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Matlab
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f(x,y) x y (SpatialCoordinate)
(x,y) (Intensity)(Pixel)
GrayLevel (MonochromeImages)
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MonochromeandColorImages
GrayScales GrayLevels
0
50
100
150
200
250
RedGreenBlue
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() ( Matlab)
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imread
imread(filename);
I
I=imread(filename);
size,whos
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matlab
imread helpimread
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I imshow
imshow(I,256); imshow(I);
[lowhigh]
imshow(I,[100200]); 100 200
pixval,impixelinfo
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imwrite Syntax
imwrite(A,filename,fmt)imwrite(X,map,filename,fmt)imwrite(...,filename)imwrite(...,Param1,Val1,Param2,Val2...)
A myFile tif imwrite(A,myFile,tif); imwrite(A,myFile.tif); path
myFile.tif
imwrite JPEG
imwrite(A,myFile.jpg,quality,q) q (quality) q
0-100
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jpeg imfinfo
S=imfinfo(myFile10.jpg); myFile10.jpg S
(Height Width)
S.Height,S.Width
ByteNum =S.Height*S.Width*S.BitDepth/8;CompressRation
=ByteNum/S.FileSize
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TIF imwrite TIF
imwrite(A,myFile.tif,compression,parameter,resolution,[colres
rowres])
parameter={none,packbits,ccitt};,
[colres rowres] [7272] 72 (dpi:dotperinch)
xray resolution 200 dpi 450450 pixels [450 450]/200=[2.25 2.25]
tif cb.tif [1.5 1.5] [colres rowres] = 200*[1.5 1.5]
imwrite(A, cb.tif, compression, non, resolution [300 300])
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Matlab Class
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DataClass
Matlab double unit8
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IPT Intensityimages Binaryimages Indeximages RGBimages
Intensityimageisadatamatrixwhosevalueshavebeenscaledtorepresent
intensities.
Pixelvaluesareofclassuint8,orclassuint16,theyhaveintegervaluesintherange[0,255]and[0,65535],respectively.
Iftheimageisofclassdouble,thevaluesarefloatingpointnumbers,thepixelsarescaledintherange[0,1].
} 6
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BinaryImages AbinaryimageisalogicalarrayofOs and1s. ArrayofOs
and1swhosevaluesareofdataclass,say,uint8,isnot
consideredabinaryimageinMATLAB.
Anumericarrayisconvertedtobinaryusingfunctionlogical.Thus,ifAisa
numericarrayconsistingofOs
and1s,wecreatealogicalarrayBusingthestatement
B=logical(A); IfAcontainselementsotherthanOs
and1s,useofthelogicalfunction
convertsallnonzeroquantitiestologicalIsandallentrieswithvaluetologicalOs.Usingrelationalandlogicaloperators(seeSection2.10.2)alsocreateslogicalarrays.
Totestifanarrayislogicalweusetheislogicalfunction:islogical(C)
IfCisalogicalarray,thisfunctionreturnsa1.OtherwiseitreturnsaO.
Logicalarrayscanbeconvertedtonumericarraysusingthedataclass
conversionfunctions.
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ConvertingbetweenDataClassesandImageTypes
ThegeneralsyntaxisB=data_class_name(A);
Wheredata_class_name isoneoftheimagedataclass
Forexample,IfAisanarrayofclassuint8.Adoubleprecisionarray,B,is
generatedbythecommandB=double(A).
ThisconversionisusedroutinelythroughoutthebookbecauseMATLAB
expectsoperandsinnumericalcomputationstobedoubleprecision,floatingpointnumbers.
IfCisanarrayofclassdoubleinwhichallvaluesareintherange[0,255](butpossiblycontainingfractionalvalues),itcanbeconvertedtoanuint8arraywiththecommandD=uint8(C).
