Sesors 0 694-709; doi:0.3390/s09694 Aricle OPEN ACCESS sesors SSN 44-80 www.mdpi.com/joural/sesors Opimal Filer Esimaio for Lucas-Kaade Opical Flow Nusra Sharmi ad Remus Brad * Compuer Sciece Deparme Lucia Blaga Uiersi of Sibiu B-dul Vicoriei 0 55004 Sibiu Romaia; E-Mail: usra_ik@ahoo.com * Auhor o whom correspodece should be addressed; E-Mail: remus.brad@ulbsibiu.ro; Tel.: +40-06-9-606; Fa: +40-06-9-049. Receied: 7 Jue 0; i reised form: 3 Sepember 0 / Acceped: 4 Sepember 0 / Published: 7 Sepember 0 Absrac: Opical flow algorihms offer a wa o esimae moio from a sequece of images. The compuaio of opical flow plas a ke-role i seeral compuer isio applicaios icludig moio deecio ad segmeaio frame ierpolaio hree-dimesioal scee recosrucio robo aigaio ad ideo compressio. he case of gradie based opical flow implemeaio he pre-filerig sep plas a ial role o ol for accurae compuaio of opical flow bu also for he improeme of performace. Geerall i opical flow compuaio filerig is used a he iiial leel o origial ipu images ad aferwards he images are resized. his paper we propose a image filerig approach as a pre-processig sep for he Lucas-Kaade pramidal opical flow algorihm. Based o a sud of differe pes of filerig mehods ad applied o he eraie Refied Lucas-Kaade we hae cocluded o he bes filerig pracice. As he Gaussia smoohig filer was seleced a empirical approach for he Gaussia ariace esimaio was iroduced. Tesed o he Middlebur image sequeces a correlaio bewee he image iesi alue ad he sadard deiaio alue of he Gaussia fucio was esablished. Fiall we hae foud ha our selecio mehod offers a beer performace for he Lucas-Kaade opical flow algorihm. Kewords: opical flow; Lucas-Kaade; Gaussia filerig; opimal filerig
Sesors 0 695. roducio Ulike he processig of saic images much broader iformaio ca be eraced from ime arig image sequeces his beig oe of he primar fucios of a compuer isio ssem. Obaiig moio iformaio is a challegig ask for machies howeer seeral echiques hae bee deeloped i order o obai he requesed moio field. B defiiio he opical flow is he paer of appare moio of objecs surfaces ad edges i a isual scee caused b he relaie moio bewee he obserer ad he scee. 98 wo differeial-based opical flow algorihms were proposed ow cosidered as classics: oe b Hor ad Schuck [] ad he oher b Lucas ad Kaade []. Followig Hor s defiiio he moio field is he D projecio of he 3D moio of surfaces i he world whereas he opical flow is he appare moio of he brighess paers i he image. O he oher had he Lucas-Kaade approach assumes ha he flow is esseiall cosa i a local eighborhood of he piel uder cosideraio ad soles he basic opical flow equaios for all he piels i ha eighborhood b he leas squares crierio. Ma differe opical flow algorihms hae bee deeloped sice 98 icludig eesios ad modificaios of he Hor-Schuck ad Lucas-Kaade approaches. Black ad Aada [3] preseed a robus esimaio framework o deal wih such ouliers bu did o aemp o model he rue saisics of brighess cosac errors ad flow deriaies. While iroducig differe opical flow mehods i was also ecessar o ealuae he proposed mehods. Barro Flee ad Beauchemi [4] proided a performace aalsis of a umber of opical flow echiques which emphasizes o he accurac ad desi of measuremes. 000 Chrismas [5] iroduced a filerig requireme for he compuaio of gradie-based opical flow. Also differe auhors recommeded he use of a filerig mehod such as Flee ad Lagle [6] ad Xiao e al. [7]. mos cases he auhors emploed oe filerig mehod i he ealuaio of opical flow. [7] a muli-cue drie adapie bilaeral filer was proposed i order o regularize he flow compuaio which was able o achiee a smooh opical flow field wih highl desirable moio discoiuiies. Accordig o Flee e al. [6] applig a simple recursie filer is ecessar o achiee emporal smoohig ad o compue he D flow from compoe eloci cosrais usig a spaio-emporal leas square miimizaio. Neerheless he imporace of filerig echiques i obaiig a accurae opical flow is emphasized i [8]. The desig of opimal spaio-emporal filers especiall he oes proposed