Nature of Computer mages' Talents

Transcription

1 Parallelzng Tracng Algorthms María Carna Roldan, Marcelo Naouf, Armando De Gust 3 mcroldan@vttal.com.ar, {mnaouf, degust}@ld.nfo.unlp.edu.ar LIDI. Laboratoro de Investgacón y Desarrollo en Informátca 4 Facultad de Informátca. UNLP Abstract In several applcatons, the traectory of an entty, a feature or an obect has to be traced over a sequence of mage frames. When the processng s to be performed n real tme, there are mportant constrants leadng to the parallelzaton of tracng algorthms. Ths paper presents the results of a concrete mplementaton, whch deals wth the partcular case of smple obects movng n an context reachable by the vson element (vdeo camera). The steps nvolved n the soluton development are detaled, specally n relaton to ther parallelzaton by usng a computer heterogeneous networ and MPI (Message Passng Interface) support. Fnally, an analyss of the dfferent algorthms behavor s carred out together wth the obtaned results assessment, whch allows nowng the performed parallelzaton effcency, and determnng under whch condtons ths soluton turns out to be the best one. Key words: Parallel Algorthms. Tracng. Computer Vson. Heterogeneous Multprocessors. MPI. Introducton There exsts a growng nterest n the processes automaton based n the vsual percepton of the world around us, all of whch requres mages acquston and processng. Ths s related to the feld of Computer Vson [Har9][Ja95]; such systems ntend to copy human vson processes nto tass of hgh complexty regardng exactness and tme, or of excessvely routne. The obectve of a computer vson system s to create a model of the real world from mages, recoverng useful nformaton about a scene from ts D proecton. There exst developed technques n other felds used for recoverng data from mages. Some of them are Image Processng (generally n the frst stages n order to upgrade partcular data and suppress nose) [Gon9][Bax94] [Ja89], Computer Graphcs (where mages are generated from geometrc prmtves), Pattern Recognton (classfyng numerc and symbolc data) [Sch9], etc. Computer vson systems encompass dfferent applcatons, among whch we can menton medcal dagnoss by computed tomography mages or product qualty control, from food to ndustral peces [Law9]. Another type s related to an envronment three-dmensonal structure recovery,.e. scene movements recognton and nterpretaton; these applcatons are useful n cars, planes or robots navgaton. A thrd group ncludes the analyss and management of large data volumes obtaned by satelltes used for weather forecast, the study of the planet behavor, agrculture, etc. Obect tracng n an sequence of mage frames s partcularly assocated to: - Obects recognton and classfcaton. - Tracng of the same obects through that sequence. Graduate n Computer Scences Lcencature. Full-tme Assocate Professor. 3 Prncpal Researcher of CONICET. Full-tme Char Professor. 4 LIDI Faculty of Computer Scences. UNLP - 50 y 5 st Floor, (900) La Plata, Argentna. TE/Fax +(54)()

2 It s also necessary to operate n real tme, mplyng the use of specalzed hardware and robust algorthms n order to reduce falure possbltes; the systems must be flexble enough n order to rapdly adapt themselves to changes n the process. The temporal constrant naturally leads to the dea of a problem soluton based on parallelsm n order to fulfll the requrements [Al97][Br95][Tn98][Zom96]. In ths paper, the stages related to computng vson systems are analyzed, such as the tracng mechansm and obect recognton n the mage sequence obtaned wth a vdeo camera. A frst sequental soluton s developed, consstng n an algorthm set that allows capturng obects data and ther movement from the sequence. In the second stage, algorthms are parallelzed both n the recognton process and n the tracng process. Ths s mplemented over an heterogeneous networ wth a MPI programmng support. The found solutons allow mang a comparson and assessment of the performance, whose results are shown at the end of the artcle. Tracng n Computer Vson The obectve of a computer vson system s to create a model of the real world from mages. For ths purpose, a closely related feld s that of dgtal mage processng ncludng subect matters such as enhancement, compresson and correcton of blurred or out of focus mages. Computer vson algorthms tae mages as nputs and produce outputs as a representaton of the obect contour found n an mage. Image processng algorthms are useful n the frst stages of a vson system, usually to emphaszed data and suppress nose. The obectve of the enhancement s to emphasze the features for further analyss or for a dsplay n an output devce. Segmentaton dentfes the semantcally sgnfcant components n an mage, and groups the ponts belongng to the same; the proceedng s smplfed f the mages are