Precision Landmark Location for Machine Vision and Photogrammetry: Finding and Achieving the Maximum Possible Accuracy

162 Pages·2008·5.91 MB·English

by  Brian S.R. Armstrong

Precision Landmark Location for
Machine Vision and Photogrammetry
José A. Gutierrez
Brian S.R. Armstrong
Precision Landmark
Location for
Machine Vision and
Photogrammetry
Finding and Achieving
the Maximum Possible Accuracy
123
JoséA.Gutierrez,PhD BrianS.R.Armstrong,PhD,P.E.
EmersonCorporation DepartmentofElectricalEngineering
CorporateTechnology andComputerScience
St.Louis UniversityofWisconsin–Milwaukee
Missouri Milwaukee
USA Wisconsin
USA
BritishLibraryCataloguinginPublicationData
Gutierrez,JoseA.
Precisionlandmarklocationformachinevisionand
photogrammetry:findingandachievingthemaximumpossible
accuracy
1.Computervision2.Photogrammetry-Digitaltechniques
I.TitleII.Armstrong,BrianStewartRandall
006.3’7
ISBN-13:9781846289125
LibraryofCongressControlNumber:2007936782
ISBN 978-1-84628-912-5 e-ISBN 978-1-84628-913-2
Printedonacid-freepaper
©Springer-VerlagLondonLimited2008
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ToClaire,Amanda,andBeatrice
Preface
Precision landmark location in digital images is one of those inter-
esting problems in which industrial practice seems to outstrip the
resultsavailableinthescholarlyliterature.Approachingthisproblem,
we remarked that the best-performing commercial close-range pho-
togrammetrysystemshavespecifiedaccuraciesofapartper100,000,
whichtranslatesto10–20millipixelsofuncertaintyinlocatingfeatures
formeasurement.Atthesametime,articlesweidentifiedintheaca-
demicliteraturedidn’tseemtogiveanyfirmansweraboutwhenthis
levelofperformanceispossibleorhowitcanbeachieved.
Wecametotheproblemofprecisionlandmarklocationbyaprocess
thatmustbefamiliartomany:outofadesiretocalibrateanimage-
metrologytestbenchusinglandmarksinwell-knownlocations.Itis
straightforwardtoperformthecalibration,minimizingerrorsinaleast
squaressense;butwewerealsointerestedtoknowwhatfractionofthe
residualerrorsshouldbeattributedtothedeterminationoflandmark
locationsintheimages,andwhetherthiserrorsourcecouldbereduced.
Toaddressthesequestions,weknewwehadtogobeyondthecon-
siderationofbinaryimages.Atthelimitofsensitivity,itisclearthatall
ofthegrayscaleinformationmustbeused.Likewise,weknewwehad
togobeyondanidealizedmodelofimageformationthatconsidersthe
pixels to be point-wise samples of the image; since we were looking
for changes to the image that arise with landmark displacements of
asmallfractionofapixelwidth,thedetailsofthephotosensitivearea
within each pixel were going to play a role. Finally, rather than fo-
cusingontheperformanceofaparticularalgorithm,itseemedbetter
to pursue the Cramér–Rao lower bound, and thereby determine an
algorithm-independent answer to the question. There was, after all,
asheercuriositytoknowwhetherpart-per-100,000accuracyisreally
possibleforclose-rangephotogrammetrywithdigitalimages.
In a convergence of necessity and opportunity, it turns out that
considering a richer model of the image formation process is itself
instrumental in making the calculation of the uncertainty tractable.
The smoothing introduced into the image by diffraction and other
sources has been neglected in some past investigations, which have
viii Preface
idealized the digital image as point-wise samples from a discontin-
uousdescription of theimage. Far frombeing an unwanted compli-
cation, the smoothing makes the calculations feasible. If the image
werediscontinuous,wewouldhavebeenobligedtorepresentitwith
asmoothedapproximationinordertocalculatetheCramér–Raolower
bound.
WiththeCramér–Raoboundinhand,itispossibletodeterminethe
gapbetweentheperformanceofwell-knownalgorithmsforlandmark
locationandthetheoreticallimit,andtodevisenewalgorithmsthat
performnearthelimit.
Inresponsetothequestionofwhetherpart-per-100,000measure-
mentispossiblefromdigitalimages,thereaderisinvitedtoturnthe
pageandjoinusinexploringthelimitstoprecisionlandmarklocation.
Contents
1 Introduction .......................................... 1
1.1 PriorArt ......................................... 5
1.2 ModelingImageFormation......................... 11
1.3 MathematicalSymbolsandNomenclature............ 15
1.3.1 CoordinateSystems ......................... 15
1.3.2 OriginoftheCoordinateSystem.............. 16
1.3.3 ImageFormation ........................... 16
1.3.4 EstimationBasics........................... 18
1.3.5 Estimators ................................. 19
1.4 ContentOrganization.............................. 19
2 PhysicsofDigitalImageFormation ...................... 21
2.1 ImageFormationandLandmarkLocationUncertainty. 28