Ifanarrayofclassdouble
hasanyvaluesoutsidetherange[0,255]anditisconvertedtoclassuint8
inthemannerjustdescribed,MATLABconvertsto0allvaluesthatarelessthan0,andconvertsto255allvaluesthataregreaterthan255.
Numbersinbetweenareconvertedtointegersbydiscardingtheirfractionalparts.Thus,properscalingofadoublearraysothatitselementsareintherange[0,255]isnecessarybeforeconvertingittouint8.
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ConvertingbetweenImageClassesandTypes
IPTprovidesspecificfunctionsthatperformthescalingnecessarytoconvertbetweenimageclassesandtypes.
Functionim2uint8
detectsthedataclassoftheinputandperformsallthenecessaryscalingforthetoolboxtorecognizethedataasvalidimagedata.
Forexample,considerthefollowing2x2imagefofclassdouble,whichcouldbetheresultofanintermediatecomputation:
f=[0.50.5;0.751.5]; Performingtheconversion
g=im2uint8(f)
im2uint8
setsto0allvaluesintheinputthatarelessthan0,setsto255allvaluesintheinputthataregreaterthan1,andmultipliesallothervaluesby255.
Roundingtheresultsofthemultiplicationtothenearestintegercompletestheconversion.
Notethattheroundingbehaviorofim2uint8
isdifferentfromthedataclassconversionfunctionuint8discussedintheprevioussection,whichsimplydiscardsfractionalparts.
g=0128191255
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ConvertingbetweenImageClassesandTypes
Convertinganarbitraryarrayofclassdouble
toanarrayofclassdoublescaledtotherange[0,1]canbeaccomplishedbyusingfunctionmat2graywhosebasicsyntaxis
g=mat2gray(f,[Amin,Amax]) ThespecifiedparametersAmin andAmax
aresuchthatvalueslessthanAmin
infbecome0ing,andvaluesgreaterthanAmax infcorrespondto1ing.
Ex:x=mat2gray(f)g=im2uint8(x)
X=00.5000
0.62501.0000
x=(f+0.5)/(1.5+0.5)
g=0 128
159 255
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Functionim2double Iftheinputisofclassuint8,uint16,orlogical,
functionim2double
convertsittoclassdouble withvaluesintherange[0,1].
Iftheinputisalreadyofclassdouble,im2double returnsanarray
thatisequaltotheinput. Forexample,ifanarrayofclassdouble
resultsfromcomputations
thatyieldvaluesoutsidetherange[0,1],inputtingthisarrayintoim2double
willhavenoeffect.
Asmentionedintheprecedingslide,adouble
arrayhavingarbitraryvaluescanbeconvertedtoadouble
arraywithvaluesintherange[0,1]byusingfunctionmat2gray.
Ex:h=uint8([2550;128200]);
Performingtheconversiong=im2double(h); g =double(h)/255;
g=0.09800.19610.50200.7843
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Functionim2bwg=im2bw(f,T)g f thresholdT
g=im2bw(f),IPT T=0.5
f uint8,f=f/255; f uint16,f=f/65535; f doubleim2bw T f g=f;
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ArrayIndexing
VectorIndexing:anarrayofdimension1Niscalledarowvector,
whichisaccessedusingonedimensionalindexing.
Thus,v(1)isthefirstelementofvectorv,v(2)itssecondelement,
andsoforth.