sharp, reason why the enhancement generally consttutes an mportant prevous step. The segmentaton result s a set of regons or obects whch can be dentfed by a locaton or a set of features. An obect recognton system fnds real world tems from an mage captured usng already nown models. The recognton s related to the segmentaton, and mples the consderaton of the obect representaton manner, the mportant features to be detected, the way of comparng the features wth those of the models, etc. Recognton complexty depends on several factors, such as for example whether the condtons n whch the mage was taen (llumnaton, bacground, pont of vew) are not smlar to those under whch the model was defned. Another factor s the occluson: f there s only one obect, t can be entrely vsble; but as the quantty ncreases, the possblty of occluson ncreases as well, and the recognton process may be hndered. Dynamc Vson Although the frst computer vson systems were prncpally related to statc scenes, solutons that analyzed dynamc scenes have been desgned for several applcatons. The nput of the same s a sequence of frames taen from a real movng scene. Each frame represents an mage of the scene n a tme nstant; the changes occurrng n the same may be due to the movement of the camera, of the obects, or to modfcatons n the llumnaton or n the obects shape or sze. The system must detect the changes, determne the movements characterstcs, recover obects structure and recognze them. There are four possbltes for analyzng a dynamc scene: statonary camera and statonary obects (SCSO), statonary camera and movng obects (SCMO), movng camera and statonary obects (MCSO), movng camera and movng obects (MCMO). Dependng on the case, dfferent technques wll be needed. SCMO has receved the greatest attenton; the obectve usually conssts n detectng the movement, recognzng the movng obects and computng the characterstcs of those movements. The correspondence process tres to dentfy the same obect n two or more frames and determne changes n ts locaton (.e., ts movement). An mage pont p = (x, y ) s meant to be coupled wth a pont p = (x, y ) of the followng one n a temporarly ordered sequence. The dsparty between these two ponts s gven by the dsplacement vector d = (x x, y y ). The result of the correspondence between two consecutve frame ponts s a set of conugated pars.

3 In order to solve the correspondence problem we should consder: whch crteron s used to determne whether two ponts correspond to each other; whch the characterstcs to be compared are; whch constrants, f any, are mposed to the dsplacement vectors. As parameters for answerng these questons, t s essental to bear n mnd the followng propertes: - Smlarty: t s a measure for determnng the lelhood of two pxels. It s gven by a smlarty between the obects, determned from the features found durng the segmentaton. - Movement Consstency: due to nerta, a physcal entty movement cannot change nstantaneously. If the sequence s obtaned wth such a frequency that there are not decsve changes n two consecutve frames, the mages reflect the movement smoothness for most of the obects. Tracng Gven an mage sequence over whch one or more traectores are traced. If there s only one obect, the tracng problem can be easly solved. In the presence of several enttes movng ndependently, the use of constrants based n the nature of the obects and ther movements wll be requred. Consderng the consstence property n the movement, the path coherence can be formulated: t mples that an obect movement n any pont of a frame sequence wll not change abruptly. Thus, the formulaton of a soluton to the correspondence problem s smplfed snce t can be mpled that (a) a gven pont locaton, (b) a pont scalar speed, and (c) a pont movng drecton reman relatvely wthout change from one frame to another one. The devaton functon, or traectory functon, s used n order to assess the movement propertes n a sequence. Its nput s a route and the return value must be nversely proportonal to the route smoothness (or drectly proportonal to the path devaton degree). 3 n Let a traectory be T = P, P, P, L, P, where P represents a pont n the -th mage. If the coordnates of P are gven by vector of the frame, the coordnates of the -th frame can be represented as. Vectoraly, T =,,,., 3 L n d devaton n the path - of the pont n the -th frame - s gven by ( ) D = φ,, where φ s the path coherence functon (whch gves an dea of how much coherent an obect movement passng through theses two ponts could be). The devaton for all the traectory s defned as = D d. = If there are m ponts n a sequence of n frames, whch results n m traectores, all traectores devatons = m n D T m d. = = should be consdered, gven by ( T, T, T3, L, ) Then, the correspondence problem s solve by mnmzng the total devaton D (or, what would be the same, maxmzng the movement smoothness), n order to fnd the rght traectory set. If the camera sampled frequency s hgh enough, the change n the drecton and the speed of any movng pont n temporarly consecutve frames s smooth. Ths s descrbed wth the devaton functon + dd φ ( P,, ) = ( cos ) + P P ω θ ω. d + d = Vectoraly: φ ( P, P, P ) ω + ω. n