2.1.1 SceneProperties............................ 28
2.1.2 LandmarkGeometry........................ 29
2.1.3 OpticsSystem .............................. 30
2.1.4 ImagerSystem ............................. 34
2.2 SpatialandIntensityQuantizationandLocales........ 40
2.3 IllustrativeExample ............................... 43
3 AnalyticFrameworkforLandmarkLocationUncertainty ... 45
3.1 Cramér–RaoLowerBound ......................... 45
3.1.1 AnalyticFramework
forCramér–RaoLowerBound................ 46
3.1.2 CRLBConfidenceInterval ................... 49
3.2 UncertaintyofPracticalEstimators.................. 50
3.2.1 AnalyticFrameworkforPracticalEstimators... 51
3.2.2 LandmarkLocationEstimator
ConfidenceInterval ......................... 54
3.3 Discussion ....................................... 56
4 Model-basedLandmarkLocationEstimators.............. 57
4.1 EllipsoidalContourLandmarkLocationEstimator .... 58
4.2 ButterworthTepuyLandmarkLocationEstimator ..... 60
4.3 Discussion ....................................... 63
x Contents
5 Two-dimensionalNoncollocatedNumericalIntegration .... 65
5.1 NoncollocatedSimpsonRule:1-D ................... 66
5.2 NoncollocatedSimpsonRule:2-D ................... 70
6 ComputationalTools ................................... 79
6.1 EyeEntity......................................... 79
6.2 EyeQsandEyeRasterQs ............................ 82
6.3 EyeQiandEyeRasterQi............................. 84
6.4 EyeT............................................. 84
6.5 EyeCI ............................................ 85
7 ExperimentalValidation ................................ 87
7.1 ExperimentDesignandSetup....................... 87
7.2 ExperimentalArtworkandMeasuringLandmark
LocationAccuracy................................. 89
7.3 CameraCalibration................................ 94
7.4 ImagerNoiseCharacterization...................... 96
7.5 ExperimentalTool................................. 97
7.6 ExperimentalResults .............................. 99
8 StudiesofLandmarkLocationUncertainty................ 103
8.1 TheoreticalandExperimentalDetermination
ofLandmarkLocationUncertainty .................. 104
8.2 StudyofEffectsofImagerNoise..................... 109
8.3 StudyoftheEffectsofSmoothingRadius
onLandmarkLocationUncertainty.................. 110
8.4 StudyoftheEffectsofLuminosityDynamicRange .... 111
8.5 StudyoftheEffectsofLandmarkSize................ 112
8.6 StudyoftheEffectsofLandmarkTilt ................ 113
8.7 StudyoftheEffectsofthePixelSensitiveArea
andAspectRatio .................................. 114
8.8 StudyoftheEffectsofNonuniformIllumination
onLandmarkLocationUncertainty.................. 116
8.9 StudyoftheEffectsofAmplitudeQuantization........ 117
9 Conclusions ........................................... 121
AppendixA
ListofSymbols ........................................ 123
AppendixB
Glossary .............................................. 125
AppendixC
ErrorEstimateoftheNoncollocated2-DSimpsonRule ..... 129
Contents xi
ColorSection ............................................. 145
References................................................ 155
Index .................................................... 159
1 Introduction
Many applications in machine vision and photogrammetry involve taking mea-
surements from images. Examples of image metrology applications include, in
medicine:image-guidedsurgeryandmultimodeimaging;inrobotics:calibration,
objecttracking,andmobilerobotnavigation;inindustrialautomation:component
alignment, for example for electronic assembly, and reading 2-Dbar codes; and
indynamictesting:measurementsfromhigh-speedimages.Intheseapplications,
landmarksaredetectedandcomputeralgorithmsareusedtodeterminetheirlo-
cationintheimage.Whenlandmarksarelocatedthereis,ofcourse,adegreeof
uncertaintyinthemeasurement.Thisuncertaintyisthesubjectofthiswork.
Examples of landmarks used for metrology are shown in Figures 1.1–1.4. In
Figure 1.1, we see a standard artificial landmark on the head of the crash test
dummy.Quadraturelandmarkssuchasthisonearerecordedinhigh-speedimages
duringtests,andbylocatingthelandmarks,measurementsofmotionscanbetaken
fromtheimages.Inanotherapplication,landmarkssuchasthoseseeninFigure1.2
aresometimesimplantedformedicalimagingpriortosurgery.Fiducialmarksare
landmarks used for registration. This and other terms are defined in a glossary
provided in Appendix B. Amongst other uses, these fiducial marks in medical
imagesandassociatedimage-basedmeasurementtoolscanpermitthesurgeonto
Figure1.1.Crashtestdummiescarryartificiallandmarkstoimprovetheaccuracyofmotionmeasurementsfromimages
(PhotocourtesyofNASA)