsubsetsK
w,w=1,2,……,W,eachof
whichincludesthefeaturevectorsxforwhichd(x)=w
w,whered(.)isthe
decisionrule.
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46. Minimum Distance Classifier
•Theminimumdistanceclassifier(alsoknowasthenearest-classmeanclassifier)
worksbycomputingadistancemetricbetweenanunknownfeaturevectorandthe
centroids(i.e.meanvectors)ofeachclass:
dj(x)=??????−????????????,
•whered
jisadistancemetricbetweenclassjandtheunknownfeaturevectorx,mj
isthemeanvectorforclassj,definedas
m
j=
1
??????
�
σ
??????????????????�??????
??????
•WhereN
jisthenumberofpatternvectorsformclassw
j.
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47. Minimum Distance Classifier
Figure: Example of two classes and their mean vectors.
Figure: Example of three classes with relatively complex
structure
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48. K-Nearest Neighbors Classifier
•Thek-nearestneighbours(KNN)classifierworksbycomputingthedistance
betweenanunknownpattern’sfeaturevectorxandtheclosestpointstoitinthe
featurespace,andthenassigningtheunknownpatterntotheclasstowhichthe
majorityoftheksamplespointsbelong.
•Themainadvantagesofthisapproachareitssimplicity(e.g.,noassumptionsneed
tobemadeabouttheprobabilitydistributionofeachclass)andversatility(e.g.,it
handlesoverlappingclassesorclasseswithcomplexstructureaswell.
•Itmaindisadvantageisthecomputationalcostinvolvedincomputingdistances
betweentheunknownsampleandmanystoredpointsinthefeaturespace.
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49. K-Nearest Neighbors Classifier
Figure: (a) Example of KNN classifier ( k = 1) for a five-class classifier in a 2D feature space. (b) Minimum
distance classifier results for the same data set.
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50. Bayesian Classifier
•TheBayesianClassifieristhataclassificationdecisioncanbemadebasedontheprobability
distributionsofthetrainingsamplesforeachclass;thatis,anunknownobjectisassignedtothe
classtowhichitismorelikelytobelongbasedontheobservedfeatures.
•ThemathematicalcalculationsperformedbyaBayesianclassifierrequirethreeprobability
distributions:
•Theapriori(orprior)probabilityforeachw
k,denotedbyP(w
k).
•Theunconditionaldistributionofthefeaturevectorrepresentingthemeasuredpatterx,denotedbyp(x).
•Theclassconditionaldistribution,thatis,theprobabilityofxgivenclassw
k,denotedbyp(x|w
k).
•ApplyingBayes’rule,thesethreedistributionsarethenusedtocomputetheaposteriori
probabilitythatapatterxcomesfromclassw
k,representedasp(w
k|x),asfollows:
p(w
k|x)=
??????????????????
�
).??????(??????�)
??????(??????)
=
??????????????????
�
).??????(??????�)
σ
??????=1
??????
??????????????????
�
).??????(??????�)
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51. Overview of Neural Network in image processing
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Connectionizm
NNisahighlyinterconnectedstructureinsuchawaythatthestateofone
neuronaffectsthepotentialofthelargenumberofanotherneuronstowhichit
isconnectedaccordingtoweightsofconnections
Not Programming but Training
NNistrainedratherthanprogrammedtoperformthegiventasksinceitis
difficulttoseparatethehardwareandsoftwareinthestructure.Weprogram
notsolutionoftasksbutabilityoflearningtosolvethetasks
�
11�
11�
11�
11
�
11�
11�
11�
11
�
11�
11�
11�
11
�
11�
11�
11�
11
Distributed Memory
NNpresentsandistributedmemorysothatchanging-adaptationofsynapse
cantakeplaceeverywhereinthestructureofthenetwork.

52. compiled by: Deepak Bhatta 52()
2
xy=
Learning and Adaptation
NNarecapabletoadaptthemselves(thesynapsesconnectionsbetween
units)tospecialenvironmentalconditionsbychangingtheirstructureor
strengthsconnections.
Non-Linear Functionality
Everynewstatesofaneuronisanonlinearfunctionoftheinput
patterncreatedbythefiringnonlinearactivityoftheotherneurons.
Robustness of Assosiativity
NNstatesarecharacterizedbyhighrobustnessorinsensitivityto
noisyandfuzzyofinputdataowingtouseofahighlyredundance
distributedstructure

53. compiled by: Deepak Bhatta 53
Human brain contains
a massively
interconnected net of
10
10
-10
11
neurons or
nerve cells
Brain Computer: What is it?
Biological Neuron
-The simple
arithmetic
computing”
element

54. Biological Prototypes and Artificial Neurons
The schematic model
of a biological neuron
Synapses
Dendrites
Soma
Axon
Dendrite
from
other
Axon from
other neuron
1.Somaorbodycell-isalarge,round
centralbodyinwhichalmostallthelogical
functionsoftheneuronarerealized.
2.Theaxon(output),isanervefibre
attachedtothesomawhichcanserveasa
finaloutputchanneloftheneuron.Anaxon
isusuallyhighlybranched.
3.Thedendrites(inputs)-representa
highlybranchingtreeoffibres.Theselong
irregularlyshapednervefibres(processes)
areattachedtothesoma.
4.Synapsesarespecializedcontactsona
neuronwhicharetheterminationpointsfor
theaxonsfromotherneurons.