b Simocelli [9] is eesiel preseed i [0] alog wih he use of D Gaussia as pre-processig. Ol wo alues for he Gaussia sadard deiaio hae bee iesigaed as he combiaio wih oher 3D filers proided a improeme of opical flow deecio. The same approach of combiig he spaio-emporal filers of Baro ad Simocelli ad opimal i he aim of reducig he moio esimaio error is preseed b Elad e al. i []. order o measure he coceraio field of a ijeced gaseous fuel ffa e al. [] emplo a pramidal Lucas-Kaade flow deermiaio i cojucio wih a 5 5 kerel Gaussia filer. his paper we focused o improig he accurac of opical flow esimaio b usig he appropriae filerig mehod. As image filerig is esseial i ma applicaios icludig smoohig oise remoal or edge deecio i he case of opical flow we hae iesigaed he filerig echique as a required preprocessig sep. Also i Secio 3 we hae aalzed differe filerig
Sesors 0 696 mehods i order o selec he mos suiable oe. Secio 4 preses a oel mehod for he selecio of he appropriae Gaussia filer parameer as discussed ad sumarized i Secio 5.. The Lukas-Kaade Opical Flow ad Coarse-o-Fie Approach We focused our iesigaio o he Lucas-Kaade opical flow deermiaio. This gradie-based approach uses he cosrai of piel iesiies cosac: d d d The opical flow cosrai equaio deried from he Talor epasio of Equaio was iroduced b Hor ad Schuk i []. Haig wo ukow ariables i oe equaio i gies he aperure problem: 0 where ad deoe he deriaies of he image fucio wih respec o ad see Figure. The ecor V = defies he eloci ecor i ad direcio. Figure. Opical flow cosrai lie. 0 This problem cao be soled as here are wo ukows i oe equaio bu if a small regio is supposed o hae he same eloci he problem has a soluio. Thus V ca be foud a he iersecio of he Hor-Schuk cosrais for each piel. f we cosider ol wo piels we obai oe iersecio poi as i Figure. Accordig o Lucas-Kaade usuall a regio of seeral piels is cosidered haig he same eloci. The equaios ssem is ow oer deermied. Therefore he leas squared error soluio is supposed o gie a good esimaio of he opic flow alue for a piel as depiced i Figure b.
Sesors 0 697 Figure. ersecio of a wo opical flow ad b seeral opical flow cosrai lies. a b The opical flow equaio is assumed o be used for all piels wihi a widow ceered o piel p. Eplicil he local flow ecor mus saisf he opical flow cosrai for a regio of piels wih he same eloci epressed b: 3 The equaio ssem 3 ca be rewrie usig mari-ecor oaio: b A 4 This ssem has more equaios ha ukows ad hus i is usuall oer-deermied. The Lucas-Kaade mehod obais a compromise soluio usig he leas square echique. cosequece i soles he ssem: b A A A or b A A A T T T T 5 The Lucas-Kaade approach is a local opimizaio problem ha cao perform properl if he objec moemes are oo large. As he gradie iformaio is obaied b eighborig piels he real objec moio cao eed beod he cosidered regio. Also he local eighborhood ake io
Sesors 0 698 accou for he leas squares approach is fiie ad here are few chaces o correcl deermie large moemes. Therefore i is commo o use a pramidal implemeaio. The ipu images are resized o a lower resoluio firs b filerig wih a low pass filer ad he subsampled b a facor of echique called coarse-o-fie approach as show i Figure 3. The compuaio of he opical flow is sared wih he lowes resoluio images a he highes pramidal leel. The resul is passed he o he higher resoluio leel as a iiial esimae. Ruig he algorihm o higher resoluios will cause higher accurac for he flow field. Figure 3. Coarse-o-fie opical flow esimaio. Bougue describes i [3] a ieraie implemeaio of he Lucas-Kaade mehod usig a Gaussia pramid. The eraie Lucas-Kaade algorihm requires a esimae of he eloci for eer piel usig he classical algorihm. The b meas of a warpig echique he esimaed flow will be warped o he image ad he process is repeaed uil coergece. 3. A Empirical Mehod for Opimal Filer Selecio his secio we prese ad discuss he resuls of our iesigaio. We hae eamied he performace of ieraie Lucas-Kaade pramidal opical flow algorihm ogeher wih differe filerig echiques usig well-kow image sequeces proided wih groud ruh opical flow. The eperimeal were performed o a MATLAB R00 plaform usig he sadard aailable oolbo fucios. 3.. The Coe of Ealuaio he aim of eperimeal ealuaio we hae emploed he Middlebur daase [4] which proides he groud ruh. The esig se preses a arie of sequeces icludig hidde eure realisic ad comple scees ad o-rigid moio. For fair comparisos we hae used gra-scale images wo frame sequece ad he brighess cosac assumpio. Three daa ses such as Dimerodo RubberWhale ad Hdragea coais real world images wih comple occlusios