TheelementsofvectorsinMATLABareenclosedbysquarebrackets
andareseparatedbyspacesorbycommas. Forexample,
>>V=[13579]>>W=V%W V(V)
>>A=V(1:3) A=[135]>>A=V(2:4)
A=[357]>>A=V(3:end) A=[579]
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ArrayIndexing>>W=V(:)% W=V W
>>A=V(1:end)%A=V>>A=V(1:2:end)%A=[159]
for(i=1;i>A=V(end:2,1)%A=[951]
for(i=end;i>1;i=i2)>>A=V([145])%A=[179] [145]
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MatrixIndexing
M=[123;456;789]
%M 3x3
x=M(1,3)
% x=3
M=
123456789
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MatrixIndexing (Colon,:)
c3=M(:,3)%c3= c3=M(1:3,3)
c3
r2=M(2,:)%r2=[456]
S23=M(2:3,:)%% S23=M(2:3,1:3)
S23=
456789
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MatrixIndexing B=M; B
>>B=M;>>B(:,1)=0;
end>>x=M(end,end:2:1)%x=[97]
>>S=M([12],[23])
B=023056089
, ,
, ,
2 35 6
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MatrixIndexing
>>L=logical([101;100;001]);>>X=M(L)%X=[1439]
>>A=M(:)%A=[1 47258369]
>>X=sum(M(:))%X=45
>>X=sum(sum(M))% sum(121518)=45
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X peppers.png
>>imshow(X)
%>>imshow(X(end:1:1,:,:))
% end:1:1
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>>imshow(X(:,:,1))%
imshow(I(100:end100,100:end100,:))% 100 end100%
imshow(I(1:2:end,1:2:end,:))% 1,3,5,,end% 1,3,5,,end
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0 100 200 300 400 500 6000
50
100
150
200
250
300>>plot(X(200,:,1),'r')>>holdon>>plot(X(200,:,2),'g')>>plot(X(200,:,3),'b')
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size matlab >>d=size(X);%d=[3845123]
>>d=size(X,1);%d=384
>>d=size(X,2);%d=512>>d=size(X,3);%d=3
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zeros(M,N)generatesanMxN matrixofOs
ofclassdouble>>x=zeros(2,2);%x=[00;00];
ones(M,N)generatesanMxN
matrixof1sofclassdouble.>>x=ones(2,2);%x=[11;11]
true(M,N) generatesanMxN
logicalmatrixof1s.>>x=true(2,2);%x=[11;11]
false(M,N)
generatesanMxNlogicalmatrixofOs.>>x=false(2,2);%x=[00;00]
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magic(N) generatesanNxN
"magicsquare."%MAGIC(N)isanNbyNmatrixconstructedfrom
theintegers1throughN^2withequalrow,column,anddiagonalsums.
ProducesvalidmagicsquaresforallN>0exceptN=2.Magicsquaresareusefularraysfortestingpurposesbecausetheyareeasytogenerateandtheirnumbersareintegers.
>>x=magic(3)
x=
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rand(M,N) generatesanMxN
matrixwhoseentriesareuniformlydistributedrandomnumbersintheinterval[0,1].
randn (M,N) generatesanMxN
matrixwhosenumbersarenormallydistributed(i.e.,Gaussian)randomnumberswithmean0andvariance1.
>>x=rand(3)>>y=randn(3)
x=
0.81470.91340.27850.90580.63240.54690.12700.09750.9575
y=
2.76940.72540.20501.34990.06310.12413.03490.71471.4897
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IntroductiontoMFunctionProgramming
MATLABfunctionprogrammingisflexibleandparticularlyeasytolearn.
MFiles
Mfiles texteditor filename.m average.m andfilter.m
Mfile Thefunctiondefinitionline TheH1line Helptext
Thefunctionbody Comments
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FunctionDefinition Thefunctiondefinitionlinehastheform
function [outputs]=name(inputs)
Forexample,afunctiontocomputethesumandproduct(twodifferentoutputs)
oftwoimageswouldhavetheform
function [s,p]=sumprod(f,g)
wheref,andgaretheinputimages,sisthesumimage,andpistheproductimage.
Thenamesumprod
isarbitrarilydefined,butthewordfunctionalwaysappearsontheleft,intheformshown.
Outputargumentsareenclosedbysquarebracketsandtheinputs
areenclosedbyparentheses.Ifthefunctionhasasingleoutputargument,itisacceptabletolisttheargumentwithoutbrackets.Ifthefunctionhasnooutput,onlythewordfunctionisused,withoutbracketsorequalsign.