4 The frst term s the vectoral product of the dsplacement vectors and represents the drecton coherence (the vectoral product s the angle between two magnary segments between two ponts -, and +): the smaller the angle, the greater the devaton. The second term consders the geometrcal and arthmetcal mean of the magntude, and represents the speed coherence. ω and ω are weghts chosen to assgn dfferent mportance to drecton and speed changes. They can be chosen from a range from 0.00 to.00, only f ther sum s. One of the maor dffcultes wth the sequences s the occluson,.e., the total or partal dsappearance of obects, or the appearance of others. The changes n data due to movements and scene llumnaton varatons can lead to ncorrect correspondences. Traectores can nevertheless be obtaned even n the presence of occluson by forcng them to fulfll some of the local constrants, and allowng them to reman ncomplete where necessary. One path coherence algorthm lmtaton s that t assumes that n all of the frames, the same ponts set s avalable. When searchng for a traectory set, t should be permtted to obtan ncomplete traectores ndcatng occluson, obects appearance, or temporal obects dsappearance due to bad qualty data. Furthermore, certan constrants should be mposed to the possble maxmum dsplacement and the maxmum local devaton. Gven a P set of m ponts for each of the n frames, t can be found the maxmum set of complete or partally complete traectores that mnmzes the sum of local devatons for all of the obtaned traectores, provded that the maxmum devaton for any of the traectores does not surpass φ max, and that the dsplacement between any par of successve frames for any traectory s always nferor than d max. In order to ustfy the ponts left due to occluson, ghost ponts are used (hypothetcal ponts used as a fller to extend all the routes over a gven frame set). In order to mae use of the noton of ghost ponts, the dsplacement and local devaton values must be defned for a route contanng such ponts. - In order to compute the dsplacement for T n the -th frame, the dsplacement functon s defned: Ths mples that a ghost pont always moves n a fxed quantty d ma x. - In order to compute the local devaton for T n the -th frame, the devaton functon s defned: Ths local devaton functon defnton s equvalent to the path coherence functon f the three ponts are real. It ntroduces a penalty of φ max n case there s no real pont for T n the current frame or the followng one, and does not penalze f the traectory begns n the frame under consderaton. The followng set of steps roughly shows the traectory buldng process. Intalzaton: Dsp Desv P + EucldeanDstance( P, P ) f po s are real ( P P ) { both nt, = d max (, P, P ) = n othercase 0 φ ( P, P, P+ ) φ max f P sa ghost pont f thethree ponts arereal n othercase. For each pont m n P, =,..., n- ( P set of ponts of the frame ), determne the closest + neghbor n P wthn dstance d max. Solve arbtrarly n case of multple alternatves.. Form ntal traectores channg the closest neghbors found n the successve frames. Extend all the ncomplete traectores usng ghost ponts n order to lead them through n frames. 3. For each traectory n step, form an addtonal route only wth ghost ponts.

5 Interchange cycle: For each frame from = to n- For = up to m- For = + up to m If d max constrants are fulflled, compute G = + [ φ( P, P, P ) + φ( P, P, P )] [ φ ( P, P, P ) + φ( P, P, P )] Tae par wth maxmum gan (G ) If the gan s superor to zero then Interchange the ponts of the frame +, P + wth P +. Termnaton: Repeat the nterchange cycle untl there s no more frames left. The number of traectores bult n ntalzaton step depends on the data qualty. Only m routes wll be formed and none of them wll have ghost ponts n the deal case where the same m number of ponts s consstently present n all the frames. In the worst of the cases, when the ponts of some of the frames do not have any correlaton to the ponts of any other frame, the number of routes formed can be as large as the total sum of all the ponts of all the frames. In general, the route number wll be at least m max where m max = max(m, m,...,m n ) and the dfferent routes wll have dfferent quanttes of ghost ponts. A case wth several obects s always mpled. In the partcular case n whch a nown obect must be traced, the soluton for economzng the process tme s to chec n each mage only the part where the obect locaton s estmated, n