55. 55
Artificial Neural Networks
ArtificialNeuralNetworksprovide…
-Anewcomputingparadigm
-Atechniquefordevelopingtrainableclassifiers,memories,dimension-reducing
mappings,etc
-Atooltostudybrainfunction

56. 56
Vision, AI and ANNs
•1940s:beginningofArtificialNeuralNetworks
McCullogh&Pitts,1942
S
iw
ix
iq
Perceptronlearningrule(Rosenblatt,1962)
Backpropagation
Hopfieldnetworks(1982)
Kohonenself-organizingmaps
input outputneuron
m M
Sm

57. 57
Vision, AI and ANNs
1950s:beginningofcomputervision
Aim:givetomachinessameorbettervisioncapabilityasours
Drive:AI,roboticsapplicationsandfactoryautomation
Initially:passive,feedforward,layeredandhierarchicalprocess
thatwasjustgoingtoprovideinputtohigherreasoning
processes(fromAI)
Butsoon:realizedthatcouldnothandlerealimages
1980s:Activevision:makethesystemmorerobustbyallowingthe
visiontoadaptwiththeongoingrecognition/interpretation

58. 58
•AMcCulloch-Pittsneuronoperatesonadiscrete
time-scale,t=0,1,2,3,... withtimetickequalto
onerefractoryperiod
•Ateachtimestep,aninputoroutputis
onoroff—1or0,respectively.
•Eachconnectionorsynapsefromtheoutputofoneneuronto
theinputofanother,hasanattachedweight.
Warren McCulloch and Walter Pitts (1943)x (t)
1
x (t)
n
x (t)
2
y(t+1)
w
1
2
n
w
w
axon
q

59. 59
Excitatory and Inhibitory Synapses
•Wecallasynapse
excitatoryifw
i>0,and
inhibitoryifw
i<0.
•Wealsoassociateathresholdqwitheachneuron
•Aneuronfires(i.e.,hasvalue1onitsoutputline)attimet+1iftheweightedsum
ofinputsattreachesorpassesq:
y(t+1) = 1 if and only if Sw
ix
i(t) q

60. 60
From Logical Neurons to Finite Automata
AND
1
1
1.5
NOT
-1
0
OR
1
1
0.5
Brains, Machines, and
Mathematics, 2nd Edition,
1987
X Y→
Boolean Net
X
Y Q
Finite
Automaton

61. 61
Hopfield Networks
•ApaperbyJohnHopfieldin1982wasthecatalyst
inattractingtheattentionofmanyphysiciststo
"NeuralNetworks".
•InanetworkofMcCulloch-Pittsneurons
whoseoutputis1iffSwijsjq
iandisotherwise0,
neuronsareupdatedsynchronously:everyneuronprocessesits
inputsateachtimesteptodetermineanewoutput.

62. 62
Hopfield Networks
•AHopfieldnet(Hopfield1982)isanetofsuchunitssubjecttotheasynchronous
ruleforupdatingoneneuronatatime:
"Pickaunitiatrandom.
IfSwijsjq
i,turniton.
Otherwiseturnitoff."
•Moreover,Hopfieldassumessymmetricweights:
wij=wji

63. 63
Multi-layer Perceptron Classifier

64. 64
Multi-layer Perceptron Classifier

65. 65
Classifiers
•1-Stageapproach
•2-Stageapproach

66. 66
Example: face recognition
•Hereusingthe2-stageapproach:

67. 67
SOM : Self Organized Map
•Provideawayofrepresentingmultidimensionaldatainmuchlowerdimensional
spaces-usuallyoneortwodimensions.
•Vectorquantization:Reducingthedimensionalityofvectors.

68. 68
Nuro Fuzzy Systems
NeuralNetworks
Neuralnetworksaregoodatrecognizingpatterns,theyarenotgood
atexplaininghowtheyreachtheirdecisions.
FuzzySystems
Fuzzylogicsystems,whichcanreasonwithimpreciseinformation,are
goodatexplainingtheirdecisionsbuttheycannotautomatically
acquiretherulestheyusetomakethosedecisions.
Need a Intelligent Hybrid System !!