c# pdf reader table : Delete blank pages in pdf control Library system azure asp.net windows console SzeliskiBook_20100903_draft33-part607

Chapter 6
Feature-based alignment
6.1 2Dand3Dfeature-basedalignment . . . . . . . . . . . . . . . . . . . . . . 311
6.1.1 2Dalignmentusingleastsquares. . . . . . . . . . . . . . . . . . . . 312
6.1.2 Application:Panography . . . . . . . . . . . . . . . . . . . . . . . . 314
6.1.3 Iterativealgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
6.1.4 RobustleastsquaresandRANSAC . . . . . . . . . . . . . . . . . . 318
6.1.5 3Dalignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
6.2 Poseestimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
6.2.1 Linearalgorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
6.2.2 Iterativealgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
6.2.3 Application:Augmentedreality . . . . . . . . . . . . . . . . . . . . 326
6.3 Geometricintrinsiccalibration . . . . . . . . . . . . . . . . . . . . . . . . . 327
6.3.1 Calibrationpatterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
6.3.2 Vanishingpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
6.3.3 Application:Singleviewmetrology . . . . . . . . . . . . . . . . . . 331
6.3.4 Rotationalmotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
6.3.5 Radialdistortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
6.4 Additionalreading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
6.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
Delete blank pages in pdf - remove PDF pages in C#.net, ASP.NET, MVC, Ajax, WinForms, WPF
Provides Users with Mature Document Manipulating Function for Deleting PDF Pages
delete pdf pages reader; delete pages from pdf document
Delete blank pages in pdf - VB.NET PDF Page Delete Library: remove PDF pages in vb.net, ASP.NET, MVC, Ajax, WinForms, WPF
Visual Basic Sample Codes to Delete PDF Document Page in .NET
delete pages from pdf; delete page in pdf document
310
ComputerVision:AlgorithmsandApplications(September3,2010draft)
(a)
(b)
x
1
x
0
x
2
x
1
x
0
x
2
c
(c)
(d)
Figure6.1 Geometricalignmentandcalibration:(a)geometricalignmentof2Dimagesfor
stitching(SzeliskiandShum1997)  c c 1997ACM;(b)atwo-dimensionalcalibrationtarget
(Zhang2000)
c
2000IEEE;(c)calibrationfromvanishingpoints;(d)scenewitheasy-to-
findlinesandvanishingdirections(Criminisi,Reid,andZisserman2000)  c c 2000Springer.
C# PDF Page Insert Library: insert pages into PDF file in C#.net
such as how to merge PDF document files by C# code, how to rotate PDF document page, how to delete PDF page using Add and Insert Blank Pages to PDF File in
add or remove pages from pdf; delete pages in pdf reader
VB.NET PDF Page Insert Library: insert pages into PDF file in vb.
Able to add and insert one or multiple pages to existing adobe PDF document in VB.NET. Ability to create a blank PDF page with related by using following online
delete pages from pdf file online; delete page numbers in pdf
6.12Dand3Dfeature-basedalignment
311
y
x
similarity
Euclidean
affine
projective
translation
Figure6.2 Basicsetof2Dplanartransformations
Oncewehaveextractedfeaturesfromimages,thenextstageinmanyvisionalgorithmsis
tomatchthesefeaturesacrossdifferentimages(Section4.1.3). Animportantcomponentof
thismatching istoverifywhetherthesetofmatchingfeaturesisgeometrically consistent,
e.g.,whetherthefeaturedisplacementscanbedescribedbyasimple2Dor3Dgeometric
transformation.Thecomputedmotionscanthenbeusedinotherapplicationssuchasimage
stitching(Chapter9)oraugmentedreality(Section6.2.3).
Inthischapter,welookatthetopicofgeometricimageregistration,i.e.,thecomputation
of2Dand3Dtransformationsthatmapfeaturesinoneimagetoanother(Section6.1). One
special caseof thisproblemisposeestimation, whichisdeterminingacamera’sposition
relativetoaknown3Dobjectorscene(Section6.2). Anothercaseisthecomputationofa
camera’sintrinsiccalibration,whichconsistsoftheinternalparameterssuchasfocallength
andradialdistortion (Section6.3). InChapter7,welookattherelatedproblemsofhow
toestimate3Dpointstructurefrom2Dmatches(triangulation)andhowtosimultaneously
estimate3Dgeometryandcameramotion(structurefrommotion).