functon of ts locaton n the prevous frames, and consderng the estmated obect movement. On the other hand, n ths route montorng algorthm, the obects are consdered as a set of ndvsble enttes. A more nterestng stuaton s that n whch the searched obect/s model s nown, and as the mage s checed, the segments that do not ft wth any of these models can be dscarded. Problem presentaton and Sequental Soluton Consderng the system as applcable to realty, the data source must come drectly from a devce capturng mages n real tme. Wth the purpose of development and assessment, data was completely avalable before the applcaton executon. Images were taen wth a camcoder. The obtaned analogcal vdeo was dgtalzed and converted nto a sequence of mages. In order to generate a code n whch the management of mages was smple and clear, pgm format mages were used, codfed n the grey scale form 0 to 55. The followng algorthm gves a frst dea about the prncpal system runnng cycle: Whle (there are frames) Tae a frame Identfy the obects of the frame Identfy and buld up the found obects traectores What does whle there are frames mean? In the case of mages comng from a real tme capturng devce, t s equvalent to whle the mages are beng captured. For already avalable mages, t means whle there stll are unprocessed mages. Snce sample mages were captured specfcally wth ths end, they had no damage or bad qualty. However, they dd not show a clear dfference between obects and bacground (due to the lac of llumnaton durng the capturng), and besdes, before an ncreasng movement of the obects, some frames of the sequence were blurred. Ths rased the need of enhancng mages n order to facltate recognton. Ths was carred out frst by calculatng an spatal average n order to upgrade the defnton, and then by hghlghtng the ponts belongng to the obects by means of a contrast enhancement functon. For the obect recognton, the mages were run from left to rght and from top to bottom. Snce the mplementaton was focused n the tracng rather than n obects recognton, t was mpled that these were dstngushable enough n the bacground, and that the nterest features were mnmum: locaton, area,

6 average ntensty (grey or color level). These features were enough to characterze them, snce any scene obects were searched and not obects wth specfc characterstcs. The technque used for the dentfcaton of the obects wthn an mage combnes thresholdng wth labelng. Once the routng of all the mages was fnshed, data was debugged, dscardng all segments small enough or wea n color that they do not requre much consderaton - snce they may be ust stans or shadows. One constrant mposed to mages was that the obects could not be n touch wth each other. When the process was fnshed, a lst of the obects found n the scene wth the features dentfyng them was obtaned as a result. The mplementaton s general, n the sense that n the scene there are several obects and that they are not ndvsble one from the other. For more specfc cases, the soluton can be mproved by checng only the part n whch the obect may be located n functon of ts locaton n the prevous frames. Havng n mnd that the mages come from realty, t maes no sense searchng an obect far from where t appeared n the precedng frame. Obects Correspondence and Tracng It s mpled that the sequence corresponds to a flmng where the camera s fxed, and that the obects movement s parallel to the mage plane. For the traectores buldng, the ntal algorthm was modfed (whch supposed that all the sequence was avalable from the begnnng) for the case n whch mages are ncorporated n real tme. Whle (there are frames) Tae a frame Identfy the obects of the frame Update th e found obects traectores Lets suppose that the current sequence frame s and that n each of the prevous ones, P, P...P- obects were dentfed. Up to the moment there are bult n routes that go from frame to -. The process must assocate frame obects one-to-one wth one of the traectores under constructon. The algorthm that solves the problem s the followng: For each exstent obect n the frame +, create a ghost traectory // Compute the maxmum global devaton For = up to m- For =+ up to m If d max, constrants are fulflled n the nterchange, compute + [ φ( P, P, P ) + φ( P, P, P )] [ φ ( P, P, P ) + φ( P, P, P )] G = Tae par as maxmum gan (G ) If the gan G s greater than zero then Interchange the ponts of the frame +, P + wth P +. Save the result of ths step n the traectory fle In order to mplement the devaton functon, some decsons should be taen: - The method to be used for the dstance between two ponts. In ths case, cty-bloc : d = + was used. - The weghts to be used for the drecton coherence and the speed coherence n the formula, ω and ω. In ths case, there was no preference for any of the measures, thus ω = ω = 0,5.