Sesors 0 699 while sheic compuer geeraed graphics are coaied i four ses amed Groe Groe3 Urba ad Urba 3 [5]. The las se called Veus coais sereo images. We hae measured he performace of he esimaed opical flow usig boh aerage agular error AAE ad aerage edpoi error AEE. The firs error meric is he agle differece bewee he correc ad esimaed flow ecors defied b: AAE cos cˆ eˆ where ĉ is he ormalized correc moio ecor ad ê is he ormalized esimae opical flow ecor. We hae also ealuaed he resuls b meas of a absolue error he flow edpoi error EE defied b: 6 AEE u u GT GT 7 where u is he esimaed flow ad u GT GT is he groud ruh opical flow. A he er firs sage of our ealuaio we hae used he Pramidal eraie Lucas-Kaade algorihm wih hree pramidal leels combied wih differe filerig echiques o he eigh daa ses of he Middlebur bechmark. For he preprocessig sep of he opical flow esimaio eigh differe filerig echiques were emploed amel he Gaussia Media Mea High Boos Laplacia LOG Bilaeral ad Adapie Noise Remoal filerig. Bilaeral filerig is a oliear filerig mehod firs proposed b Tomasi e al. [6]. Alhough here are arious applicaios as repored b Paris e al. [7] ad Elad [8] our idea was o smooh images while preserig heir edges. The effecs of seeral smoohig filers ogheer wih he process of opimal parameers selecio were preseed b Malik e al. i [9]. he case of he Gaussia filer a sadard deiaio σ = was used he media filer had a 3 3 kerel he LOG filer had a size of 5 5 ad sadard deiaio σ = 0.5. The Mea filer had a 3 3 size he Laplacia filer a alue of alpha = ad for he case of Bilaeral filer a spaial-domai sadard deiaio of 0. ad iesi-domai sadard deiaio of 0. were emploed. We hae also esed o all image ses he High Boos Filer wih 5 5 mask widow ad all pass facor weigh ad he Adapie Noise Remoal filer ha use eighborhoods of 3 3 o esimae he local image mea ad sadard deiaio. The preious meioed parameers were obaied afer a large se of ess i which he parameers of each filer were aried ad seleced based o he miimum error AAE ad AEE. Thus we hae diided our eperimeal research io hree secios as preseed i he followig subsecios. 3.. Eperimeal Mehodolog A he earlier sage of our iesigaio he goal was o fid he appropriae mehod for filerig i Lucas-Kaade opical flow esimaio. Cosequel we hae diided our eperime io hree pars Figure 4: Filerig applied o ipu images for pramidal opical flow compuaio Filerig applied o all resized ipu images for pramidal opical flow compuaio 3 Compariso bewee case ad
Sesors 0 700 Figure 4. Coarse-o-fie opical flow esimaio a iiial filerig ad b filerig a all leels. Filerig applied o all resized images iial filerig a b 3... Applig Filerig o pu mages a he iial Leel of Opical Flow Compuaio his secio we prese he eperimeal resuls for he pramidal implemeaio of Lucas-Kaade i he case where he filerig echiques hae bee applied before he opical flow esimaio. We hae coceraed our aeio o he Aerage Agular Error ad Aerage Edpoi Error esimaed usig eigh differe filerig echiques. We hae foud ha AAE follows he same paer as AEEs. Figure 5 shows a compariso bewee he AAEs i degrees compued o he Middlebur daa ses while he AEE ariaios are displaed i Figure 6. From he graphics depiced i Figure 6 oe ca obsere he followig: Gaussia Mea Media Adapie Noise Remoal ad Bilaeral filerig resul are comparaiel beer ha he oher oe esed Smoohig filer icreases sigifical he accurac of he deeced flow field Figure 5. Aerage agular errors usig differe filers ol o ipu images.