6.1 2D and3Dfeature-basedalignment
Feature-basedalignmentistheproblemofestimatingthemotionbetweentwoormoresets
ofmatched2Dor3Dpoints.Inthissection,werestrictourselvestoglobalparametrictrans-
formations,suchasthosedescribedinSection2.1.2andshowninTable2.1andFigure6.2,
orhigherordertransformationforcurvedsurfaces(ShashuaandToelg1997;Can,Stewart,
Roysamet al. 2002). Applicationstonon-rigidorelasticdeformations(Bookstein 1989;
SzeliskiandLavall´ee1996;Torresani,Hertzmann,andBregler2008)areexaminedinSec-
tions8.3and12.6.4.
C# Word - Insert Blank Word Page in C#.NET
Users to Insert (Empty) Word Page or Pages from a to specify where they want to insert (blank) Word document rotate Word document page, how to delete Word page
delete a page from a pdf in preview; delete pdf pages in reader
C# PowerPoint - Insert Blank PowerPoint Page in C#.NET
to Insert (Empty) PowerPoint Page or Pages from a where they want to insert (blank) PowerPoint document PowerPoint document page, how to delete PowerPoint page
delete pages from pdf online; delete pages pdf file
312
ComputerVision:AlgorithmsandApplications(September3,2010draft)
Transform
Matrix
Parametersp
JacobianJ
translation
"
1 0 t
x
0 1 t
y
#
(t
x
;t
y
)
"
1 0
0 1
#
Euclidean
"
c
s
t
x
s
c
t
y
#
(t
x
;t
y
;)
"
1 0  s
x c
y
0 1
c
x s
y
#
similarity
"
1+a
b
t
x
b
1+a t
y
#
(t
x
;t
y
;a;b)
"
1 0 x  y
0 1 y
x
#
affine
"
1+a
00
a
01
t
x
a
10
1+a
11
t
y
#
(t
x
;t
y
;a
00
;a
01
;a
10
;a
11
)
"
1 0 x y 0 0
0 1 0 0 x y
#
projective
2
6
4
1+h
00
h
01
h
02
h
10
1+h
11
h
12
h
20
h
21
1
3
7
5
(h
00
;h
01
;:::;h
21
)
(seeSection6.1.3)
Table6.1 Jacobiansofthe2Dcoordinatetransformationsx=f(x;p)showninTable2.1,
wherewehavere-parameterizedthemotionssothattheyareidentityforp=0.
6.1.1 2Dalignmentusingleastsquares
Givenasetofmatchedfeaturepointsf(x
i
;x
0
i
)gandaplanarparametrictransformation
1
of
theform
x
0
=f(x;p);
(6.1)
howcanweproducethebestestimateofthemotionparametersp?Theusualwaytodothis
istouseleastsquares,i.e.,tominimizethesumofsquaredresiduals
E
LS
=
X
i
kr
i
k
2
=
X
i
kf(x
i
;p) x
0
i
k
2
;
(6.2)
where
r
i
=f(x
i
;p) x
0
i
=
^
x
0
i
~
x
0
i
(6.3)
istheresidual between themeasuredlocation ^x
0
i
and itscorresponding currentpredicted
location~x
0
i
=f(x
i
;p).(SeeAppendixA.2formoreonleastsquaresandAppendixB.2for
astatisticaljustification.)
Forexamplesofnon-planarparametricmodels,suchasquadrics,seetheworkofShashuaandToelg(1997);
ShashuaandWexler(2001).