7 Traectory-related data s mantaned n a traectory fle. In order to smplfy the nterchange algorthm and to save computng tme, route data related to the last three frames s ept n memory. The order n whch the obects are saved s that resultng from the tracng algorthm applcaton. In the case of the ghost ponts as part of a traectory, they are also saved wth an nvald row and column value (-,-), dstngushng them from a common pont. The mplementaton also allows plan data (wth text format) whch consttutes the found traectores to be represented graphcally. An mage s generated that, for each dentfed obect, dsplays wth a trace the traectory performed by t all throughout the mages sequence. The followng algorthm shows the buldng of the routes mages: Let MA be the obect quantty of the frst frame. For each of these obects, generate an mage assocated to ts traectory. For each frame For I= up to MA If the pont exsts n the frame Generate an lne from the obect pont n the prevous mage, up to the obect pont n the current mage If the pont does not exst n the frame (ghost) Proect the poston and draw n another color or leave t n whte For each new obect appearng n the frame Increase MA n Create a new traectory mage. Parallel Soluton The Parallelzaton was performed over an heterogeneous computer networ and support MPI [GDB95] [Ml98] [Mor94] [MPI] [MPI] [MPI3] [PBM] [Sm97] [Sn96] [Ste96] [Wel96]. The operaton dealt wth was the contrast enhancement by means of a spatal average. For the parallel code, a root or master process dstrbutes per columns the mage among all the processes, and comples the results buldng the fnal mage. Obect recognton process combnes thresholdng wth labelng. The parallelzaton s based n the same dea but ntroduces some detals. The root dstrbutes the columns equtably among the processes and performs part of the general operaton. Each process runs over the submage extractng the canddate obects data. Then, each of them send data to the root n such a way that the result of the obect recognton process n the mage s focused n a sngle node. In order to solve the case of obects belongng to more than one submage, each process dentfes the canddates stc to the left edge of ts submage, and then t forgets that t has found that obect; t s delegated to the left process and dscarded from ts own set of obects. When recevng the process data of the rght neghbor, t verfes f t concdes wth the edge of some of the rght-edge adacent obects. If ths s so, the process unfes data, addng the receved obect data wth that of the own obect. Fnally, each process sends the found obect data to the master, fnshng wth the process. Once mage obects are dentfed, the traectores are to be bult. Remember that n the sequental soluton - beng P, P,..., P the obects sets found n an mage sequence for each mage P obects were taen and hooed n the traectores bult for the prevous mages followng the algorthm. Data related to the dfferent routes s saved n a fle as the process advances. In man memory, there s always nformaton about the last three frames by performance and easness of processng. Revewng the gven soluton, the sequental process for performng the obect tracng can be summarzed as follows: t s a repettve cycle n whch, as new sequence frames are avalable, the traectores bult for the prevous frames are updated wth the dentfed obects n the new frame. That s, let the nstance be one where frame has to be processed. There are N ncomplete traectores dentfed n the - of the prevous frames. The followng step conssts n hoong the x obects dentfed n the frame n the prevous routes. In order to do ths, t s necessary to perform several comparng operatons for determnng whch obect dsplay renderng the best traectores set s.

8 As a result of these operatons, t s probable that the order of some of the found obects has to be nterchanged. If ths s so, the cycle s repeated untl there are no more nterchanges. If n s the maxmum between the bult traectory quantty and the number of obects found n the new frame, the quantty of comparng or verfcaton operatons to be performed n each cycle s (n-) + (n-) It can be proved n = that ths sum s equal to ( ) [ + n ] n / : Remember that each mentoned operaton s a functon that, gven two trads of ponts or obects (where each corresponds to one to three consecutve mages), determnes a possble traectory verfyng whch combnaton renders the best total devaton (whether both of the gven routes, or those resultng from nterchangng the thrd pont of the trads). When the result s favorable for the trads wth the nterchanged pont, the mentoned nterchange must be carred out. The quantty of nterchanges and necessary cycles obvously depends on the sample data set. A parallelzaton conssts n dstrbutng equtably that quantty of operatons among the processes. If the number of operatons s not an exact multple of the number of processes, the remanng operatons wll be dstrbuted one for each of the frst process. As for the rest, all of them would perform the same functons, wth a local copy of the most recent mage data. Here are some examples of the quantty of operatons accordng to the number of processes: for a small number of obects, the dstrbuton of the operatons would be an nsgnfcant quantty of processes to be performed for each one, addng up to the communcaton tmes. Before ths, the best s to dscard ths possblty and search a more approprate alternatve. For t, the soluton s consdered from a lower refnement level. The problem n ts general expresson conssts n dentfyng the obects n a sequence n order to trac ther route. Traectory updatng can be carred out only f the obect dentfcaton s completed n at least three mages of the sequence. When there s more than one process, nstead of parallelzng the nternal algorthm of the route montorng, the two central tass are separated