Functionnamesmustbeginwithaletter,andtheremainingcharacterscanbeanycombinationofletters,numbers,andunderscores.Nospacesareallowed.MATLABdistinguishesfunctionnamesupto63characterslong.
Functionscanbecalledatthecommandprompt;forexample,[s,p]=sumprod(f,g);
ortheycanbeusedaselementsofotherfunctions(subfunctions).Asnotedinthepreviousparagraph,iftheoutputhasasingleargument,itisacceptabletowriteitwithoutthebrackets,asin
y=sum(x);
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H1line TheH1lineisthefirsttextline.Itisasinglecommentline
thatfollowsthefunctiondefinitionline.TherecanbenoblanklinesorleadingspacesbetweentheH1lineandthefunctiondefinitionline.
AnexampleofanH1lineis%SUMPRODComputesthesumandproductoftwoimages.
H1lineisthefirsttextthatappearswhenaUsertypeshelpfunction_name
attheMATLABprompt.Also,asmentionedinthatsection,typinglookforkeyworddisplaysalltheH1linescontainingthestringkeyword.
Thislineprovidesimportantsummaryinformationabout
theMfile,soitshouldbeasdescriptiveaspossible.
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HelptextHelptext
HelptextisatextblockthatfollowstheH1line,withoutanyblanklinesinbetweenthetwo.
Helptextisusedtoprovidecommentsandonlinehelpforthefunction.
Whenausertypeshelpfunction_name
attheprompt,MATLABdisplaysallcommentlinesthatappearbetweenthefunctiondefinitionlineandthefirstnoncomment
(executableorblank)line.
ThehelpsystemignoresanycommentlinesthatappearaftertheHelptextblock.
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functionbody&comment
ThefunctionbodycontainsalltheMATLABcodethatperformscomputationsandassignsvaluestooutputarguments.
Alllinesprecededbythesymbol"%"thatarenottheH1lineorHelptextareconsideredfunctioncommentlinesandarenotconsideredpartoftheHelptextblock.
Itispermissibletoappendcommentstotheendofalineofcode.
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EditMfiles
Mfilescanbecreatedandeditedusinganytexteditorandsaved
withtheextension.m
inaspecifieddirectory,typicallyintheMATLABsearchpath.
AnotherwaytocreateoreditanMfileistousetheeditfunctionattheprompt.Forexample,
editsumprodopensforeditingthefilesumprod .m
ifthefileexistsinadirectorythatisintheMATLABpathorinthecurrentdirectory.
Ifthefilecannotbefound,MATLABgivestheusertheoptiontocreateit.
MATLABeditorwindowhasnumerouspulldownmenusfortaskssuchassaving,viewing,anddebuggingfiles.Becauseitperformssomesimplechecksandusescolortodifferentiatebetweenvariouselementsofcode,thistexteditorisrecommendedasthetoolofchoiceforwritingandeditingMfunctions.
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Operators
MATLABoperatorsaregroupedintothreemaincategories:
Arithmeticoperatorsthatperformnumericcomputations
Relationaloperatorsthatcompareoperandsquantitatively
LogicaloperatorsthatperformthefunctionsAND,OR,andNOT
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ArithmeticOperators
MATLABhastwodifferenttypesofarithmeticoperations.
Matrixarithmeticoperationsaredefinedbytherulesoflinearalgebra.
Arrayarithmeticoperationsarecarriedoutelementbyelementand
canbeusedwithmultidimensionalarrays.
Theperiod(dot)character(.)distinguishesarrayoperationsfrom
matrixoperations.
Forexample,A*Bindicatesmatrixmultiplicationinthetraditional
sense,
whereasA.*Bindicatesarraymultiplication,inthesensethatthe
resultisanarray,thesamesizeasAandB,inwhicheachelementistheproductofcorrespondingelementsofAandB.Inotherwords,
ifC=A.*B,thenC(I,J)=A(I,J)*B(I,J).