Sesors 0 70 Figure 6. Aerage edpoi errors usig differe filers ol o ipu images. Therefore selecig he fie bes performig filers we hae aried he filers parameers i order o obai he smalles AEE as lised i Table. Table shows ha he Gaussia Filer has he lowes error bu for differe sadard deiaios depedig o he ipu images. We hae sudied he correlaio bewee he image saisics ad he σ alue i Secio 4. Filer Gaussia smoohig σ Table. Lowes aerage edpoi error for bes performig filers. Hidde eure Sheic Sereo Dimerodo RubberWhale Hdragea Groe3 Groe Urba Urba3 Veus 4.705 σ = 0.6 8.7 σ = 0.3 8.3686 σ = 0.4 8.587 σ = 3.99 σ = 0.7 4.7064 σ = 4.8.539 σ = 3.6 0.7046 σ = 0.3 Mea 5.70 0.43 9.33 8.6578 4.3 6.565 3.789.8439 Media 7.846 0.5369 9.439 9.758 5.896 9.549.5063.983 Adapie Noise Remoal Bilaeral σ = [0. 0.] 5.896 0.4 9.69 9.69 4.39 7.897 4.5003.968 7.4394 0.5945 8.76 0.383 8.3447 9.384.88 4.3764 3... Applig Filerig o All mages for he Pramidal Opical Flow Compuaio he case of he pramidal implemeaio of Lucas-Kaade he ipu images are resized a each leel o a lower resoluio. Aerage agular error ad aerage edpoi error are preseed i Figures 7 ad 8 respeciel.
Sesors 0 70 Figure 7. Aerage agular errors obaied usig differe filers o all resized images. Figure 8. Aerage edpoi errors obaied usig differe filers o all resized images. From he preseed resuls ad graphics we ca coclude ha: Gaussia Mea Media Adapie Noise Remoal ad Bilaeral filers resul are comparaiel beer ha he ohers Smoohig filers performs beer ha sharpeig filers We recommeded ha for he Lucas-Kaade opical flow calculaios i is beer o use smoohig filers order o decide which mehod performs beer we made a checklis ad a aerage rakig of he differe filerig echiques. As a geeral coclusio from he eperimes preseed i Secios 3.. ad 3.. i he case of pramidal Lucas-Kaade opical flow smoohig filers are recommeded as he accurac is improed. order o decide which he bes performig filer is ad whe i has o be applied a compariso has bee carried ou as show i he followig subsecio.
