Precision Landmark Location for Machine Vision and Photogrammetry: Finding and Achieving the Maximum Possible Accuracy PDF
Preview Precision Landmark Location for Machine Vision and Photogrammetry: Finding and Achieving the Maximum Possible Accuracy
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 MATLAB®isaregisteredtrademarkofTheMathWorks,Inc.,3AppleHillDrive,Natick, MA01760-2098,USA.http://www.mathworks.com Apartfromanyfairdealingforthepurposesofresearchorprivatestudy,orcriticismor review,aspermittedundertheCopyright,DesignsandPatentsAct1988,thispublication mayonlybereproduced,storedortransmitted,inanyformorbyanymeans,withthe priorpermissioninwritingofthepublishers,orinthecaseofreprographicreproduction inaccordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency.En- quiriesconcerningreproductionoutsidethosetermsshouldbesenttothepublishers. Theuseofregisterednames,trademarks,etc.inthispublicationdoesnotimply,evenin theabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantlawsand regulationsandthereforefreeforgeneraluse. Thepublishermakesnorepresentation,expressorimplied,withregardtotheaccuracyof theinformationcontainedinthisbookandcannotacceptanylegalresponsibilityorlia- bilityforanyerrorsoromissionsthatmaybemade. 987654321 SpringerScience+BusinessMedia springer.com ToAlanAlejandroandNatacha 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 from being 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
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