Proposal Maps driven MCMC for Estimating Human Body Pose in Static Images

Transcription

1 Proposal Maps drven MCMC for Estmatng Human Body Pose n Statc Images Mun Wa Lee and Isaac Cohen Insttute for Robotcs and Intellgent Systems Integrated Meda Systems Center Unversty of Southern Calforna Los Angeles, CA , USA {munlee, cohen}@usc.edu Abstract Ths paper addresses the problem of estmatng human body pose n statc mages. Ths problem s challengng due to the hgh dmensonal state space of body poses, the presence of pose ambguty, and the need to segment the human body n an mage. We use an mage generatve approach by modelng the human nematcs, the shape and the clothng probablstcally. These models are used for dervng a good lelhood measure to evaluate samples n the soluton space. We adopt a data-drven MCMC framewor for searchng the soluton space effcently. Our observaton data nclude the face, head-shoulders contour, sn color blobs, and rdges; and they provde evdences on the postons of the head, shoulders and lmbs. To translate these nferences nto pose hypotheses, we ntroduce the use of proposal maps, whch s an effcent way of consoldatng the evdence and generatng 3D pose canddates durng the MCMC search. As epermental results show, the proposed technque estmates the human 3D pose accurately on varous test mages. 1. Introducton Estmatng human body pose s mportant for automatc recognton of human actvtes n mage understandng applcatons. For statc mages, the major dffcultes are the hgh dmensonalty of the soluton space, pose ambguty, and body segmentaton. The human body has about 31 parameters and pose estmaton nvolves searchng n a hgh dmensonal and mult-modal soluton space. In addton, there s an nherent non-observablty of some of the degrees of freedom, causng forwards/bacwards flppng ambgutes [10] n the depths of body jonts. Ambguty s also caused by nosy or spurous mage features. The segmentaton of the human body s requred because the human boundary n an mage s dependent on the body pose, and ths boundary affects the feature etracton needed to estmate the body pose. Ths calls for a method that smultaneously solves the dualproblem of segmentaton and pose estmaton. We propose to address ths problem by buldng an mage generatve model and usng the Marov chan Monte Carlo (MCMC) framewor [2] to search the 31- D soluton space. Our human model represents the nematcs structure, shape and clothng of the human body. Gven a pose canddate, a human mage can be syntheszed and compared wth the real mage. Ths model-based approach s appealng as t sees to eplan away the data from the mage generaton standpont [14]; and t solves the segmentaton problem smultaneously. The set of samples drawn by MCMC wealy converges to a statonary dstrbuton equvalent to the posteror dstrbuton. However, wth only the use of random-wal sampler algorthm, the MCMC framewor s neffcent. The data-drven MCMC framewor [14] allows us to desgn complementary jump proposal functons, derved from mage observatons, to eplore the soluton space more effcently. Each jump dynamc has a much larger scope and allows the transtons between nonneghborng regons of hgh denstes. Useful mage observatons are obtaned from appearance-based face detecton, matchng head and shoulders contours, sn color blobs detecton, and lmbs detecton. However, these observatons only provde 2D nferences on local body parts but not the 3D pose. Also, these observatons have localzaton errors, contan false alarms, and may not be ndependent. A mechansm s needed to properly translate these observatons nto proposal dstrbutons for the 3D pose, whle addressng the above ssues. In ths paper, we descrbe the use of proposal maps to consoldate the nferences provded by the collectve set of mage observatons. Each proposal map represents the proposal dstrbuton of the mage poston of a body jont and t s used to generate proposals of 3D pose durng MCMC. We focused on mddle resoluton mages, where the body heght s about 150 pels. We mae no restrctve assumptons about the bacground, the human shape, and clothng ecept for not wearng any headwear or gloves. The paper s organzed as follows: Secton 2 dscusses related wor; Secton 3 descrbes the MCMC framewor and ts etenson to pose estmaton; the generatve model and mage observaton are presented n Sectons 4 and 5, respectvely; and Secton 6 shows epermental results. 2. Related Wor Pose estmaton n vdeo sequences has been addressed n many prevous wors, usng ether multple

