y+2 vertical position y y+1 existing sample sub-pixel interpolated sample y-1 y-2 y-3 y-4 n field number n-1 n field number n-1

Transcription

1 Anlysis of su-pixel Motion Estimtion E.B. Bellers nd G. de Hn Philips Reserch Lortories, Television Systems Group, Prof. Holstln 4, 5656 AA Eindhoven, The Netherlnds ABSTRACT The use of interpoltion lters in motion estimtor to relize su-pixel shifts, my led to unintentionl preferences for some velocities over other. In this pper we nlize this phenomenon, focussing on the cse of interlced imge dt where the prolem leds to the most pronounced errors. Liner interpoltors, either pplied directly or indirectly using generlized smpling re discussed. The conclusions re pplicle to ny type of motion estimtor. Keywords: Motion Estimtion, Interpoltion, Su-pixel, Generlized Smpling. INTRODUCTION Vrious video processing functions prot from motion nlysis. In predictive coding, motion vectors re used to reduce the temporl redundncies, while in video formt conversion, motion informtion is used to interpolte picture dt t sptio-temporl positions tht where not stored nd/or trnsmitted. Especilly in the ltter cse, true-motion vectors re required. In high qulity pplictions, these motion vectors need to e estimted with su-pixel ccurcy. To this end, we either need to interpolte dt ville only on pixel grid, or we hve to mesure motion over longer temporl intervl nd otin the required ccurcy y division. The second option is not very ttrctive, since vectors in generl will not e constnt over longer temporl intervls, nd temporl delys re costly. Therefore, in this pper we shll concentrte on the use of interpolting lters. In motion estimtor (ME) with video input, interpoltion in the verticl direction, due to interlce (susmpling), is not trivil. The Nyquist criterion is generlly not met, which cuses lis. In the literture, methods hve een proposed tht perform de-interlcing, either prior to motion estimtion, or implicitly while estimting, in order to reduce the impct of lis. An exmple of the rst method is the recursive pproch,,2 while the methods sed on generlized smpling theorem 3,4 provide n exmple of the second clss. (See lso Ref. 5 tht presents n overview of de-interlcing techniques). In either cse, dierent su-pixel motion vector frctions, require dierent lter. This lter is dependent on the su-pixel frction s well s on the interpoltor used. Due to the individul dierences of the su-pixel frction dependent lters, in prticulr dierent mplitude nd/or phse chrcteristics, unintentionl preferences for certin su-pixel frctions my occur. As consequence, inccurte motion vectors results, which led to su-optiml output of the video processing lgorithms tht hope to prot from these motion vectors. This implies tht the demnds for the interpoltor used in motion estimtion my dier from the demnds for the interpoltor used in de-interlcing or frme-rte conversion. Since we hve the ojective to estimte true motion in scene, it is importnt tht the interpoltor used in the ME does not led to preferred vectors. This is severe demnd tht my conict with the demnd to optimlly pproximte the underlying higher resolution imge. To fully prot from su-pixel ccurte motion vectors, su-pixel interpoltion is usully required in oth sptil dimensions. Both seprle nd non-seperle interpoltors cn e used, however, in this pper we restrict the nlysis to the ctegory of seperle interpoltors. Since the sptil su-smpling (interlce) is prolem in the verticl direction only, we put the emphsis of this nlysis on the sptilly one-dimensionl interpoltors. We will consider oth pure sptil nd sptio-temporl (2D) interpoltors. In this pper, we shll nlyze the inherent preferences in the ME s they result from dierent types of liner interpoltors. In Section 2, we present dierent interpoltors used in the experiments. In Section 3, we show the results with these dierent interpoltors, compring them in n experiment nd on sis of their lter chrcteristics. Finlly, we drw our conclusions in Section 4. Other uthor informtion: E.B.: Emil: ellers@ntl.reserch.philips.com; Telephone: ; Fx: ; G.H.: Emil: dehn@ntl.reserch.philips.com; Telephone: ; Fx:

2 y+2 y n- x n field numer verticl position y y+ y y- y-2 y-3 y-4 n- existing smple su-pixel interpolted smple n field numer Figure. Two eld motion estimtion 2. SUB-PIXEL INTERPOLATION FOR ACCURATE TRUE MOTION ESTIMATION Su-pixel interpoltion is needed if the required ccurcy of the motion vector is etter thn pixel distnce, or etter thn (eld) line distnce in the verticl domin. The ME optimizes n error function, (), sed on the dierence etween the su-pixel ccurte motion compensted smple nd the corresponding (non-shifted) smple in the reference imge for which motion vectors re desired. We will distinguish three cses; Motion estimtion sed on two successive elds, Motion estimtion sed on frme (previously explicitly de-interlced eld) nd eld, Motion estimtion sed on three successive elds, pplying generlised smpling for implicit de-interlcing. 2.. Two eld ME The two eld ME ims t estimting the motion etween the current eld nd the previous (or next) eld s shown in gure. To otin integer even nd su-pixel ccurte motion vectors, n idel interpoltor cn reconstruct signls with frequency up to :5f s, with f s the smpling frequency on frme grid. The motion estimtor ims t minimizing F (y; n) F (y C; n ), in which F (y; n) is the current eld t time instnce n t verticl position y, nd C the cndidte motion component. Interpoltion is required if C=2 Z, nd if Cmod2 =. In our experiments, the error function ws dened y: (F (y; n);f(y; n );C;B)= X y2b jf (y; n) F (y C; n )j () with B set of smples. We nlyzed the ehviour of the populr rst-order liner interpoltor, the Ctmull-Rom Cuic 6 nd tht of liner poly-phse lter First-order liner interpoltion An interpoltor tht is often used is the (rst-order) liner interpoltor, dened y: for interpoltion etween F (y; n) nd F (y +2;n). s =( )F (y; n)+f(y +2;n) ( ) (2) If C is limited to 4 pixel ccurcy on frme grid, then jc int(c)j 2f; 8 ; 4 ; 3 8 ; 2 ; 5 8 ; 3 4 ; 8 7 g, with int(p) dened s the integer prt of p. Note tht due to the su-smpling the distnce etween two verticlly neighouring pixels on the eld grid equls 2. The mplitude nd group-dely responses of the (rst-order) one-dimensionl liner lters re shown in gure 2. (Reltive frequency.5 corresponds to hlf the verticl smpling frequency (:5f s )).

3 mplitude responses.5. group dely f / f / Mgnitude f 3/ f 3/ Figure 2. ) Amplitude responses, ) group dely responses of the rst-order liner interpoltor in pixels on the su-smpled grid, with f i the response of impulse response h i =[i; ( i)] If i indictes the su-pixel position etween two existing smples with i, then f i descries the lter chrcteristic, with impulse response h i, used for interpoltion t position i. Since the mplitude response of f=8 equls tht of f7=8, nd f=4 tht of f3=4 nd so on, the frequency responses of f5=8, f3=4 nd f7=8 re not drwn. The group dely responses of f5=8::f7=8 re equl to tht of f3=8; ::; f=8 nd re therefore not plotted seprtely. The frequency response of f is not plotted, since it is trivil. The dshed line in the group-dely responses represents the line with the idel constnt group dely. From these responses it cn e oserved tht oth the mplitude nd the group dely responses re quite dierent for individul lters. The dierence etween the idel nd relized group dely is lso rther lrge Ctmull-Rom Cuic interpoltion The rst-order liner interpoltor with its tringulr shped impulse response is rough pproximtion of the idel interpoltor with the sinc-shped impulse response. The cuic B interpoltor with ell-shped interpoltor wveform lredy pproximtes the sinc wveform of the idel interpoltor etter. The cuic B-spline is widely used for imge interpoltion. Another memer of the cuic interpoltors is the Ctmull-Rom Cuic interpoltor. This interpoltor is found to e superior over the cuic B-spline interpoltor. 6 Its impulse response is dened y: 8< h(k) = : 3 2 jkj3 5 2 jkj2 + ; (jkj ) 2 jkj jkj2 4jkj +2 ; ( < jkj 2) ; (otherwise) with k = the interpoltion position. Figure 3 shows the impulse response of the Ctmull-Rom Cuic interpoltor. The mplitude nd group dely chrcteristics of the Ctmull-Rom cuic interpoltor re plotted in gure 4. The chrcteristics show slightly etter mplitude responses compred to tht of the rst-order liner interpoltion (for very low frequencies, it pproximtes the idel (t) mplitude response etter), nd similr group dely responses Poly-phse lter interpoltion The ojective of interpoltion is to clculte smples on denser smpling grid nd/or phse shifted compred to the current smples. In oth cses, ltering on higher density grid is the common recipe to clculte the desired smples. An eective wy to clculte the smples uses poly-phse lters. A poly-phse lter is smple rte converter tht comines up-smpling, ltering nd down-smpling into one function (see lso gure 5). (3)