from the dfferent processes. That s, on the one hand, there s a set of processes that carry out the dentfcaton, whereas a separated process s n charge of updatng the dfferent routes. Wth ths, the traectores updatng can be supermposed wth the obect dentfcaton phase n the followng mage. If that tme s short and eeps the dle responsble process for a long tme, ths part of the process can be carred out by one of the frst group processes. Results Assessment One of the orgnal obectves was to obtan acceptable results for real tme problems. The speedup and effcency of the parallel soluton were analyzed usng dfferent quantty of processors and processes, and dfferent mage szes. Ideally, effcency s meant to be. If the deal s taen as parameter, t can be measured how far the mplementaton of that deal s. In the best of the cases, the tme for executng a soluton decreases proportonally to the number of processes. Ths s, f N = number of processes and T N = tme for usng the problem employng N processes, then as N ncreases, T N should ncrease as well. In the deal case: T N = T / N o N = T / T N. Ths last formula gves a speedup marer. In general, T / T N N. The quotent between the real speedup n N processes and the deal gves a measure for the effcency. Formally speang, effcency = real / deal = real speedup n N processes / N. Low effcency values represent a waste of the processng power [Hwa93] [Kum94][Le9]. In general, for each part of the parallel soluton, the total runtme can be dvded n two components. On the one hand, the part of the problem parallelzed, where the addton of processors actually reduces the tmes, even really close to the deal. Gven T p as the tme used for executng ths part of the problem n the sequental soluton. On the other, the part of the problem nherently sequental or non-parallelzable, whch s not gong to be more rapd by addng processors. Namng T S the tme that taes to execute ths part of the problem, T = T S + T p

9 T S s an nferor lmt for the processng tme, thus n the best of the cases, T N = T S + (T p / N). The fracton of the total runtme correspondng to the non-parallelzable part, T S / T, mposes a constrant n the reducton of the tmes ndependently of the number of processes. The greater ths fracton, the less effcent the parallel soluton would be. It s mportant to bear n mnd that ths factor s not a constant, but t vares wth the problem sze: as t changes, T S / T factor changes as well. Typcally, T p ncreases much faster than T S. As a consequence, a complete assessment should be extended over at least two parameters: the problem sze and the processors number. To ths, t may be added the fact that the performance can be serously affected both by nput/output operatons and by the communcaton quantty among the processes. In order to determne the characterstcs that the mage sequences should contan, n a way that the assessment could contemplate all the possble stuatons, the algorthms of each part of the system were analyzed n frst place. From there, dfferent testng cases were defned and the necessary mages sequences were generated. Then the algorthms were assessed over each of these cases varyng the quantty of processes and the machnes nvolved. In the enhancement, T S ncludes mages obtanng, openng and closng of fles and format recognton (e.g., fnd out ts dmensons). T p ncludes computng the value for each pont of the new mage. In the case of more than one process, ths tme s no purely processng tme, but t carres the sendng and recepton tmes of data among the processes. Wth a temporal graphc: tme lne process 3 process process data sendng data recepton non-parallelzable processng parallelzable processng tme lne In ths case, the sze of the problem s drectly proportonal to the mage sze whch s beng processed. If we consder that each process receves, apart from the data columns to be processed, both adacent columns, t can be notced that as there are more processes, more data traffc s generated. But at the same tme, the addton of processes mples a decrease n the processng tme per process. Thus, t s necessary to search an equlbrum between these two ponts. In order to measure the soluton performance for the enhancement, testng cases were generated wth dfferent mage szes (problem sze) and dfferent number of processes. The results showed that, ndependently of the type of mages, the tmes used up by the enhancement tass were smlar. What t could be frst observed was that a small sze mage sequence s not the best canddate for beng enhanced n parallel. In ths case, the tmes used up by a sngle process to enhance the operaton were better than those resultng form the parallelzaton. On the other hand, for a larger sze of mage, the speedup was of % over the base tme when ncorporatng a second process; t s not an optmal result, but s nevertheless postve. The same dd not happen when a thrd process was added, wth whch the processng tmes were agan ncreased. Secondly, the recognton process was assessed. Here, T S ncludes the mage obtanng and the format recognton, and T p s the tme used up by the obects dentfcaton; t can be observed - n the case of the parallel soluton - that ths tme carres tself data sendng among the processes, plus the eventual assembly of obects whch have remaned dvded n the dstrbuton. In a temporal graphc : dle tme lne process 3 process process data sendng data recepton non-parallelzable processng parallelzable processng tme lne dle