2 or a sngle camera [1][9]. Many of these wors used partcle flter to trac the body poses, by relyng on a good ntalzaton, temporal smoothness, and sometmes a low dmensonal dynamc model [1]. For statc mages, some wors have been reported for recognzng prototypcal body poses usng shape contet descrptors [5], mappng of features nto body confguratons [7], and parameter-senstve hashng [8]. These wors rely on ether a clean bacground or a presegmented human regon and not sutable for automatc pose estmaton. There are reported wors on detectng body parts n mages. In [6][3], the authors model the appearance and the 2D geometrc confguraton of body parts. These methods focus on real-tme detecton of people and do not estmate the 3D body pose. Recoverng 3D pose was studed n [11], but the proposed method assumes that the mage postons of body jonts are nown and therefore smplfes the problem. 3. Estmaton Framewor 3.1. Data-Drven MCMC In ths secton, we descrbe the MCMC framewor [2][14] and ts adaptaton for pose estmaton. Denotng as the vector of model parameters and Y as the mage observatons, pose estmaton s formulated as a Bayesan nference for estmatng the posteror dstrbuton: p( Y ) p( Y ) p( ). (1) The desred output s dependent on the applcaton. A smple soluton s the mamum a posteror estmate (MAP) gven by: MAP = argma p( Y ). (2) Snce the posteror dstrbuton s mult-modal, t s often desrable to etract multple solutons of. A smple approach conssts n appromatng the posteror dstrbuton as a mture of Gaussans: p ( Y ) w N( µ, Σ). (3) MCMC s a sutable methodology for fndng these solutons by drawng samples from the posteror dstrbuton usng a Marov chan based on the Metropols- Hastngs algorthm [2]. At the t-1 th teraton, a canddate s sampled from a proposal dstrbuton q(. t 1 ) and accepted as the new state t wth a probablty a where ( ) t 1 p( Y ) q( ( t 1 ) a t 1 ) = mn 1,. p( t 1 Y ) q( t 1 ) (4) A smple proposal dstrbuton s provded by the random-wal sampler [2]. In the data-drven MCMC paradgm, mage observatons are used to generate addtonal proposals to enhance the convergence of the MCMC [14]. As the mappng of 2D mage features to 3D poses s non-trval, we desgn a proposal mechansm based on the mssng data u that represents the mage postons of body jonts (head, elbows, etc.). The observaton Y s condtonally dependent on u only,.e. p(y u,) = p(y u). In addton, u can be computed from by a determnstc functon u=f() whch s a many-to-one mappng. We can decompose u nto ts components u={u }, where u s the mage poston of the th body jont, and use local observatons, Y Y, to generate the proposal dstrbuton for ths jont, denoted by q ( u Y, t 1 ). The functon f(.) can be decomposed nto ts components f(.)={f (.)} such that u = f (). (See Fgure 1 for graphcal models of these varables.) Y f() f () u Y z (a) (b) (c) Fgure 1: Graphcal Models: (a) shows the basc model between model parameters and mage observaton Y, (b) ntroduces the mssng data u, representng mage postons of body jonts, and z representng the depth, (c) shows relatonshp between the mage poston of the th body part u, and the local observaton Y, whch s used to generate proposals. In ths fgure, u n() represents mage postons of other body jonts ecept the th, and Y n() represents the correspondng local observatons for these jonts. Usng a component-based proposal approach, the th component proposal dstrbuton for becomes: q = ( t, Y ) q ( u, t, Y ) q ( u t, Y ) du. (5) The samplng of the proposal dstrbuton s smplfed n two ways. Frst, we construct the proposal for u so that t s ndependent of the prevous sample t-1 : q( u t 1, Y ) = q( u Y ). (6) Second, we construct the proposal q( u, t 1, Y ) as a determnstc functon. Gven the prevous state t-1 and a sample u, a canddate s computed easly usng drect nverse nematcs (IK) so that the mage poston of the th body jont s shfted to u, whle all the other body jonts are left unchanged: u Y u n() Y n() Y z