Becausematrixandarrayoperationsarethesameforadditionand
subtraction,thecharacterpairs.+and. arenotused.
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Arrayandmatrix
arithmeticoperators
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ArithmeticoperatorsforIPT
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Illustrationofarithmeticoperatorsandfunctionsmaxandmin.
function[p,pmax,pmin,pn]
=improd(f,g)%IMPRODComputestheproductoftwoimages.%[P,PMAX,PMIN,PN]=IMPROD(F,G)toutputstheelementby%elementproductoftwoinputimages,FandG,theproduct%maximumandminimumvalues,andanormalizedproductarraywith%valuesintherange[0,1].Theinputimagesmustbeofthesame%size.TheycanbeofclassUinta,unit16,ordouble.Theoutputs%areofclassdouble.fd
=double(f);gd =double(g);p=fd.*gd;pmax =max(p(:));pmin
=min(p(:));pn =mat2gray(p);
Supposethatf=[12;34]andg=[12;21].Typingtheprecedingfunctionatthepromptresultsinthefollowingoutput:[p,pmax,pmin,pn]=improd(f,g)p=
1464
pmax =6
pmin =1
pn =00.6000
1.00000.6000
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Relationaloperators
Syntax AB A=B A==B A~=B
Relationaloperatorsperformelementbyelementcomparisonsbetweentwoarrays.
Theyreturnalogicalarrayofthesamesize,withelementssettological1(true)wheretherelationistrue,andelementssettological0(false)whereitisnot.
Theoperators,=useonlytherealpartoftheiroperandsforthecomparison.
Theoperators==and~=testrealandimaginaryparts.
>>X=5;>>X>=[123;456;7810]ans=
111110000
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LogicalOperator
MATLABoffersthreetypesoflogicaloperatorsandfunctions:
Elementwise operateoncorrespondingelementsoflogicalarrays.
Bitwise operateoncorrespondingbitsofintegervaluesorarrays.
Shortcircuit operateonscalar,logicalexpressions.
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ElementwiseThefollowinglogicaloperatorsandfunctionsperformelementwiselogicaloperationsontheirinputstoproducealikesizedoutputarray.
TheexamplesshowninthefollowingtableusevectorinputsAand
B,where>>A=[01101];>>B=[11001];
Operator Description Example
&
Returns1foreveryelementlocationthatistrue(nonzero)inbotharrays,and0forallotherelements.
A&B=01001
|
Returns1foreveryelementlocationthatistrue(nonzero)ineitheroneortheother,orbotharrays,and0forallotherelements.
A|B=11101
~ Complementseachelementoftheinputarray, ~A=10010
xor
Returns1foreveryelementlocationthatistrue(nonzero)inonlyonearray,and0forallotherelements.
xor(A,B)=10100
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BitWiseFunctions
Thefollowingfunctionsperformbitwiselogicaloperationson
nonnegativeintegerinputs.Inputsmaybescalarorinarrays.Ifinarrays,thesefunctionsproducealikesizedoutputarray.
TheexamplesshowninthefollowingtableusescalarinputsAandB,where
A=28;%binary11100 B=21;%binary10101
Operator Description Example
bitand ReturnsthebitwiseANDoftwononnegativeintegerarguments.
bitand(A,B)=20(binary10100)
bitor ReturnsthebitwiseORoftwononnegativeintegerarguments.
bitor(A,B)=29(binary11101)
Bitcmp
Returnsthebitwisecomplementasannbitnumber,wherenisthesecondinputargumenttobitcmp.
bitcmp(A,5)=3(binary00011)
bitxor
ReturnsthebitwiseexclusiveORoftwononnegativeintegerarguments.
bitxor(A,B)=9(binary01001)
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ShortCircuitOperatorsShortCircuitOperators
ThefollowingoperatorsperformANDand
ORoperationsonlogicalexpressionscontainingscalarvalues.Theyareshortcircuitoperatorsinthattheyevaluatetheirsecondoperandonlywhentheresultisnotfullydeterminedbythefirstoperand.