4 existing smple interpolted smple position -3/2 -/2 /2 3/2 k Figure 3. Ctmull-Rom cuic interpoltor wveform mplitude responses.5 group dely f / f / Mgnitude.5.4 f 3/ f 3/ Figure 4. ) Amplitude responses, ) group dely responses of the Ctmull-Rom cuic interpoltor smpling frequency f in Kf in Kf in (K/L)f in K poly-phse filtering low pss filtering L Figure 5. Poly-phse ltering comines up smpling, low-pss ltering nd down smpling If we ssume xed up smpling nd down smpling fctors (K nd L), the low pss lter cn e optimized for this setting. Note tht for otining dierent phses of the signl, only the down-smpler selects dierent smples, ut the low-pss lter is not chnged! Since the poly-phse lter descries the complete chin of up-smpling, ltering nd down-smpling, the poly-phse lter chnges with the phse only. Moreover, due to the xed internl low-pss lter, the frequency responses of the derived poly-phse lters eqully mtches the idel frequency response over signicnt prt of the frequency spectrum. In our experiments, we used oth n up-smpling (K) nd down-smpling fctor (L) of 8, nd 48 tps lowpss lter. Consequently, the derived poly-phse lters for the dierent frctions contin 6 tps. The frequency chrcteristics of these lters re shown in gure 6. The mplitude responses, s shown in gure 6, re out similr up to out :5 f s. The group dely chrcteristics lso pproximte up to out :5 f s the idel group dely (dshed line in gure 6). Therefore, no motion preferences re expected to occur up to out :5 f s. Note, however, tht the interpoltion resolution is still limited to interpoltion on the eld grid. Frequencies ove :25 f s cn therefore not correctly e recovered.

5 mplitude responses.5.2 group dely f f f. /4.5 f / f / f 3/ f 3/ Figure 6. ) Amplitude responses, ) group dely responses of the poly-phse lters y+2 y n- x n field numer verticl position y y+ y y- y-2 y-3 y-4 n- n existing smple motion compensted smple su-pixel interpolted smple field numer 2.2. Frme nd eld ME Figure 7. Frme-eld ME The recursive de-interlcer, s mentioned in Ref.,2 is n exmple of de-interlcer using frme (previously de-interlced eld) nd the current eld (see lso gure 7). Motion estimtion sed on the previously de-interlced eld nd the current eld ims t minimizing the dierence F (y; n) F out (y C; n ) with F out the previously de-interlced eld. The error function is ccordingly dened y: (F (y; n);f out (y; n );C;B)= X y2b jf (y; n) F out (y C; n )j (4) In the experiments F out () is perfectly de-interlced eld. Although this is in prctice generlly not possile, it serves s n upperound. As frme insted of eld is ville, interpoltion is only required if C=2 Z. If we im t the sme ccurcy s in the two eld ME, we identify three equidistnt interpolted positions etween the existing pixels. Insted of 8, only 4 lters re required in this cse (for the su-pixel positions,.25,.5 nd.75 pixel). The frequency responses re scled version of the plots in gure 2, 4 nd 6. The responses f=4 nd f=2 correspond to the su-pixel frctions.25 nd.5, respectively. Due to the interpoltion t twice the verticl resolution compred to the eld grid, the frequency xis...25 is scled to...5. All interpoltors prot from the incresed verticl resolution, ut the individul dierences in frequency responses remin.