3 f j ( t 1 ) when j (7) f j ( ') = u when j = When multple solutons est, due to depth ambguty, we choose the soluton wth the smallest change n depth. Due to space lmtaton, we wll not dscuss the nverse nematcs n detals. Instead, readers may refer to [10] for a dscusson. Denotng the IK computaton as a functon g(.), we have: = g( t 1, u ). (8) The proposal dstrbuton then becomes: q ( t 1, Y ) = δ ( g( t 1, u )) q ( u Y ) du, (9) where δ(.) s the Drac delta functon. We can draw a sample for, by frst drawng a sample u from q( u Y ), and computng usng Equaton (8). At each Marov chan teraton, ths step s repeated for dfferent body jont, n a parttonng approach. Sometmes there s no vald IK soluton due to nematcs and no self-penetratng constrants. (For eample, the proposed hand poston mght be too far from the elbow.) In ths case, the functon g(.) outputs an nvald state, denoted by null, whch has the property p( null )=0. The proposal drven by u s then rejected accordng to Equaton (4) Proposal Maps Ths secton dscusses the proposal mechansm for drawng a sample u ~ q( u Y ), where Y represents the observaton of the th body jont. The observaton usually ncludes false alarms and generates multple weghted hypotheses on the mage poston of the th jont. We epress Y as the set of hypotheses: Y = w, Y ; = 1,..., n }, (10) {,, wherey, represents each hypothess, w, ts confdence, and n s the number of hypotheses. The nference of each hypothess s appromated by a Gaussan dstrbuton wth mean µ, and covarance matr Σ, correspondng to the measurement uncertanty. The proposal dstrbuton for the jont mage poston derved from each hypothess s gven by: q u Y ) N( u, µ, Σ ), (11) (,,, and the contrbutons of all the hypotheses are combned as follows: q u Y ) ma{ w q( u Y )}. (12) (,, The hypotheses are, n general, not ndependent. For eample, matchng the head-shoulders contour to mage edges usually results n multple local mnma. In addton, the hypotheses are generated usng dfferent types of mage cues and ths leads to redundancy. We therefore use the ma functon n Equaton (12) nstead of the summaton to avod eaggerated domnant peas. We present n ths secton a method for mprovng samplng effcency. The proposal dstrbuton s appromated by a grd space representaton called the proposal map, wth samples correspondng to every pel poston. The proposal dstrbuton s thus correctly bounded wthn the mage. As ths dstrbuton s unchanged durng the MCMC process, t s computed beforehand. Ignorng the quantzaton nose (whch s small compared to the measurement errors), ths proposal s reversble: for any vald proposal jump, there s another vald reverse jump because the functon g(.) n Equaton (8) has a one-to-one mappng. In Fgure 2 we show the grey level representaton of the proposal maps for varous body jonts. They are generated from mage observatons that we wll descrbe n Secton Other Proposal Mechansms The Marov chan dynamc conssts of three types of proposals: () data-drven proposal, whch was descrbed earler, () random-wal sampler, and () flp nematcs jump. The last two are brefly descrbed here. Random-wal Sampler. Ths process serves as a local optmzer and the correspondng proposal dstrbuton s gven by: q ) N(,0, Σ ). (13) ( t 1 t 1 dffuson Flp Knematc Jump. Ths dynamc nvolves flppng a body part (.e. head, hand, lower arm, entre arm, lower leg, or entre leg) along the depth drecton, around ts pvotal jont [10]. Flp dynamc s balanced so that forward and bacward flps have the same proposal probablty.

4 Image Head Nec Hp Left Shoulder Rght Shoulder Left Elbow Rght Elbow Left Hand Rght Hand Left Knee Rght Knee Left Anle Rght Anle Fgure 2: Grey level representaton of proposal maps for varous body jonts (overlad on edge mage for clarty). 4. Generatve Model 4.1. Human Model The human model s an eplct representaton of the human body structure. It defnes the pose parameters as well as the parameters for shape and clothng. Human Knematcs Model. Ths model represents the artculated structure of the human body and has 31 degrees of freedom. The pose s descrbed by a 6D vector g representng global poston, scale, and orentaton, and a 25D vector j representng the jont angles. We assumed an orthographc projecton. The pror dstrbutons of these parameters, denoted by p(g) and p(j), are learned from the tranng data. For smplcty, these dstrbutons are appromated as Gaussans and the jont angles of non-neghborng body locatons are assumed to be ndependent. Probablstc Shape Model. Each human body part s represented by a truncated 3D cone and the shape of the human s represented by a vector s whch has 23 parameters descrbng the relatve lengths and wdths of these 3D cones. PCA s used to reduce the shape space to 6 dmensons. The pror dstrbuton p(s) s assumed to be Gaussan. Clothng Model. Ths model descrbes the type of clothng the person s wearng and allows the predcton of whether sn s eposed so that sn blob features are correctly nterpreted. As there are many clothng types, the modelng requres a trade-off between generalty and smplcty. The clothng model has 3 parameters, c = [c 1 c 2 c 3 ] T, representng the sleeve length, the hem length, and the socs length. For computaton effcency, these parameters are quantzed nto coarse dscrete levels (5 levels for c 1, and 10 levels for c 2 and c 3 ). The pror dstrbuton, P(c), s learned from the tranng data Pror Dstrbuton The parameters from the varous components of the human model are combned nto a complete state vector, now consstng of four subsets: = { g, j, s, c }. (14) For smplcty, we assume that the subsets of parameters are ndependent and the pror dstrbuton, denoted by p(), s gven by: p() p(g) p(j) p(s) P(c). (15) Ths pror dstrbuton s combned wth the mage lelhood functon to form the posteror densty functon, whch s used for evaluatng samples and computng the acceptance probablty for the Marov chan, as gven by Equaton (4). The followng sub-secton descrbes the mage lelhood functon Image Lelhood Functon The mage lelhood functon p(y ) conssts of two components, based on regon and color respectvely. Ths approach s motvated by the wor n [15] where smlar lelhood measure s used for segmentng multple persons n statc mage. Regon Lelhood. Color-based segmentaton s used to dvde a gven mage nto a set of regons denoted by