10 In ths case, the sze of the problem depends on two man factors: - the mage sze. The more rows and columns are, the more ponts or pxels have to be checed n order to fnd the obects data. - the partcular data set. The quantty, sze and dsplay of the obects drectly nfluence n the processng tme, and the data quantty whch wll have to travel between the processes. For example, a large problem s characterzed by hgh resoluton mages, or wth several obects, or wth obects whose shape s enlarged n such a way that when dvdng the mage, they can be parttoned. Wth respect to the processes quantty, as wth the prevous case, when two more columns are dstrbuted per process, the traffc ncreases wth the number of processes, but each of them has less number of data to be checed. The dsadvantage s that when the mage s more parttoned, there exsts the possblty of parttonng the obects even more, all of whch adds tme of assembly of obects n the end. In order to measure the solutons performance suggested for the recognton, testng cases were generated wth mages resultng n dfferent problem szes and wth dfferent quantty of processes. The dfferent tests were grouped accordng to the mentoned characterstcs, n a way to mae the assessment more nterestng. In ths way, results were obtaned for tests grouped accordng obects quantty and for tests grouped by the sze of them. Obects dsplay was not consdered as a groupng crteron snce we are dealng wth sequences n whch obects move, and thus wthn a same test ths characterstc s not fxed obects are movng n a sector whch may be very dfferent from ther locaton at the end of the sequence. The tests regardng the recognton algorthm reveal better results than the prevous case, though always n the case of larger szed mages. For smaller mages sequences, n most of the cases, the tmes ncrease wth the process quantty (except when the mages contan large obects, but the gan s relatvely small and the effcency s so reduced that the fnal results are actually poor). Instead, for larger sze mages, the ncorporaton of processes upgrades the tmes, prncpally n the cases n whch the mages contan large obects. Also, the speedup attaned when ncorporatng a thrd process s even better that the one obtaned when gong from one process to two processes. Fnally, t remans assessng the obect tracng process. The gven soluton, represented temporarly, renders the followng stuaton: tme lne process 3 process routes updatng obects recognton process tme lne Ths s smlar to the recognton case. The dfference s gven by the processng whch must perform the master or root after each mage s analyzed. For ths, n order to deal wth the problem dmenson, the same concepts posed for that case are vald: obect quantty, dsplay, etc. Also, snce the quantty of operatons to be performed (as regards the traectores updatng) depends on the obects movement characterstcs, speed and dsparty wth whch they move wll also nfluence n the total runtme of both sequental and parallel solutons. The tas of traectory updatng, as t was already assessed, represents a very small fracton of all the nvolved tass. Because of ths, t would mae no sense dedcate a process exclusvely for t. It could be done n the presented case as an upgradng: generated mages showng graphcally the traectores drawn by the movng obects. In that case, a separated process would update the routes and would also generate those mages, obtanng the followng graphc:

11 tme lne process 3 process traectores updatng obects recognton process tme lne In order to measure the tracng process performance, mages sequences that vary the problem dmenson were generated: two or three obects sequences, sequences wth more than three obects, sequences wth slow and even movng obects, sequences wth rapd and uneven movng obects. As n the recognton case, the tests were grouped accordng to the mentoned characterstcs. On the one sde, tests grouped by movements speed and coherence (slow and even movement, moderated and even speed, hgh speed and even movement, uneven speed and coherence), and on the other, tests grouped by obects quantty. It s mportant to bear n mnd that tracng algorthm tests refer to the ntegral test whch goes from the enhancement of each ndvdual frame to the fnal result. It s not the montorng exclusve algorthm test. These tests encompass all the mages processng cycle. As the route mantenance exclusve porton s a very small part of the algorthm, and t s a tas of a sngle process, t s probable that the result wll not be reverted n respect to the prevous tests about obects enhancement and recognton over the mages. Actually, ths s what happened. Summarzng, - For small mages (n partcular, 30 x 40) t s not sutable parallelzng the algorthms snce, n proporton, the communcaton tme s greater than the one used up by each of them n order to perform the dfferent tass. Worng wth more than one process lower the tmes only when the mages obects were large, but the speedup resulted so low that, even these cases, does not deserve consderaton. - For larger mages (n partcular 70 x 540), the results were acceptable, not so much n the ntal algorthm of mages enhancement, but n partcular n that of obect recognton and, of course, n the ont test of all the system. Specally, the results were better n the cases n whch the mages had large obects n relaton to the frame sze. Fnally, when analyzng the algorthms accordng to the types of the movements of the obects, the results were better though not by a great dfference n relaton to the others. Conclusons After havng completed the mplementaton and the assessments of the descrbed algorthms, the result obtaned fulflled the presented expectatons, namely: - A soluton for dentfyng obects n an mages sequence and dentfyng the traectores of ther movements was fully developed. - The cases n whch the parallel soluton s good were dentfed as well as those cases n whch s preferable adoptng the tradtonal soluton. On the other hand, all throughout the proect, upgradngs or alternatves to the mplemented soluton were presented. They are here summed up together wth some addtonal suggestons: a) As regards the proect: - Generate addtonal mages reflectng the scene obects movement.