C# Create PDF Library SDK to convert PDF from other file formats
String outputFile = Program.RootPath + "\\" output.pdf"; // Create a new PDF Document object with 2 blank pages PDFDocument doc = PDFDocument.Create(2
copy pages from pdf to new pdf; delete pages of pdf reader
VB.NET PDF File & Page Process Library SDK for vb.net, ASP.NET
is unnecessary, you may want to delete this page is the programmatic representation of a PDF document instance may consist of newly created blank pages or image
delete page pdf file reader; pdf delete page
6.12Dand3Dfeature-basedalignment
313
Many ofthemotion modelspresented in Section2.1.2 and Table2.1, i.e., translation,
similarity,andaffine,havealinearrelationshipbetweentheamountofmotionx=x
0
x
andtheunknownparametersp,
x=x
0
x=J(x)p;
(6.4)
whereJ =@f=@pistheJacobianofthetransformationfwithrespecttothemotionparam-
etersp(seeTable6.1).Inthiscase,asimplelinearregression(linearleastsquaresproblem)
canbeformulatedas
E
LLS
=
X
i
kJ(x
i
)p x
i
k
2
(6.5)
= p
T
"
X
i
J
T
(x
i
)J(x
i
)
#
p 2p
T
"
X
i
J
T
(x
i
)x
i
#
+
X
i
kx
i
k
2
(6.6)
= p
T
Ap 2p
T
b+c:
(6.7)
Theminimumcanbefoundbysolvingthesymmetricpositivedefinite(SPD)systemofnor-
malequations2
Ap=b;
(6.8)
where
A=
X
i
J
T
(x
i
)J(x
i
)
(6.9)
iscalledtheHessianandb=
P
i
J
T
(x
i
)x
i
. Forthecaseofpuretranslation,theresult-
ingequationshaveaparticularlysimpleform,i.e.,thetranslationistheaveragetranslation
betweencorrespondingpointsor,equivalently,thetranslationofthepointcentroids.
Uncertaintyweighting. Theaboveleastsquaresformulationassumesthatallfeaturepoints
arematchedwiththesameaccuracy. Thisisoftennotthecase,sincecertainpointsmayfall
intomoretexturedregionsthanothers. Ifweassociateascalarvarianceestimate2
i
with
eachcorrespondence,wecanminimizetheweightedleastsquaresprobleminstead,
3
E
WLS
=
X
i
2
i
kr
i
k
2
:
(6.10)
AsshowninSection8.1.3,acovarianceestimateforpatch-basedmatchingcanbeobtained
bymultiplyingtheinverseofthepatchHessianA
i
(8.55)withtheper-pixelnoisecovariance
Forpoorlyconditionedproblems,itisbettertouseQRdecompositiononthesetoflinearequationsJ(x
i
)p=
x
i
insteadofthenormalequations(Bj¨orck1996;GolubandVanLoan1996). However,suchconditionsrarely
ariseinimageregistration.
3
Problemswhereeachmeasurementcanhaveadifferentvarianceorcertaintyarecalledheteroscedasticmodels.
VB.NET Create PDF Library SDK to convert PDF from other file
Dim outputFile As String = Program.RootPath + "\\" output.pdf" ' Create a new PDF Document object with 2 blank pages Dim doc As PDFDocument = PDFDocument
delete page in pdf; delete page pdf online
How to C#: Cleanup Images
returned. Delete Blank Pages. Set property BlankPageDelete to true , blank pages in the document will be deleted. Remove Edges or Borders.
delete page on pdf file; cut pages from pdf preview
314
ComputerVision:AlgorithmsandApplications(September3,2010draft)
Figure6.3 Asimplepanograph consisting of threeimagesautomaticallyalignedwith a
translationalmodelandthenaveragedtogether.
2
n
(8.44).Weightingeachsquaredresidualbyitsinversecovariance
1
i
=
2
n
A
i
(which
iscalledtheinformationmatrix),weobtain
E
CWLS
=
X
i
kr
i
k
2
1
i
=
X
i
r
T
i
1
i
r
i
=
X
i
2
n
r
T
i
A
i
r
i
:
(6.11)
6.1.2 Application:Panography
Oneofthesimplest(andmostfun)applicationsofimagealignmentisaspecialformofimage
stitchingcalledpanography.Inapanograph,imagesaretranslatedandoptionallyrotatedand
scaledbeforebeing blended withsimpleaveraging (Figure6.3). Thisprocessmimicsthe
photographiccollages created by artist David Hockney,although hiscompositionsusean
opaqueoverlaymodel,beingcreatedoutofregularphotographs.
InmostoftheexamplesseenontheWeb,theimagesarealignedbyhandforbestartistic
effect.4 However,it isalso possibletousefeaturematching and alignment techniquesto
performtheregistrationautomatically(Nomura,Zhang,andNayar2007;Zelnik-Manorand
Perona2007).
