外文文献翻译Word格式.docx
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外文文献翻译Word格式.docx
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在本文中,通过使用加权最小二乘法直线拟合,其线的斜率l得到的旋转角度,一个是计算。
最后整个图像旋转的一个图像倾斜校正fmished。
本文的其余部分组织如下。
第2节描述的实现详细说明本方法。
第3节中给出了实验结果为了测试我们的方法比较。
得出的结论是在第4节。
II。
车牌倾斜校正在加权最小二乘法当存在一定的倾斜车牌图像(见图1),有一个倾斜角度的主轴线X”之间的倾斜车牌区域的水平X轴。
鉴于此,我们认为,一旦得到了,整个图像可以旋转通过一个和倾斜校正完成。
在图1a,一>0表示修正角是一个,反之,他是一个修正角。
A.基于最小二乘直线拟合
在工程设计和试验过程
统计,分析和处理的一批数据
数据往往拟合曲线。
LSM是一种广泛使用的拟合
方法。
如果我们用一个平滑的曲线y=f(x)去拟合一组
数据(x
我
“Y
;
(我)
=1,2,。
..,N),然后在原则上,偏差
数据和曲线之间应尽量减少。
的
偏差e:
(X=我
)-Y;
通常被称为残留。
LSM
使笔和2达到最小值,即,其
n
目标函数Q=LE:
2
是最小的。
在本文中
=1
我们使用一个直线拟合数据。
让线性方程
可以表示为
Y
=α+
O
然后目标
函数Q:
VehicleLicensePlateTiltCorrectionbasedontheWeightedLeastSquareMethod
YifuWang
MathematicsandComputerScienceCollege
HunanNormalUniversity
Changsha,P.R.C
wangyifu20I054@
Abstract-TiltcorrectionisaverycrucialpartoftheVehicle
LicensePlate(VLP)automaticrecognition.Inthispaper,
accordingtotheWeightedLeastSquareMethod(WLSM),the
VLPregionisfittedtoastraightlineandthenthelineslope
a
l
isobtained,bywhichtherotationangleaiscalculated.
Finallythewholeimageisrotatedby-aandtheimagetilt
correctionisperformed.Theexperimentalresultsdefinitely
showthat,thispapermethodcanquicklyandaccuratelyget
thetiltangleandhasgreatrobustnessandadaptability.
ComparedwiththeLeastSquareMethod(LSM),inthispaper
methodthetiltangleismorepreciseandthevalueofobjection
functionissmaller;
ComparedwithHoughTransformation
(HT)andRadomTransformation(RT),thispapermethodis
featuredinfasterprocessingtimeandmoreprecisetiltangle,
whichisparticularlywelladaptedtothereal-timetilt
correctioninIntelligentTransportationSystem(ITS).
Keywords-Vehiclelicenseplate;
image;
leastsquaremethod;
Houghtransformation
I.INTRODUCTION
IntheprocessionoftakingtheVLPimages,becauseof
theweather,theillumination,theroadconditionandsoon,
theVLPintheimagefrequentlyhassomeclearandserious
tiltsothatthetouchingandbrokencharactersarecreated,
which,asweknowtoowell,isatremendousandserious
obstacletothecharactersegmentationandrecognition[1-4].
Inordertoapproachtheaboveproblem,expertsathomeand
abroadhaveundertakencolossalandin-depthresearchand
explorationovermanyyearsandhaveconceivedmany
ingeniousandpracticalsolutions,amongwhichHough
TransformationMethod(HTM),ProjectionProfileMethod
(PPM),andComponentNearestNeighborClustering
Method(CNNCM)arethemosttypicalones.HTM[2-4],as
themostextensively-employedandprevalentone,usesHT
tocalculatethepossibletrackinparameterspaceaccording
totargetpixelcoordinatesintheimagespace.Itisverywell
adaptedtolineargraphic,butwithalotofcomputational
loadandlackofrobustnessforatiltVLPimage.PPM[1],
whichisbuiltontheanalysisfortheprojectionshape,hasan
extremelyheavycomputationalloadbecauseitneedsto
calculatetheprojectionshapeofeachangle.CNNCM[5],
bydiscoveringKnearestneighborsofthecentralpointof
allconnectedcomponents,computesthevectordirectionof
eachcouplenearestneighborandgetsthestatistical
histogramwherethepeakvaluedenotestheentireimagetilt
angle.Sincethereexistsomeconnectedcomponentsinthe
978-1-4244-5540-9/10/$26.00©
2010IEEE
126
PengXu
image,itsprocessingtimeisalsoaquiteprodigiousload[6-8].
Onthebasisofacomprehensiveandthorough
investigationintoWLSM,weproposevehiclelicenseplate
tiltcorrectionbasedontheweightedleastsquaremethod.In
thispaper,throughfittingthestraightlineusingWLSM,the
lineslopea
isobtained,bywhichtherotationangleais
calculated.Finallythewholeimageisrotatedby-aand
imagetiltcorrectionisfmished.Therestofthispaperis
organizedasfollows.Section2describestheimplementation
ofthismethodindetail.Section3givesexperimentalresults
andcomparisonstotestourmethod.Theconclusionsare
giveninSection4.