12 - Identfy the obects based n those features dstngushng them. In ths paper, the obects were ndvsble. Ths upgradng s completed wth a modfcaton n the tracng algorthm appearng n the obects not only due to ts poston n the consecutve frames but also to the features ndvdualzng them. - In the case that a sngle obect has to be traced, modfy the recognton algorthm n order to chec only one part of the mage dependng on where the obect has been found n the prevous frames. Ths upgrades the soluton, wthout wastng the processng tme. - Modfy or upgrade the presented algorthms n order to render a better response accordng to the dfferent sequences to be assessed. The proect s mplemented n a such way that t s easy to change any of ts parts by another one, respondng better to the requrements (e.g. t may be desred to change the mage recognton algorthm, or to wor wth another mage format). b) As regards performance - Assess how often t s necessary to perform a selecton of the threshold for the segmentaton. Gven the natural smoothness n the mages movements, t s no necessary to recompute that value for each frame snce sgnfcant changes wll not be obtaned from one mage to the followng one. However, the necessary frequency can depend on the speed of the obects movements. - Implement an alternatve n order to handle the auxlary data (labels and obects) n memory nstead of obects. Ths opton would be better n tme, but t would requre the avalablty of machnes wth enough memory. - Assess the possblty of sppng frames n the cases where t s beforehand nown that the obects n the scene move really slow; ths allows obtanng the same data wth better tmes. - For the case where t s nown that the obects are of consderable sze, mplement a varant that does not chec every pxel but taes one every two or more so as to reduce the processng. It s expected that the results do not change, but the tmes probably do. - Vary the dstrbuton of the tass among the dfferent processes; for example, that the enhancement s carred out by two processes, whle the recognton tas s performed by three. Ths dstrbuton has to do wth tang advantage of the conclusons obtaned from the performed tass. On the other hand, f more machnes are avalable, other possblty s to dstrbute the tas n a way that a group performs the enhancement and another group of processes n the other machnes performs the recognton. Also, the mplementaton can be mgrated towards an homogeneous multprocessor (for example, the transputers hypercube avalable n the Laboratory of Parallel Processng of the Faculty of Computer Scences UNLP), wth the obectve of comparng the performance on both platforms. Bblography [Al97] Al S, Parallel Computaton. Models and Methods, Prentce-Hall, Inc., 997. [Bax94] G. A. Baxes, "Dgtal Image Processng. Prncples and Applcatons", John Wley & Sons Inc., 994. [Br95] Brnch Hansen, P., Studes n computatonal scence: Parallel Programmng Paradgms, Prentce- Hall, Inc., 995. [Gon9] R. C. González, R. E. Woods, "Dgtal Image Processng", Addson-Wesley Publshng Comp., 99. [GDB95], GDB/RBD, "MPI Prmer / Developng wth LAM", The Oho State Unversty, 995. [Gup93] Gupta A., Kumar V., Performance propertes of large scale parallel systems, Journal of Parallel and Dstrbuted Computng, November 993. [Har9] R. M. Haralc, L. G. Shapro, Computer and Robot Vson, Addson-Wesley Publshng Company, 99. [Hwa93] K. Hwang, "Advanced Computer Archtecture. Parallelsm, Scalablty, Programmablty", McGraw Hll, 993. [Ja89] A. Jan, "Fundamentals of Dgtal Image Processng", Prentce Hall Inc., 989. [Ja95] R. Jan, R. Kastur, B. G. Schunc, Machne Vson, McGraw-Hll Internatonal Edtons, 995.

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