13 Pages
English

Noname manuscript No will be inserted by the editor

-

Gain access to the library to view online
Learn more

Description

Noname manuscript No. (will be inserted by the editor) FOLKI-SPIV: a new, ultra-fast approach for Stereo PIV B. Leclaire · Y. Le Sant · S. Davoust · F. Champagnat · G. Le Besnerais Received: date / Accepted: date Abstract We propose a new paradigm for Stereo Par- ticle Image Velocimetry (S-PIV), in which the three- component (3C) displacement vector is estimated di- rectly in one single step, instead of the traditional S- PIV method in which proceed in two steps: (i) separate cross-correlation of the images of the two cameras, and (ii) stereo reconstruction. In our algorithm, folki-spiv, we search for the 3C displacement of particles in an in- terrogation window defined in the laser sheet plane and formulate a non linear least-squares criterion involving all warped images, from the two cameras at the two time instants. Optimization is done by an iterative de- scent approach originally proposed by Lucas-Kanade in computer vision, but modified so as to produce dense, oversampled vector fields with very limited comput- ing cost. Validation tests show that, depending on the cases, folki-spiv's approach has a similar or increased accuracy compared to state-of-the-art traditional meth- ods relying on the separate two-component (2C) vector calculation followed by a stereo reconstruction, whereas it does not involve any vector filtering or rejection at any stage of the algorithm.

  • numerical al- gorithm

  • folki-spiv

  • linear systems

  • piv

  • iw grid

  • squares criterion

  • linear least-squares


Subjects

Informations

Published by
Reads 10
Language English
Document size 2 MB
NonamemanuscriptNo.(willbeinsertedbytheeditor)FOLKI-SPIV:anew,ultra-fastapproachforStereoPIVB.LeclaireY.LeSantS.DavoustF.ChampagnatG.LeBesneraisReceived:date/Accepted:dateAbstractWeproposeanewparadigmforStereoPar-ticleImageVelocimetry(S-PIV),inwhichthethree-component(3C)displacementvectorisestimateddi-rectlyinonesinglestep,insteadofthetraditionalS-PIVmethodinwhichproceedintwosteps:(i)separatecross-correlationoftheimagesofthetwocameras,and(ii)stereoreconstruction.Inouralgorithm,folki-spiv,wesearchforthe3Cdisplacementofparticlesinanin-terrogationwindowdefinedinthelasersheetplaneandformulateanonlinearleast-squarescriterioninvolvingallwarpedimages,fromthetwocamerasatthetwotimeinstants.Optimizationisdonebyaniterativede-scentapproachoriginallyproposedbyLucas-Kanadeincomputervision,butmodifiedsoastoproducedense,oversampledvectorfieldswithverylimitedcomput-ingcost.Validationtestsshowthat,dependingonthecases,folki-spiv’sapproachhasasimilarorincreasedaccuracycomparedtostate-of-the-arttraditionalmeth-odsrelyingontheseparatetwo-component(2C)vectorcalculationfollowedbyastereoreconstruction,whereasitdoesnotinvolveanyvectorfilteringorrejectionatanystageofthealgorithm.Gainsareobtainedinpar-ticularinflowzoneswithimportantgradients.Further-more,folki-spiv’salgorithmcanbeparallelizedinanearlyoptimalway.ThisfeaturehasallowedtofullyimplementitonaGPU.Thetypicalprocessingtimetocomputedensevectorfieldsfor1mega-pixelS-PIVimagesislessthan0.2s,whichprovidesagainofoneB.Leclaire,Y.LeSantandS.DavoustONERA/DAFE,8ruedesVertugadins,92190Meudon,FranceE-mail:benjamin.leclaire@onera.frF.ChampagnatandG.LeBesneraisONERA/DTIM,chemindelaHuniere,FR-91761Palaiseau,Franceortwoordersofmagnitudecomparedtoadvancedcon-ventionalS-PIVmethods.KeywordsStereoPIVPIValgorithm1IntroductionThepresentkeyideaofS-PIVistoseparatelyprocess2Cvectorsfromtwocamerasviewingalasersheetwithdifferentincidenceangles,andthenrecombinetheminastereoreconstructionsteptoformthe3Cvec-tors(Prasad,2000).Toourknowledge,allalgorithmstodaterelyonthisprinciple,thoughindifferentforms(i.e.imagemapping,vectorwarping,orSoloff’smethod,seeStanislasetal,2008).Thismotionextractionissimpleandenablesadirecttransferofimprovementsfromthe2Ctothe3Cframework,forinstanceregard-ingthecross-correlationalgorithmsorthesubpixelin-terrogation.However,itdoesnotexploitoptimallyalltheavailableinformation,thatis,bothcameraimagesandthegeometricalconfiguration,sincethecompatibil-itybetweenthefinal3Cvectorsandtheintermediate2Cvectorsisonlyanaposterioridiagnosistool(theso-called“stereoreconstructionerror”)andnotafirmconstraint.Wehereproposeanewmethodwhichover-comesthisproblembyseekingdirectlythe3Cvectorfrombothimagesinonestep.Thisismadepossiblebydefininganonlinearleastsquarescriteriondependingonthe3Cdisplacementinagiveninterrogationwin-dow(IW),thenbyiterativeminimizationofthiscri-terioninsteadofdirectcorrelation.Theresultingalgo-rithm,folki-spiv(FrenchacronymforIterativeLucas-KanadeOpticalFlow-StereoPIV)isbuiltsoastoyielddensefields,i.e.one3Cvectorpergridpointonthelasersheetplane(LSP).Aswillbeexplainedinthear-ticle,andasisusuallydoneinS-PIV,thespacingofthis