Sesors 0 703 3..3. Compariso of Filerig Mehods As seeral filerig mehods are cosidered a checklis ad a aerage rakig are preseed i Tables ad 3 for selecio of opimum filerig mehod. Table. Compariso bewee filerig mehods a iiial leel ad all leels o pramidal Lucas-Kaade opical flow. Differe filerig echiques Gaussia Smooh Hidde Teure Sheic Sereo Dimerdo RubberWhale Hdragea Groe3 Groe Urba Urba3 Veus Filerig X - - - - - Media Filerig X - - - - LOG filerig - X - - - - - Mea Filerig X - - - - - High Boos Filerig - - - - - X - Laplacia Filerig - X - - - - - Adapie Noise Remoal filerig X - - - - Bilaeral Filerig - - - - - - - - Where recommeded for iiial filerig ad X recommeded for all leels. Filer Table 3. Compariso bewee filerig mehods a iiial leel ad all pramidal leels usig aerage rakig. Filerig applied o ipu images a iiial leel aerage rakig Aerage agular error degrees Aerage edpoi error Filerig applied o all resized images a pramidal leels aerage rakig Aerage agular error degrees Aerage edpoi error Gaussia smooh 9.80985.5683 8.9477 0.9484 Media.765.355.965.30788 LOG 0.6046875.7355 7.969.005838 Mea 9.9558875.705 9.08563 0.947563 High Boos 6.4665.89388 5.97896.90373 Laplacia 0.863375.688675 8.05495.08488 Adapie Noise Remoal 0.96.493 9.64585.035 Bilaeral 3.909975.35365 3.90998.35365 Eamiig he alues obaied i he aboe iesigaio we ca coclude ha: filerig a all pramidal leels is beer ha filerig ol he iiial images amog all filerig mehods he Gaussia filer is opimal for compuig Lucas-Kaade opical flow as error is decreasig As he Gaussia filer performs beer he a oher cosidered filer we hae focused our iesigaio o fidig he sadard deiaio parameer opimum alue ad drawig is depedec
Sesors 0 704 wih error. Values preseed i Figure 9 are for he case of a pramidal Lucas-Kaade opical flow usig Gaussia filer o all resized images. Figure 9. Aerage agular error for differe σ alues. 4. A Noel Mehod for Esimaig he Appropriae Gaussia Filerig Parameer From he graphs i Figure 9 i is clearl show ha he appropriae σ alue aries from image o image bu shows some commo characerisic for he si image ses Dimerodo RubberWhale Hdrage Groe3 ad Groe Veus. The AAE icreases wih he icrease of sadard deiaio as for Urba ad Urba3 image sequeces i has a reerse behaior. Therefore we hae ried o fid he correlaio bewee he image coes ad he σ alue b compuig a geeral measure as he aerage iesi for each image ad for he eire daase. Based o seeral empirical ess ad obseraios we are proposig a algorihm for he esimaio of he opimal filerig parameer: compue he mea iesi from ipu images fid he referece poi of Gaussia fucio usig he alues colleced aboe ake a decisio abou he opimal parameer afer a series of comparisos The mea iesi of he es sequeces was esimaed usig he alues compued for wo of he images ad aerageig of i a he ed. For isace i he case of he Dimerodo image se frame has a aerage image iesi of 0.3564 frame a aerage image iesi of 0.3567 ad he aerage esimaed iesi for he se was 0.3564. Table 4 we hae lised he esimaed aerage iesi alue of he Middlebur daase. Eamiig he plos i Figure 9 we hae oiced he ariaio of he Gaussia fucio alue accordig o sadard deiaio. our iesigaio we hae emploed a Gaussia fucio wih he kerel defied o ksize/ ksize/ wih a sep of -ksize where ksize = 6 σ ad a sadard deiaio of. his case he highes alue of he Gaussia fucio was 0.35 as show i Table 5.
Sesors 0 705 Table 4. Aerage iesi alue of Middlebur daase. mage ses Mea iesi alue Dimerodo 0.3564 RubberWhale 0.55 Hdragea 0.454 Groe3 0.39945 Groe 0.3945 Urba 0.684 Urba3 0.504 Veus 0.39645 Table 5. Large alues of Gauss fucio. 3.83 0.6667 0.5.667.8333 G 0.0044 0.0743 0.394 0.35 0.0995 0.007 Afer he esimaio of aboe meioed alues we hae compared for each image se he referece poi colleced from he Gaussia fucio ad he aerage image iesi. The sadard deiaio alue of he Gaussia filer accordig o he image characerisics was esablished afer performig wo pes of comparisos. he firs case we hae jus checked which alue is greaer ha he oher: f aerage image iesi Highes Gaussia fucio alue The choose sadard deiaio less ha f aerage image iesi < highes Gaussia fucio Value The choose sadard deiaio higher ha Oce compleig his sep for all image ses we hae obaied he resuls i Table 6. The bolded alues are for image iesiies greaer ha he referece poi. Therefore we ca affirm ha if he aerage iesi alue is equal or higher ha he highes Gaussia fucio alue i is recommeded o emplo a sadard deiaio alue of or less ha ad ice ersa. Table 6. Resuls of firs compariso. mage ses Mea iesi alue Dimerodo 0.3564 RubberWhale 0.55 Hdragea 0.454 Groe3 0.39945 Groe 0.3945 Urba 0.684 Urba3 0.504 Veus 0.39645 From Table 6 we hae also oiced ha he mea iesi alue for he si image ses Dimerodo RubberWhale Hdragea Groe3 Groe ad Veus is greaer ha he referece alue. Those are he sequeces for which he AAE icrease wih he icrease of σ alue see Figure 9.