Considerasimpletranslationalmodel.Wewantallthecorrespondingfeaturesindifferent
imagestolineupasbestaspossible.Lett
j
bethelocationofthejthimagecoordinateframe
intheglobalcompositeframeandx
ij
bethelocationoftheithmatchedfeatureinthejth
image.Inordertoaligntheimages,wewishtominimizetheleastsquareserror
E
PLS
=
X
ij
k(t
j
+x
ij
) x
i
k
2
;
(6.12)
4
http://www.flickr.com/groups/panography/.
VB.NET PDF: Get Started with PDF Library
Auto Fill-in Field Data. Field: Insert, Delete, Update Field. RootPath + "\\" output.pdf" ' Create a new PDF Document object with 2 blank pages Dim doc
copy pages from pdf to another pdf; delete pages from pdf acrobat
6.12Dand3Dfeature-basedalignment
315
wherex
i
istheconsensus(average)position offeaturei in theglobalcoordinateframe.
(Analternativeapproachistoregistereachpairofoverlappingimagesseparatelyandthen
computeaconsensuslocationforeachframe—seeExercise6.2.)
Theaboveleastsquaresproblemisindeterminate(youcanaddaconstantoffsettoallthe
frameandpointlocationst
j
andx
i
).Tofixthis,eitherpickoneframeasbeingattheorigin
oraddaconstrainttomaketheaverageframeoffsetsbe0.
Theformulasforaddingrotationand scaletransformationsarestraightforwardandare
leftasanexercise(Exercise6.2). Seeifyoucancreatesomecollagesthatyou wouldbe
happytosharewithothersontheWeb.
6.1.3 Iterativealgorithms
Whilelinearleastsquaresisthesimplestmethodforestimatingparameters,mostproblemsin
computervisiondonothaveasimplelinearrelationshipbetweenthemeasurementsandthe
unknowns.Inthiscase,theresultingproblemiscallednon-linearleastsquaresornon-linear
regression.
Consider, forexample,theproblemofestimating arigidEuclidean2Dtransformation
(translationplusrotation)betweentwosetsofpoints.Ifweparameterizethistransformation
bythetranslationamount(t
x
;t
y
)andtherotationangle,asinTable2.1,theJacobianof
thistransformation,giveninTable6.1,dependsonthecurrentvalueof. Noticehow in
Table6.1,wehavere-parameterizedthemotionmatricessothattheyarealwaystheidentity
attheoriginp=0,whichmakesiteasiertoinitializethemotionparameters.
Tominimizethenon-linearleastsquaresproblem,weiterativelyfindanupdateptothe
currentparameterestimatepbyminimizing
E
NLS
(p) =
X
i
kf(x
i
;p+p) x
0
i
k
2
(6.13)
X
i
kJ(x
i
;p)p r
i
k
2
(6.14)
=
p
T
"
X
i
J
T
J
#
p 2p
T
"
X
i
J
T
r
i
#
+
X
i
kr
i
k
2
(6.15)
=
p
T
Ap 2p
T
b+c;
(6.16)
wherethe“Hessian”
5
AisthesameasEquation(6.9)andtherighthandsidevector
b=
X
i
J
T
(x
i
)r
i
(6.17)
The“Hessian”A
isnotthetrueHessian(secondderivative)ofthenon-linearleastsquaresproblem(6.13).
Instead,itistheapproximateHessian,whichneglectssecond(andhigher)orderderivativesoff(x
i
;p+p).
316
ComputerVision:AlgorithmsandApplications(September3,2010draft)
isnowaJacobian-weightedsumofresidualvectors. Thismakesintuitivesense,asthepa-
rametersarepulledinthedirectionofthepredictionerrorwithastrengthproportionaltothe
Jacobian.
OnceAandbhavebeencomputed,wesolveforpusing
(A+diag(A))p=b;
(6.18)
andupdatetheparametervector p   p+paccordingly. Theparameter isan addi-
tionaldampingparameterusedtoensurethatthesystemtakesa“downhill”stepinenergy
(squarederror)andisanessentialcomponentoftheLevenberg–Marquardtalgorithm(de-
scribedinmoredetailinAppendixA.3).Inmanyapplications,itcanbesetto0ifthesystem
issuccessfullyconverging.
