AN IMPROVED ALGORITHM FOR DPIV CORRELATION ANALYSIS

6Available online at www.sciencedirect.comScienceDirecttID)Journal of HydrodynamicsBESer.B, 2007,19(1):62-67sdlj.chinajournal.net.cnAN IMPROVED ALGORITHM FOR DPIV CORRELATION ANALYSIS'WU Long -huaCollege of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China,Email: jxbywlh2000@ yahoo.com.cn(Received September 27, 2005; Revised March 8, 2006)ABSTRACT: In a Digital Particle Image Velocimetry (DPIV)[12-14], capacity of resolving the directional uncertaintysystem, the correlation of digital images is normally used toproblem and inclusion of extensive areas for dynamicacquire the displacement information of particles and givemeasurement. Most PIV systems involve numeroushigh-density images (N,> 7 )5, and the amount ofcorrelation algorithm directly affect the validity of the analysisresult. In this article, an improved algorithm for the correlationdata to be processed to acquire the flow information isanalysis was proposed which could be used to optimize theenormous. The efficiency of the algorithm is thereforeselection/determination of the correlation window, analysis areaa crucial issue in the correlation analysis, that is, it isand search path. This algorithm not only reduces largely thenecessary to obtain accurate and reliable resultamount of calculation, but also improves effectively thethrough minimum amount of calculation.accuracy and reliability of the correlation analysis. ThThe general procedure of the correlation analysisalgorithm was demonstrated to be accurate and efficient in theis to select an area (interrogation window) in themeasurement of the velocity field in a flocculation pool.source image and then search for the most matchedKEYWORDS: Digital Particle Image Velocimetry (DPIV),area in the objective image. Because this search iscarried out over the entire objective image, thecorrelation analysis, improved algorithminvolvedcomputationintensiveandtime-consuming. Furthermore, it can lead to mismatch,1. INTRODUCTIONand affect the accuracy and reliability of the results. InThe Particle Image velocimetry (PIV) is a modernthis article, the correlation analysis algorithm forflow field measurement technique, which is based ondetermining the interrogation window， correlationimage processing and signal analysis, and has beenanalysis area and search path of correlation isundergoing continuous development since 1970s. Thisoptimized. The calculation can be reduced greatly andtechnique has become an important and commonlythe accuracy and reliability of the analysis result canused method in flow measurements 0. For example,be improveda large number of experiments relevant to multi-phaseflowlt.8，hydrodynamics', vortex dynamicsho andPIVACQUIREMENTMOTIONinstrumentations .The key of the PIV system is to .INFORMATIONFROMDIGITALPARTICLE IMAGEacquire the information about particle displacement.V arious methods have been developed for this2.1 Principle of PIVAs shown in Fig.1， the DPIV measurementpurpose，including the Fourier transformation, thdirect spatial correlation, the statistic methods for theobtains the particle velocity through measuring thedistance of particle images,etc. Spatialdisplacement ^X and OY respectively in the Xcross-correlation is often preferred for its accuracynd Y directions from consecutive particle images.* Biography: WU Long-hua (1974-),Male, Ph. D., Lecturer中国煤化工MHCNMH G.The displacement must be so small thatNXanddiscrete form as follows [51:△tAYrepresent the velocity components U andR(m,n)=55f(x+m,y+n)f&(x,y) (2)x=0y=0V approximately. That is to say, the trajectoryapproximately a straight line (a linear approximation)whereand the velocity along the trajectory is approximatelym=0,1,2,3,,M-1，n=0,2,3,.,N-1constant. These conditions can be satisfied, when thetime Ot is as small as the extent of the Taylordifferential scale of the accuracy constrains theEquation (2) is processed over the whole field ofq[2,3,6]Lagrange velocity fieldimage f(x, y), as shown in Fig.2.Time TPosition of Particle A (X2,X2)Image2Time 1f(m,n)1YPosition of Paricle A(0,YI)●Image;S(m.n)1/=lim2:-直y- limnImage .“n 4-11:-1DisplacementFig. 1 Schematic diagram of DPIVFig. 2 Schematic diagram of correlation analysis2.2 Principle of the correlation analysis algorithm .The DPIV obtains the displacement of the pairedparticles respectively in source and objective imagesIn f(x,y), when different coordinate (m,n)through image processing. The magnitude anare given, a series of R can be obtained from Eq. (2).direction of the velocity can then be estimated. In theReaching the maximum of R indicates thatdigital image processing, the similarity of two givenfunction is measured by the correlation functionsf(x,y) and f2(x,y)re the most matched.Thus, the velocity can be given as [3.4.6!:fc(u,)= f(x,y)_fc(x,y)=△S (m,n )V=lim(3)f””. f(x,y)f2(x+u,y+ v)drdy(1)When fc(u,v) reaches its maximum， f(x,y)where AS=√m2 +n2.and f2 (x, y )have the maximal similarity.3. OPTIMIZATION OF THE CORRELATIONANALYSIS ALGORITHMIn image processing, correlation analysis is mostlyIt can be seen from the principle of correlationused for matching models and prototypes. A digitalimage f(x,y) with a magnitude of M xN isanalysis that to set the size of interrogation window iscrucial for the analysis. It affects directly the accuracygiven, and an area contained within the image shouldand reliability of the results. On the other hand, thebe found to be most similar to the digital imagesetting of the area and search path will affect thef2(x,y) with the magnitude of JxK (J 7 "5. Itwindow in the source image through adjusting thecenter position of the matched window in theorder to acquire sufficient data and to increase theobjectiveimage.correlation coefficientsimage density of particle pairs, as many as possiblecorresponding to every center position are thenparticle images should be included in the interrogationcalculated. TH中国煤化工correlationwindow. The particles are uniformly distributed in thecoefficients iIYHthe mostflow