Sesors 0 706 Therefore i has bee show ha if we use small sigma alues he opical flow mehod will proide smaller errors. O he oher had for Urba ad Urba3 he mea iesi alue is less ha he referece poi ad comparig he wo alues we hae obsered ha i is beer o use large σ alues. Based o seeral aalses we hae also suggesed aoher mehod of choosig he sadard deiaio as he raio bewee he cosidered referece poi ad he image mea iesi alue: raio = highes Gaussia fucio alue/mea iesi of ipu images 8 Afer compuig he proposed raio for all he bechmarks he obaied alues are preseed i Table 7. For isace i he case of Urba image se he mea iesi was 0.684 he referece poi had a alue of 0.35 giig a raio of.6. Table 7. Resul for he secod compariso sep. mage ses Raio Dimerodo 0.988 RubberWhale 0.6755 Hdragea 0.8476 Groe3 0.885 Groe 0.895 Urba.638 Urba3.406 Veus 0.888 Eamiig he obaied alue oe ca obsere ha is mea iesi is wo imes lower ha he highes Gaussia alue. Therefore we hae specified ha he σ should be i he rage of [.6 ]. As a geeralizaio he obaied raio should be he lower boud for he opimal Gaussia filer parameer ad he ceilig alue of he raio he upper boud. To cofirm he aboe saeme we hae esed hree sheic ses of images hp://isual.cs.ucl.ac.uk/pubs/algorihmsuiabili/. Table 8 shows he mea iesi alues emploed for he selecio of σ ad Figure 0 he AAE measures for he pramidal L-K opical flow usig Gaussia filerig o all resized ipu images. Table 8. Aerage of image iesi alues. mage ses Mea iesi alue of each image ses Creas 0.4886 Spoza_ 0.33605 Spoaza_ 0.574
Sesors 0 707 Figure 0. Aerage agular error measures of ieraie pramidal L-K opical flow b usig Gaussia Filerig o all resized ipu images. 5. Discussio ad Coclusios his paper we hae preseed a iesigaio o image filerig as a preprocessig leel for he Lucas-Kaade opical flow compuaio framework. We hae cocluded o ol o he fac ha a opimal filerig mus be performed a eer pramidal leel bu also iroduced a oel mehod for accordig he filer o he processed coe. Also from our sud we hae foud ha he Gaussia filer performs cosiderabl beer amog differe oher filers. Geerall i pramidal opical flow compuaio he ipu images are filered ol a he begiig ad a he followig leels he images are beig resized from ha base. Our firs eperime cocered he proper use of filerig o ol a he iiial leel bu subsequel a each pramidal leel. As seeral es sequeces ogeher wih he referece groud ruh were aailable a improeme of he error was obaied. Sice i our eesie research o he subjec we could fid a specificaios regardig he opimal pe of filer we hae cosidered he mos refereced D oes as Gaussia Mea Media Bilaeral Adapie Noise Remoal or he High Boos filer. From he eperimeal resuls we hae cocluded ha he Gaussia filerig is he mos suiable i his regard o he basis of compued aerage agular error ad aerage edpoi error. As he Gaussia filer was he mos appropriae for pre-filerig he ipu images we hae iesigaed he relaio bewee he sadard deiaio alues of he Gaussia fucio ad he image coes. From he ploed resuls we hae obsered ha here is o fied σ alue achieig he lowes error for a ipu sequece. Based o empirical obseraios as he ariaio of error wih sadard deiaio we hae esablished a correlaio. Our oel mehod for selecig he σ alue cosiss i obserig he shape of he Gaussia fucio usig a sadard deiaio of ad eracig he highes alue. Comparig his referece poi wih he image aerage iesi ca gie a idicaio o he suiable alue o be used. Also we hae foud ha he raio bewee he image iesi ad he highes Gaussia alue ca gie a idicaio o he proper σ alue. Fiall we cocluded o he fac ha compuig he filer sadard deiaio from image characerisic offers a more accurae opical flow compuaio.