Operator Description
&&
Returnslogical1(true)ifbothinputsevaluatetotrue,andlogical0(false)iftheydonot.
||
Returnslogical1(true)ifeitherinput,orboth,evaluatetotrue,andlogical0(false)iftheydonot.
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FlowControl
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if,else,andelseif if ifexpression
statementsend
Theelse andelseif statementsfurtherconditionalize
theifstatement. Thegeneralsyntaxisifexpression1 statements1elseif
expression2 statements2else statements3end
function av
=average(A)%AVERAGEComputestheaveragevalueof%anarray.AV=AVERAGE(A)computesthe%averagevalueofinputarray,A,which%mustbea10or20array.Checkthe%validityoftheinput.(Keepinmindthat%a10arrayisaspecialcaseofa20%array.)if
ndims (A)>2
error('Thedimensionsoftheinputcannotexceed2.')end%Computetheaverageav
=sum(A(:))/length(A(:));%ifAisanimage,numel
(A)givesits%numberofpixels.Inthiscase,wecan%use%av
=sum(A(:))/numel(A);
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forfor Thesyntaxis
for index=start:increment:endstatements
end Itispossibletonesttwoormoreforloops,asfollows:
for index1=start1:increment1:endstatements1for
index2=start2:increment2:end
statements2endadditionalloop1statements
end Forexample,thefollowingloopexecutes11times:
count=0;for k=0:0.1:1
count=count+1;end
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while Thesyntaxis
while expressionstatements
end Asinthecaseoffor,whileloopscanbe
nested:while expression1
statements1while expression2
statements2endadditionalloop1statements
end Forexample,thefollowingnested
whileloopsterminate whenbothaandbhavebeenreducedto0:
a=10;b=5;while a
a=a1;while b
b=b 1;end
end
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break,continue breakBreakterminatestheexecutionofafor
orwhileloop.Whenabreak
statementisencountered,executioncontinueswiththenextstatementoutsidetheloop.Innestedloops,breakexitsonlyfromtheinnermostloopthatcontainsit.
continueThecontinuestatementpassescontroltothenextiterationofthefor
orwhile
loopinwhichitappears,skippinganyremainingstatementsinthebodyoftheloop.Innestedloops,continuepassescontroltothenextiterationoftheloopenclosingit.
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switch
ThisisthestatementofchoiceforcontrollingtheflowofanMfunctionbasedondifferenttypesofinputs.Thesyntaxisswitch
switch_expression
case case_expressionstatement(s)
case {case_expression1,case_expression2,...}statement(s)
otherwisestatement(s)
end
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CellArrays
AcellarrayinMATLABisamultidimensionalarraywhoseelementsare
copiesofotherarrays.Forexample,thecellarrayc={'gauss',[10;01],3}
Toselectthecontentsofacellarrayweencloseanintegeraddressincurlybraces.Inthiscase,weobtainthefollowingresults:
c{1}ans =
gaussc{2}ans
1001
c{3}ans
3
Animportantpropertyofcellarraysisthattheycontaincopiesofthearguments,notpointerstothearguments.
>>c={A,B};%AandBarematrices,andthesematriceschanged%sometimelaterinaprogram,thecontentsofcwouldnotchange.
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StructuresStructures
Structuresaresimilartocellarrays,inthesensethattheyallow
groupingofacollectionofdissimilardataintoasinglevariable.
However,unlikecellarrayswherecellsareaddressedbynumbers,theelementsofstructuresareaddressedbynamescalledfields.
Dependingontheapplication,usingfieldsaddsclarityandreadabilitytoanMfunction.
Forinstance,lettingSdenotethestructurevariableandusingthe(arbitrary)fieldnameschar_string,matrix,andscalar,thedataintheprecedingexamplecouldbeorganizedasastructurebyletting
S.char_string ='gauss';
S.matrix [10;01];
S.scalar =3;