field, and all particle pairs in the interrogationmatched positilCN MH Gon with the.65maximum coefficient as the most matched position 20coefficient C2 and its relative coordinates (m2,n2 ).In the objective image, the center position of matchedwindow is adjusted row by row and column by(4) Compare C with C2, if C≥Cz, thencolumn. The correlation coefficients are calculatedsearch is terminated and take (m,n) as the mostand the maximum value is searched for over the wholeimage. As was discussed above， the work ofcorrelative matched point, otherwise, let C = C2,correlation analysis is intensive. Furthermore, becausem=m2，η=n2 and return to Steps 3 and 4the background noise and other noise inevitably existin the sampled image, the possibility of mismatchcirculation until the most correlative matched point isincreases. This will affect the accuracy and reliabilityobtained.of the analysis. If the extent of the search field can beBy doing so, it is not necessary to search over thelimited, the effect of noise on the correlation analysis whole area. After the most correlative matched pointwill decrease, and the analysis rliability will be is obtained, the search can be terminated. By contrastimproved.with other methods, the work and consumed time ofFrom Fig.3, the maximum particle displacementanalysis are greatly reduced and the efficiency isin the sample window must not be beyond a third ofevidently improved.sample window' S size. Then， the most matchedposition of the sample window in the objective imagewill not be beyond the extent of the sample window.4. EXPERIMENTTherefore, by controlling the extent of the correlation4.1 Experimental set-upmatch, the work of the correlation analysis can beFlocculation is a crucial process in waterreduced, and thus the measurement accuracy will betreatment. In the past, because of the limitation ofexperimental methods and measurement apparatus,Another issue is the correlation search path. Itthe complex flow structure during the flocculationtraditional correlation analysis algorithms, the field isprocess cannot be explicitly observed, especially in asearched row-by-row and column-by-column， anflocculation pool with a areciprocating clapboard.hence the work of calculation is enormous. In theThrough the DPIV technology, the full flow field canfollowing，a new search path based on thebe simultaneously measured (ie,the temporallycharacteristics of fluid flow is presented.dynamic and spatially variable flow velocity can be(1) Given (m,n) as the coordinate of thobtained) and the reliability of the data can beimproved with the non-intrusive measurement.matched window's center relative toO，the matchedwindow's center moves along the path as shown in Fig.4Monitol Computer-Grab card|CTDOptics system>[- Argonion Ilaser__Flocculatc poolFig.4 Improved search paths of correlationFig. 5 Schematic ilustration of the experimental set-up(2) Calculate the correlation coefficient at everyAn argon-ion laser is used as the light source.position，search until the number of circulationThe laser beam becomes a light sheet through the lightreaches N,determine and record the maximalsystem and is shed through the water studied in watercorrelationcoefficientCand its relativetank. A CCD camera takes photographs of the flowfield from the direction of 90° to the source lightcoordinates(m,n). N, is determined by velocity.sheet. Sampling中国煤化王the prticles(3) Then continue the search for other N, times,used in the exp,CG-50 (0.5determine and record the maximal correlativeμm-5 μ m)MHCNMHGsetothatof.6water. When the fluid velocity is greater than 0.05 m/s,the particles can track flow well and are uniformlydistributed in water. The experimental set-up is shownin Fig.5. The discharge flow rate is Q = 512 l/h.十.Depositing tarkImportFig.8 Correlation analyses resultFrom Fig.9, it can be seen that if the size of theFig. 6 Schematic diagram of reciprocating clapboard flocculatepoolwindow is too large, wrong particles can possibly betaken as the particle required for match, i.e， a .In a usual flocculation pool with a reciprocatingmis-judgement/mismatch. On the other hand, if theclapboard, the cross-section of the clapboard iswindow is too large， single vector cannot fullrectangle and the turning corner of gallery has a rightdescribe the flow condition of such a large area. If theangle, as shown in Fig.6. The flow field around awindow is too small, there are too few particlesgallery head of the flocculation pool were focused indescribing the flow information in the window. Thisthe investigation 4.will also lead to misjudgement as the conditions forthe correlation analysis are not satisfied. When thesize of window is S= 31x 31, the result of correlationanalysis is the best. This has further confirmed thereliability of the principle Eq. (9) for setting thewindow.0.8.6g0.440.0L -Fig.7 Original particle imageN/pixel4.2 Results and discussionFig. 9 Curves of interrogation window versusFigure 7 is the particle image with the waterdepth h = 0.062m. The largest particle displacement inThe application of the improved algorithm to themost areas is 10 pixels. According to Eq. (9), the sizemeasurement of the flow field in the flocculation poolof the interrogation window for these areas is 30x 30demonstrated that it has improved the efficiency of thepixels, which was adopted in the application as shownanalysis by more than 95%. Compared with previousin Fig.8. Figure 9 indicates the relation curve of themethods, this algorithm also improved the accuracycorrelation window size versus the possibility oand reliability of the results.mismatch when different interrogation windows areadopted in a high-velocity area. The possibility ofmismatch is defined as the ratioof Sm to S , where5. CONCLUSIONS,，is the number of vectors which infracted the fluidIn a digital particle image velocimetry system, theacquirement of the particle displacement informationcontinuity equation, and S is the total number ofis a key issue. 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