6 verticl position y y+2 y+ y y- y-2 y-3 existing smple estimted smple from nd MC smple from previous field MC smple from preprevious field y-4 n-2 n- n field numer Figure 8. GST sed ME sptil frequency responses 3 temporl frequency responses f 3/4 2.5 f.8 2 Mgnitude.6 Mgnitude.5 f 3/ Figure 9. ) Sptil frequency response of the GST lters using rst-order liner interpoltor, ) the corresponding temporl frequency response 2.3. Three eld ME sed on generlised smpling The three eld ME sed on the generlized smpling theorem (GST) s found in Ref. 3 nd 4 uses the previous nd preprevious eld to estimte the motion for the current eld (see lso gure 8). The estimtor error function is dened y: (F (y; n);f out (y; n );C;B;p;q)= Py2B jf (y; n) (P l p(l)f (y e (2l +);n ) +P m q(m)f (y 2e 2m; n 2))j (l; m 2 Z) (5) with p(), q() pproprite lters tht compose GST lter depending oth on the motion frction nd the interpoltor used for deriving the coecients, nd e dened s the nerest even integer vlue of the motion component such tht C = e +, with jj < :. We used the erlier mentioned liner interpoltors in determining the lter coecients for p() nd q(). An exmple of the derivtion of the lter coecients is shown in Ref. 7. The frequency responses of the GST lters using rst-order liner interpoltion, Ctmull-Rom cuic interpoltion nd poly-phse ltering interpoltion re shown in gure 9,, nd respectively. The responses f, f=4, f=2 nd f3=4 correspond to the frctions.,.25,.5 nd.75 respectively. The temporl frequency responses re in contrst to the previous methods not ll-pss lter frequency responses for the dierent frctions, since these GST lters use smples from two susequent elds. The frequency oosting in temporl direction cn clerly e oserved in the chrcteristics for the frctions f nd f3=4. These gures show tht higher order interpoltor used in deriving the GST lters, etter pproches the idel interpoltor. The sptil frequency responses pproch for certin frequency rnge (dependent on the interpoltor

7 .3 sptil frequency responses 3 temporl frequency responses.2. f 3/4 2.5 f 2 f 3/4 Mgnitude.9.8 Mgnitude Figure. ) Sptil frequency response of the GST lters using the Ctmull-Rom cuic interpoltor, ) the corresponding temporl frequency response.4 sptil frequency responses 2.5 temporl frequency responses.2 f 3/4 2 f f 3/4 Mgnitude Mgnitude Figure. ) Sptil frequency response of the GST lters using the liner poly-phse lter interpoltor, ) the corresponding temporl frequency response used), the idel frequency response. Another oservtion is tht lter h3=4 oosts the highest sptil frequencies. 3. RESULTS AND EVALUATION The lter chrcteristics of the interpoltors completely dene the mplitude nd group-dely chrcteristics nd therefore the ehviour for the dierent motion frctions. The individul lter chrcteristic dierences cn cuse unintentionl preferences to occur. So, y exmining the frequency nd group dely chrcteristics, we cn predict the ehviour of the interpoltor. Our predictions proof to mtch very well with the experiments. In the remining prt, we will show the results of the experiments only. 3.. Evlution environment In order to test the interpoltor, we creted test sequence contining multiple nds with sine-wves. The frequency increses per nd in verticl direction. The strting phse chnges slightly every line y. A snpshot of the test sequence is shown in gure 2. Figure 2 shows the velocity nds with grnulrity of.25 pixels/eld pplied to the test sequence. This test sequence is used in our experiments with nd without white gussin noise dded to the sequence. The Signl-to-Noise Rtio (SNR) of the sequence with noise is set to 32 db. As mentioned in Ref. 7, prt of the informtion is contined in the derivtive, which is dierent for the dierent su-pixel positions. A lrger contriution of the derivtive cuses stronger frequency 'oosting' eect. y Since lock of smples is used in lock sed ME, the phse chnges per line prevents dominnce in this lock for prticulr phse. Rememer tht su-smpling is pplied in the horizontl direction (which simultes interlce).