Forthecaseofour2Dtranslation+rotation,weendupwitha33setofnormalequations
intheunknowns(t
x
;t
y
;). An initialguessfor(t
x
;t
y
;)canbeobtainedbyfittinga
four-parametersimilaritytransform in (t
x
;t
y
;c;s)andthensetting = tan
1
(s=c). An
alternativeapproachistoestimatethetranslationparametersusingthecentroidsofthe2D
pointsandtothenestimatetherotationangleusingpolarcoordinates(Exercise6.3).
Fortheother2Dmotionmodels,thederivativesinTable6.1areallfairlystraightforward,
exceptfortheprojective2Dmotion(homography),whicharisesinimage-stitchingapplica-
tions(Chapter9).Theseequationscanbere-writtenfrom(2.21)intheirnewparametricform
as
x
0
=
(1+h
00
)x+h
01
y+h
02
h
20
x+h
21
y+1
and y
0
=
h
10
x+(1+h
11
)y+h
12
h
20
x+h
21
y+1
:
(6.19)
TheJacobianistherefore
J=
@f
@p
=
1
D
"
x y 1 0 0 0  x0x  x0y
0 0 0 x y 1  y
0
 y
0
y
#
;
(6.20)
whereD = h
20
x+h
21
y+1isthedenominatorin (6.19),whichdependson thecurrent
parametersettings(asdox
0
andy
0
).
Aninitialguessfortheeightunknownsfh
00
;h
01
;:::;h
21
gcanbeobtainedbymultiply-
ingbothsidesoftheequationsin(6.19)throughbythedenominator,whichyieldsthelinear
setofequations,
"
^x
0
x
^y
0
y
#
=
"
x y 1 0 0 0  ^x
0
 ^x
0
y
0 0 0 x y 1  ^y
0
 ^y
0
y
#
2
6
6
4
h
00
.
.
.
h
21
3
7
7
5
:
(6.21)
However,thisisnotoptimalfromastatisticalpointofview,sincethedenominatorD,which
wasusedtomultiplyeachequation,canvaryquiteabitfrompointtopoint.
6
6
HartleyandZisserman(2004)callthisstrategyofforminglinearequationsfromrationalequationsthedirect
6.12Dand3Dfeature-basedalignment
317
Onewaytocompensateforthisistoreweighteachequationbytheinverseofthecurrent
estimateofthedenominator,D,
1
D
"
^x0 x
^y
0
y
#
=
1
D
"
x y 1 0 0 0  ^x0x  ^x0y
0 0 0 x y 1  ^y
0
 ^y
0
y
#
2
6
6
4
h
00
.
.
.
h
21
3
7
7
5
:
(6.22)
Whilethismayatfirstseemtobetheexact sameset ofequationsas(6.21),becauseleast
squaresisbeingusedtosolvetheover-determinedsetofequations,theweightingsdomatter
andproduceadifferentsetofnormalequationsthatperformsbetterinpractice.
Themostprincipledwaytodotheestimation,however,istodirectlyminimizethesquared
residual equations(6.13) using theGauss–Newtonapproximation, i.e.,performingafirst-
orderTaylorseriesexpansioninp,asshownin(6.14),whichyieldsthesetofequations
"
^x
0
~x
0
^y
0
~y
0
#
=
1
D
"
x y 1 0 0 0  ~x
0
 ~x
0
y
0 0 0 x y 1  ~y
0
 ~y
0
y
#
2
6
6
4
h
00
.
.
.
h
21
3
7
7
5
:
(6.23)
Whiletheselooksimilarto(6.22),theydifferintwoimportantrespects. First,thelefthand
sideconsistsofunweightedpredictionerrorsratherthanpointdisplacementsandthesolution
vectorisaperturbationtotheparametervectorp. Second,thequantitiesinsideJ involve
predictedfeaturelocations(~x
0
;~y
0
)insteadofsensedfeaturelocations(^x
0
;^y
0
).Bothofthese
differencesaresubtleandyetthey lead to analgorithm that,when combined withproper
checkingfordownhillsteps(asintheLevenberg–Marquardtalgorithm),willconvergetoa
localminimum.NotethatiteratingEquations(6.22)isnotguaranteedtoconverge,sinceitis
notminimizingawell-definedenergyfunction.