Sesors 0 708 Refereces. Hor B.; Schuck B. Deermiig opical flow. Arif. ell. 98 7 85 03.. Lucas B.D.; Kaade T. A eraie mage Regisraio Techique wih a Applicaio o Sereo Visio. Proceedigs of he DARPA mage Udersadig Workshop Washigo DC USA April 98; pp. 674 679. 3. Black M.J.; Aada P. The robus esimaio of muliple moios: Parameric ad piecewise-smooh flow fields. Compu. Vis. mage Udersad. 996 63 75 04. 4. Barro J.; Flee D.; Beauchemi S. Performace of opical flow echiques.. J. Compu. Vis. 994 43 77. 5. Chrismas W.J. Filerig requiremes for gradie-based opical flow measureme. EEE Tras. mage Proc. 000 0 87 80. 6. Flee D.J.; Lagle K. Recursie filers for opical flow. EEE Tras. Paer Aal. Mach. ell. 995 6 35 35. 7. Xiao J.; Cheg H.; Sawhe H.; Rao C.; sardi M. Bilaeral Filerig-Based Opical Flow Esimaio wih Occlusio Deecio. Proceedigs of he 9h Europea Coferece o Compuer Visio Graz Ausria Ma 006. 8. Shobha N.; Shakapal S.R.; Kadambi G.R. A performace characerizaio of adaced daa smoohig echiques used for smoohig images i opical flow compuaios.. J. Ad. Compu. Mah. Sci. 0 3 86 93. 9. Simocelli E.P. Desig of Muli-Dimesioal Deriaies Filers. Proceedigs of he 994 EEE eraioal Coferece o mage Processig Ausi TX USA Noember 994. 0. McCarh C.; Bares N. Performace of Temporal Filers for Opical Flow Esimaio i Mobile Robo Corridor Cerig ad Visual Odomer. Proceedigs of he 003 Ausralasia Coferece o Roboics & Auomaio Brisbae Ausralia December 003.. Elad M.; Teo P.; Hel-Or Y. O he desig of opimal filers for gradie-based moio esimaio.. J. Mah. mag. Vis. 005 3 45 365.. ffa E.D.; Aziz A.R.A.; Malik A.S. Coceraio measureme of ijeced gaseous fuel usig quaiaie schliere ad opical omograph. J. Eur. Op. Soc. Rap. Pub. 00 5 009 0035. 3. Bougue J.Y. Pramidal mplemeaio of he Lucas Kaade Feaure Tracker Descripio; Techical Repor for el Corporaio Microsof Research Lab: Saa Clara CA USA 000. 4. Baker S.; Scharsei D.; Lewis J.P.; Roh S.; Black M.J.; Szeliski.R. A Daabase ad Ealuaio Mehodolog for Opical Flow. Proceedigs of he h EEE eraioal Coferece o Compuer Visio CCV 007 Rio de Jaeiro Brazil Ocober 007. 5. Baker S.; Scharsei D.; Lewis J.P.; Roh S.; Black M.J.; Szeliski R. A Daabase ad Ealuaio Mehodolog for Opical Flow.. J. Compu. Vis. 0 9 3. 6. Tomasi C.; Maduchi R. Bilaeral Filerig for Gra ad Color mages. Proceedigs of he Sih eraioal Coferece o Compuer Visio Bomba dia Jauar 998; p. 839. 7. Paris S.; Korprobs P.; Tumbli J.; Durad F. A Gele roducio o Bilaeral Filerig ad s Applicaio. Proceedigs of he Special eres Group o Compuer Graphics ad eracie Techiques Coferece Sa Diego CA USA Augus 007.
Sesors 0 709 8. Elad M. O he origi of he bilaeral filer ad was o improe i. EEE Tras. mage Proc. 00 0 4 5. 9. Malik A.S.; Choi T.S. Cosideraio of illumiaio effecs ad opimizaio of widow size for accurae calculaio of deph map for 3D shape recoer. Paer Recog. 007 40 54 70. 0 b he auhors; licesee MDP Basel Swizerlad. This aricle is a ope access aricle disribued uder he erms ad codiios of he Creaie Commos Aribuio licese hp://creaiecommos.org/liceses/b/3.0/.