8 velocity velocity Figure 2. ) Snpshot of the test sequence. (The lis is not present in the sequence used for the experiments, ut due to cpturing for printing introduced), ) the velocity nd with grnulrity of.25 pixels/eld. The velocity is rnging from -.25 t the fr left side to.25 t the fr right side in the imge (in steps of 32 ), while the frequency is incresing from :5f s t the top of the imge to :4f s t the ottom (in steps of :5f s ), with f s the smpling frequency. Higher frequencies re hrdly relevnt given ctul cmer chrcteristics. We used full serch lock mtcher for estimting the motion serching in limited rnge from - to +, with qurter pixel ccurcy. As n ojective evlution criterion, we used the Men-Squred-Error (MSE) per frequency nd s dened y: MSE f (n) = P f X ~x 2B f (d(~x ; n ) r(~x )) 2 (6) with P f the numer of pixels in frequency nd f, B f the set of pixels in f, d(~x ; n ) the predicted motion t position ~x =(x; y) T in eld n nd r(~x ) the rel motion t the sme position. Note tht the verticl motion component is not tken into ccount, since it ws found to e zero in ll experiments. The verge MSE f of the sequence is dened y: with N the numer of elds. NX MSE f = MSE f (n) (7) N n= With n idel estimtor using qurter pixel ccurcy, the minimum MSE per frequency nd is dened y: MSE min f = 6P f with Round(x) rounding to the nerest integer vlue. X ~x 2B f (Round(4r(~x )) 4r(~x )) 2 (8) In the evlution in the susequent susections we will show, next to the distriution of the velocities, two numers on top of the velocity distriution. The numer on the top right represents the reltive performnce of the complete imge compred to the performnce of the idel estimtor with ccurcy of 4 pixel s dened y: R ll = P f MSE f Pf MSEmin f nd the numer of the top left represents the reltive performnce for the lower frequencies (up to :2f s ), s dened y: P :2f s f=:5f R low = s MSE P f :2f s () f=:5f s MSEf min The results of the evlution shll e discussed for individul ME-types in seprte su-sections. (9)

9 c d e f velocity Figure 3. Simultion results of the two eld ME with dierent interpoltors; ) rst-order liner interpoltor, ) Ctmull-Rom Cuic, c) Poly-phse ltering, d) rst-order liner interpoltor nd input sequence contining noise: 32 db, e) Ctmull-Rom Cuic with 32 db SNR, f) Poly-phse ltering with 32 db SNR 3.2. Two eld ME results The results of the two eld ME experiments re shown in gure 3. If we compre gure 3 with the ctul motion with 4 pixel ccurcy s plotted in gure 2, ll results show severe prolems for frequencies higher thn :25f s. Due to the su-smpling in the reference nd shifted eld, the Nyquist frequency is :25f s, which cuses lis in the frequency nds :25f s up to :5f s. Consequently, the ME is estimting motion on video contining lis z. For exctly the frequency :25f s, lis occurs if the smpling process smples t exctly the zero-crossings in the sine-wve only. In tht cse, this frequency is mpped to DC, for which ll vectors give identicl mtch errors. Up to :2f s, gure 3 lso conrms the sttement tht generlly the lrger the numer of tps of the interpoltor, the etter the results. As in n idel sitution, the verticl velocity rs (in gure 3) should e of equl width (see gure 2), every devition from this idel sitution indictes preferences for prticulr su-pixel velocities. It cn e oserved tht the rst-order liner interpoltor exhiits more preferences thn the Ctmull-Rom cuic interpoltor, wheres the ltter is worse thn the poly-phse ltering interpoltor. In our test sequence, frequencies strting from :25f s contin pure lis, nd re therefore not relevnt for the su-pixel ccurcy experiments x. The gures 3d, e nd f show the results of the interpoltors on the test sequence with noise. As we my conclude from these imges, the inuence of noise, t lest up to 32 db SNR, does not chnge the ehviour drmticlly. The lrgest inuence cn e oserved t the lowest frequencies. For the lowest frequencies, noise hs non-neglectle inuence on the error criterion, cusing some nervousness in su-pixel motion estimtion. z Note tht the velocity of the lis is generlly not equl to the velocity of the rel signl. x Note tht 'nturl' sequences generlly contin next to lis components, low frequency components lso. Therefore, the ME cn prot from these lower frequencies in estimting the motion.