Equation (6.23)isanalogousto theadditivealgorithmfordirect intensity-basedregis-
tration(Section8.2),sincethechangetothefulltransformationisbeingcomputed. Ifwe
prependanincrementalhomographytothecurrenthomographyinstead,i.e.,weuseacom-
positionalalgorithm(describedinSection8.2),wegetD=1(sincep=0)andtheabove
formulasimplifiesto
"
^x
0
x
^y
0
y
#
=
"
x y 1 0 0 0  x
2
xy
0 0 0 x y 1  xy  y
2
#
2
6
6
4
h
00
.
.
.
h
21
3
7
7
5
;
(6.24)
wherewehavereplaced(~x
0
;~y
0
)with(x;y)forconciseness. (Noticehowthisresultsinthe
sameJacobianas(8.63).)
lineartransform,butthattermismorecommonlyassociatedwithposeestimation(Section6.2).Notealsothatour
definitionoftheh
ij
parametersdiffersfromthatusedintheirbook,sincewedefineh
ii
tobethedifferencefrom
unityandwedonotleaveh
22
asafreeparameter,whichmeansthatwecannothandlecertainextremehomographies.
318
ComputerVision:AlgorithmsandApplications(September3,2010draft)
6.1.4 RobustleastsquaresandRANSAC
Whileregularleastsquaresisthemethodofchoiceformeasurementswherethenoisefollows
anormal(Gaussian)distribution, morerobust versionsofleast squaresarerequiredwhen
thereareoutliersamongthecorrespondences(astherealmostalwaysare).Inthiscase,itis
preferabletouseanM-estimator(Huber1981;Hampel,Ronchetti,Rousseeuwetal.1986;
BlackandRangarajan1996;Stewart1999),whichinvolvesapplyingarobustpenaltyfunction
(r)totheresiduals
E
RLS
(p)=
X
i
(kr
i
k)
(6.25)
insteadofsquaringthem.
Wecantakethederivativeofthisfunctionwithrespecttopandsetitto0,
X
i
(kr
i
k)
@kr
i
k
@p
=
X
i
(kr
i
k)
kr
i
k
r
T
i
@r
i
@p
=0;
(6.26)
where (r)=
0
(r)isthederivativeofandiscalledtheinfluencefunction.Ifweintroduce
aweightfunction,w(r)= (r)=r,weobservethatfindingthestationarypointof(6.25)using
(6.26)isequivalenttominimizingtheiterativelyreweightedleastsquares(IRLS)problem
E
IRLS
=
X
i
w(kr
i
k)kr
i
k
2
;
(6.27)
wherethew(kr
i
k)playthesamelocal weighting roleas
2
i
in (6.10). TheIRLSalgo-
rithmalternatesbetweencomputingtheinfluencefunctionsw(kr
i
k)andsolvingtheresult-
ingweightedleastsquaresproblem(withfixedwvalues). Otherincrementalrobustleast
squaresalgorithmscanbefoundintheworkofSawhneyandAyer(1996);BlackandAnan-
dan(1996);BlackandRangarajan(1996);Baker,Gross,Ishikawaetal.(2003)andtextbooks
andtutorialson robuststatistics(Huber1981;Hampel, Ronchetti,Rousseeuwetal.1986;
RousseeuwandLeroy1987;Stewart1999).
WhileM-estimatorscandefinitelyhelpreducetheinfluenceofoutliers,insomecases,
startingwithtoomanyoutlierswillpreventIRLS(orothergradientdescentalgorithms)from
convergingtotheglobaloptimum. Abetterapproachisoftentofindastartingsetofinlier
correspondences,i.e.,pointsthatareconsistentwithadominantmotionestimate.
7
TwowidelyusedapproachestothisproblemarecalledRANdomSAmpleConsensus,or
RANSACforshort(FischlerandBolles1981),andleastmedianofsquares(LMS)(Rousseeuw
1984).Bothtechniquesstartbyselecting(atrandom)asubsetofkcorrespondences,whichis
Forpixel-basedalignmentmethods(Section8.1.1),hierarchical(coarse-to-fine)techniquesareoftenusedto
lockontothedominantmotioninascene.
Documents you may be interested
Documents you may be interested