II.VEHICLELICENSEPLATETILTCORRECTIONBASED
ONTHEWEIGHTEDLEASTSQUAREMETHOD
WhenthereexistssometiltintheVLPimage(seeFig.I),
thereisatiltangleabetweentheprincipalaxisX'
ofand
thehorizontalaxisXofthetiltVLPregion.Inviewofthis,
wethinkthatonceaisgot,theentireimagecanberotated
by-aandthetiltcorrectioniscompleted.InFig.la,
a>
0denotesthatthecorrectionangleis-a,contrarily,
hecorrectionangleisa.
yy
(a)a>
0(b)a<
0
FigureI.Imagetilt
A.FittingthestraightlinebasedonLSM
X'
Inthecourseofengineeringdesignandexperimental
statistics,uponanalysisandprocessiontoabatchofdata,the
dataareoftenfittedtoacurve.LSMisawidely-usedfitting
method.Ifweuseasmoothcurvey=f(x)tofitasetof
data(x
i
'
y
;
)(i
=1,2,...,n),theninprinciple,thedeviation
betweenthedataandthecurveshouldbeminimized.The
deviationE:
=I(x
)-y;
isusuallycalledresidue.LSM
enablesthesumof&
2toachievetheminimum,namely,the
n
objectivefunctionQ=LE:
2
istheminimum.Inthispaper
=1
weuseastraightlinetofitthedata.Letthelinearequation
beexpressedas
Y
=alx+a
O
andthentheobjective
functionQis:
nn
Q=�>
.;
=L(alx;
+ao-y
)2
(1)
=1;
ThematrixformofEquation
(1)isshownasfollows:
Q=(XA-Yl(XA-Y)
(2)
whereY
=[YIY
x=
[11
XI
x
...Ynf
A=[aoa
lr
and
1]
T
FromEquation
obtained:
(2),thepartialderivativeofAis
8Q
=2XT(XA-Y)=O(3)
8A
TheaboveequationissolvedandAisobtained:
A=(XTX)-IXTy(4)
Namely:
ao=
=
nnnn
LY;
LX;
-LX;
Y;
...:
=�I--�;
=�I----�;
=�I--;
_�;
=�I-
(5)
x;
andY;
areinsertedintoequation(5)andtheslopeal
isobtained.
B.FittingthestraightlinebasedonWLSM
AccordingtoEquation
(1),inthecaseofhomoscedastic
errors,itisreasonablyassumedthat8
producedbyeach
(x;
Y;
)isequallytreated,whichdenotesthateach8
providescoequallyimportantinformation.Inthecaseof
heteroskedasticerrors,however,inthefittinglinethe
positionI(x;
)whichcorrespondsto8
withdispersion
degreebeinghighisnotprecise.Therefore,fittingastraight
lineismadelittleaccountoftheinformationprovidedby8
.
Inotherwords,thehigherthedeviation8
corresponding
tox;
thesmallerthecontributiontotheinformation,
conversely,thesmallerthedeviation8
correspondingtox;
thehigherthecontributiontotheinformation.Toimprove
thecorrectionprecision,theimportanceofinformation
producingbytheresidue8
isadjustedbytheweight,which
isthebasicthoughtofWLSM.
Accordingtotheaboveanalysis,weassignahigher
weighttothesmallerresiduesquare8
2,butasmallerweight
127
tothehigherresiduesquare8
2.LetWi
betheweightand
Equation
(1)isrewritten:
Q
w
=LW;
8;
=Lw;
(a
+ao-y
)2
(6)
ThematrixformofEquation
isshownasfollows:
Qw
=(XA-YlW(XA-Y)(7)
whereW=diag(w"
w2,"
Wn),A=[aoair
Ynf,
and
[111]
X=
XIX
Xn
.FromEquation(7),thepartialderivativeofAis
8Q
=2XTW(XA
_
Y)=0(8)
A=(XTWX)-IXTwy(9)
Wesupposethat
11
w.=-=--(10)
I
u�u2y.
II
AccordingtoEquations(8)-(10),ao
andalare
expressed:
(11)
X
.nn
1
L�
-Lx;
L
-;
=1Yi;
=1Y;
(tX;
t�tX;
;
=1Yi
areinsertedintoequation(11)andtheslope
alisobtained.
C.TiltcorrectionbasedonWLSM
Supposetheoriginalimageisabinarizationimagewith
theleft-toppixelbeing(1,1),inwhichthebackgroundis
black(grayvalueis0)andthecharactersarewhite(gray
valueis1).Pisthesetofcoordinates(x,y)representing
allthewhitepixelsintheimage,Iisthenumberof
elementsinP,namelyPER2xI,whereRisareal
domain.PisinsertedintoEquation(11)andtheslopealof
thefittinglineisworkedout.Lettana=a
andcompute
thetit!
anglea.Thenthispapermethodisdescribedas
follows:
Stept.GetthesetPofcoordinates(x,y)representing
allthewhitepixelsintheimage;
Step2.PutPintoEquation(11)andcalculatea
)
Step3.Lettana=a
andgetthetiltanglea:
180
a=
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