10 c 94.9 d e f velocity.5 Figure 4. Simultion results of the frme nd eld ME with dierent interpoltors; ) rst-order liner interpoltor, ) Ctmull-Rom Cuic, c) Poly-phse ltering, d) rst-order liner interpoltor nd input sequence contining noise: 32 db, e) Ctmull-Rom Cuic with 32 db SNR, f) Poly-phse ltering with 32 db SNR 3.3. Frme nd eld ME results The results of the frme nd eld ME using dierent interpoltors is shown in gure 4. The frme-eld ME prots from previously de-interlced eld. The qulity of the ME is therefore to signicnt extend determined y the qulity of the de-interlcer. However, in these experiments we used n idel de-interlcer (which is in prctice not possile), therey eliminting the inuence of the de-interlcer. Compring gure 3 nd 4 shows the result of incresing the resolution of the smpling grid y fctor of two. The Nyquist frequency is on its mximum frequency :5f s, eliminting the lis cused y su-smpling. However, t frequency nd :25f s we cn oserve in gure 4 prolem (with dierent mgnitude) in the results. Since our current imge for which motion is to e estimted is still su-smpled imge, lis cn occur t frequency :25f s. If the smpling phse cuses smpling t the zero-crossings in the sine-wve, the frequency is mpped to DC. For ll other smpling phses, unique mtch cn e found on the previous imge. Figure 4 lso stises the expecttion tht etter interpoltor results in ME with decresing preferences. The well relized uniformity of the poly-phse lters up to out :4f s prevents preferences in the ME Three eld GST ME results The results of the three eld ME sed on GST for dierent interpoltors, re presented in gure 5. Figure 5 lso conrms the expecttion of n incresing performnce for incresing interpoltor qulity. It cn lso e oserved from gure 5d,e,f, tht the GST-lters sed ME hs reltively more prolems with estimting motion in presence of noise thn the other evluted estimtors. Some GST lters, especilly the lters h nd h3=4, contin lrge contriution of the derivtive (see section 2.3). Therefore, noise is signicntly mplied, cusing

11 c d e f velocity.5 Figure 5. Simultion results of the three eld GST ME with dierent interpoltors; ) rst-order liner interpoltor, ) Ctmull-Rom Cuic, c) Poly-phse ltering, d) rst-order liner interpoltor nd input sequence contining noise: 32 db, e) Ctmull-Rom Cuic with 32 db SNR, f) Poly-phse ltering with 32 db SNR nervousness in the estimtor. In the gures 5 d, e nd f, the velocities - nd + re hrdly present, especilly for the lower frequencies, while in gure 5, nd c, the preference for these velocities is lrge. It cn lso e oserved tht the velocities -.75 nd +.75 re not found on the correct position for the lowest frequency in gure 5d, e nd f. For low frequencies, s cn e concluded from the gures 9, nd, the individul chrcteristics hrdly dier. Consequently, in noisy environment, lters tht re less dominted y the derivtive re to e preferred Discussion Though it is evident tht n interpoltor with lrger numer of tps cn perform etter thn n interpoltor with smller numer of tps, it is interesting to oserve its suitility for su-pixel ccurte motion estimtion. The rst-order liner interpoltor (2 tps lter) hs for incresing frequencies n incresing preference for frctions deviting from.5. The Ctmull-Rom cuic interpoltor (4 tps lter) hs somewht incresing preference for frctions pproching.5, which is n opposite ehviour compred to the rst-order liner interpoltor. The Polyphse ltering interpoltor (in this pper, 6 tps), cn simply e designed to pproch the idel interpoltor for signicnt prt of the frequency spectrum, therey preventing preferences to occur. Since the memory requirements for the frme-eld ME nd the three eld GST ME re similr, it is interesting to note tht the frme-eld ME is to e preferred over the GST ME in cse of n idel de-interlcer. Noise in the input signl cn cuse nervousness in the estimtor s result of the high frequency oosting of the GST ltering. For lower frequencies (smller thn :25f s ), the frme-eld ME using the rst-order liner interpoltor is superior over the Ctmull-Rom cuic nd Poly-phse ltering sed GST ME.

