Noname manuscript No will be inserted by the editor

Benjamin Leclaire

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

Sujets

• Leclaire
• Optics
• Transform
• Linear system

Informations

• Publié par: pefav
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

NonamemanuscriptNo. (willbeinsertedbytheeditor) FOLKI-SPIV:anew,ultra-fastapproachforStereoPIV B.Leclaire ∙ Y.LeSant ∙ S.Davoust ∙ F.Champagnat ∙ G.LeBesnerais Received:date/Accepted:date AbstractWeproposeanewparadigmforStereoPar- ticleImageVelocimetry(S-PIV),inwhichthethree- component(3C)displacementvectorisestimateddi- rectlyinonesinglestep,insteadofthetraditionalS- PIVmethodinwhichproceedintwosteps:(i)separate cross-correlationoftheimagesofthetwocameras,and (ii)stereoreconstruction.Inouralgorithm, folki-spiv , wesearchforthe3Cdisplacementofparticlesinanin- terrogationwindowdefinedinthelasersheetplaneand formulateanonlinearleast-squarescriterioninvolving allwarpedimages,fromthetwocamerasatthetwo timeinstants.Optimizationisdonebyaniterativede- scentapproachoriginallyproposedbyLucas-Kanadein computervision,butmodifiedsoastoproducedense, oversampledvectorfieldswithverylimitedcomput- ingcost.Validationtestsshowthat,dependingonthe cases, folki-spiv ’sapproachhasasimilarorincreased accuracycomparedtostate-of-the-arttraditionalmeth- odsrelyingontheseparatetwo-component(2C)vector calculationfollowedbyastereoreconstruction,whereas itdoesnotinvolveanyvectorfilteringorrejectionat anystageofthealgorithm.Gainsareobtainedinpar- ticularinflowzoneswithimportantgradients.Further- more, folki-spiv ’salgorithmcanbeparallelizedina nearlyoptimalway.Thisfeaturehasallowedtofully implementitonaGPU.Thetypicalprocessingtime tocomputedensevectorfieldsfor1mega-pixelS-PIV imagesislessthan0.2s,whichprovidesagainofone B.Leclaire,Y.LeSantandS.Davoust ONERA/DAFE,8ruedesVertugadins,92190Meudon,France E-mail:[e-mail] F.ChampagnatandG.LeBesnerais ONERA/DTIM,chemindelaHuniere,FR-91761Palaiseau, France ortwoordersofmagnitudecomparedtoadvancedcon- ventionalS-PIVmethods. KeywordsStereoPIV ∙ PIValgorithm 1Introduction ThepresentkeyideaofS-PIVistoseparatelyprocess 2Cvectorsfromtwocamerasviewingalasersheetwith differentincidenceangles,andthenrecombinethem inastereoreconstructionsteptoformthe3Cvec- tors(Prasad,2000).Toourknowledge,allalgorithmsto daterelyonthisprinciple,thoughindifferentforms(i.e. imagemapping,vectorwarping,orSoloff’smethod, seeStanislasetal,2008).Thismotionextractionis simpleandenablesadirecttransferofimprovements fromthe2Ctothe3Cframework,forinstanceregard- ingthecross-correlationalgorithmsorthesubpixelin- terrogation.However,itdoesnotexploitoptimallyall theavailableinformation,thatis,bothcameraimages andthegeometricalconfiguration,sincethecompatibil- itybetweenthefinal3Cvectorsandtheintermediate 2Cvectorsisonlyanaposterioridiagnosistool(the so-called“stereoreconstructionerror”)andnotafirm constraint.Wehereproposeanewmethodwhichover- comesthisproblembyseekingdirectlythe3Cvector frombothimagesinonestep.Thisismadepossibleby defininganonlinearleastsquarescriteriondepending onthe3Cdisplacementinagiveninterrogationwin- dow(IW),thenbyiterativeminimizationofthiscri- terioninsteadofdirectcorrelation.Theresultingalgo- rithm, folki-spiv (FrenchacronymforIterativeLucas- KanadeOpticalFlow-StereoPIV)isbuiltsoastoyield densefields,i.e.one3Cvectorpergridpointonthe lasersheetplane(LSP).Aswillbeexplainedinthear- ticle,andasisusuallydoneinS-PIV,thespacingofthis