12 4. CONCLUSIONS In this pper we hve nlyzed the prolem of unintentionl preferences tht cn occur in su-pixel ccurte motion estimtion. Such preferences re due to the fct tht the lters for clculting the dierent su-pixel smples hve dierent chrcteristics. The inccurcies in the estimted motion tht occur due to these dierences generlly increse with sptil frequency. In this context, we hve investigted the ehviour of three interpoltor types: the rst-order liner interpoltor, the Ctmull-Rom cuic interpoltor nd the poly-phse ltering sed interpoltor. The motion preferences using these interpoltors hs een nlysed in three types of estimtors; two eld ME, frme-eld ME, nd three eld ME using generlized smpling, ll using full-serch lock-mtching. The superiority of the poly-phse lters pplied in the frme-eld ME hs een demonstrted. However, we hve to note tht the pplied de-interlcer in the frme-eld ME is n idel de-interlcer. The dvntge of poly-phse lters is tht these lters inherently hve common 'se' (low-pss lter), i.e. the lter chrcteristics for the dierent motion frctions re similr for signicnt prt of the spectrum. As consequence, motion preferences re eliminted for signicnt prt of the frequency spectrum. We lso found tht the three eld GST sed ME suers from su-pixel inccurcies cused y noise. This is due to the sptio-temporl frequency oosting lters for prticulr motion frctions. Therefore, this ME is less suitle for estimting su-pixel ccurte motion vectors in noisy environment {. We conclude from this nlysis tht for su-pixel ccurte ME without unintentionl preferences, it is desired to pply n interpoltor tht complies the following chrcteristics over the relevnt frequency rnge: n equl frequency response for the dierent motion frctions, nd group dely responses tht for ll motion frctions eqully mtches their individul idel group delys. REFERENCES. F. Wng, D. Anstssiou, nd A. Netrvli, \Time-recursive deinterlcing for idtv nd pyrmid coding," Signl Processing: Imge Communiction (2), pp. 365{374, G. de Hn nd E. Bellers, \De-interlcing of video dt," IEEE Tr. on Consumer Electronics 43, pp. 89{825, August P. Delogne, L. Cuvelier, B. Mison, B. vn Cillie, nd L. Vndendorpe, \Improved interpoltion, motion estimtion nd compenstion for interlced pictures," IEEE Tr. on Imge Processing 3, pp. 482{49, Septemer L. Vnderdorpe, L. Cuvelier, B. Mison, P. Quelez, nd P. Delogne, \Motion-compensted conversion from interlced to progressive formts," Signl Processing: Imge Communiction (6), pp. 93{2, G. de Hn nd E. Bellers, \De-interlcing: n overview," Proceedings of the IEEE 86, pp. 837{857, Septemer N. Dodgson, \Qudrtic interpoltion for imge resmpling," IEEE Tr. on Imge Processing 6, pp. 322{326, Septemer E. Bellers nd G. de Hn, \Advnced motion estimtion nd motion compensted de-interlcing," SMPTE Journl 6, pp. 777{786, Novemer 997. { In this pper experiments hve een relized with SNR of 32dB. Though not evluted in this pper, it is likely tht for even etter SNRs the GST ME preferences re prtly controlled y noise.