5 {R ; = 1,..., N regon }, where N regon s the number of regons. For a gven state canddate, we predct the human body regon n the mage, denoted by H. Ideally, ths human regon wll concde wth the unon of a certan subset of the segmented regons. In other words, each regon R should ether belong to the human regon H or to the bacground (non-human) regon, denoted by H. Ths regon lelhood functon measures the degree of smlarty between the human body and the segmented regons. For each segmented regon R, we count the number of pels n R, that belong to H, and that belong to H : N,human = count pels (u,v) { R H, } N,bacground = count pels (u,v) { R H } (16) We defne a bnary label, l, for each regon, so that 1 f N, human N (17), bacground l =. 0 otherwse We count the number of ncoherent pels, denoted by N ncoherent, gven by: Nregon l (1 l ) N = N N. (18) ncoherent ( ) ( human ), bacgruond, = 1 The regon-based lelhood functon s defned by: L regon = ep( λ N ), (19) regon ncoherent where λ regon (=0.2) s a constant determned emprcally wth tranng data usng a Posson model. Color Lelhood. The lelhood measures the dssmlarty between the color dstrbutons of the human regon H and the bacground regon H. Gven the predcted regon H, and H, we obtan the color dstrbuton of human regon d, and bacground regon b. They are represented by normalzed hstograms wth N hstogram bns. The color lelhood s defned by: 2 Lcolor = ep( λcolor B d, b ), (20) where λ color (=30) s a constant determned emprcally and B d,b s the Bhattachayya coeffcent measurng the smlarty of two color dstrbutons gven by: N hstogram (21) B = d b. d, b = 1 The combned lelhood measure s gven by: p ( Y ) = L regon L color. (22) 5. Image Observatons Image observatons are used to compute the proposal maps descrbed n Secton 3. These are local observatons used to nfer postons of varous body jonts, and they are weghted accordng to ther salency and jont probabltes. These observatons are etracted n 4 stages: () face detecton; () head-shoulders contour matchng; () sn blobs detecton; and (v) rdges detecton Face Detecton The AdaBoost cascade classfcaton technque [13] s used for detectng faces n the mage. Each detected face provdes a hypothess of the head poston. As the face consttutes the most relable observaton, the detected face s used to ntate the etracton of other mage observatons Head-Shoulders Contour Matchng An actve shape model approach s used to detect the head and shoulders contour usng a deformable shape model. The face observaton s used to defne a search regon wthn whch multple canddates for the headshoulders contour are detected usng a gradent descent search that algns the shape model to mage edges. Each detected contour provdes hypotheses on the postons of head, nec and shoulders (Fgure 3.b), usng a jont probablstc model of these varables. The edge matchng error s used to adjust the confdence weght of each hypothess. (a) (b) (c) (d) Fgure 3: Image observatons: (a) bo ndcates the detected face; (b) outlne ndcates one of the detected head-shoulders contour, ellpses ndcate the correspondng hypotheses for head, left and rght shoulders, and the ellpse sze represents measurement uncertanty; (c) a grey-level map of sn probablty wth etracted sn ellpses; and (d) whte pels ndcate rdges for the lower body Ellptcal Sn Blob Detecton Sn color features provde mportant cues about the postons of the arms and sometmes the legs. Sn blobs are detected n four sub-stages: () the mage s dvded nto regons usng a color-based mage segmentaton; () for each segmented regon, the probablty of sn s evaluated usng a hstogram-based sn color model; () ellpses are ftted to the boundary of these regons to form sn ellpse canddates; and fnally (v) adjacent regons wth hgh sn probabltes are merged to form larger regons and etract larger ellpses (see Fgure 3.c). The etracted sn ellpses are used for nferrng the postons of lmbs. Further detals are gven n [4].

6 5.4. Rdge Observatons In addton to sn color blobs, another type of observatons useful for the segmentaton of the lmbs s based on rdges. If most of the lmbs are clothed, especally the lower body, sn color blobs are less useful and rdge observatons are more reled upon. The centers of the rdges provde hypotheses on the medal as ponts of the lmbs and therefore provde nference on the poston of the legs. Ths approach s motvated by the wor n [3] where lmbs are detected as rectangular segments. In the followng, we dscuss two aspects of the observatons: () the detecton of rdges, and () the computaton of confdence weghts for these observatons. Detecton of Rdges. We etract the medal as ponts of mage regons derved from color-based segmentaton. Snce the lower body lmbs are usually not horzontal, the medal as ponts are easly etracted by scannng each horzontal lne n the mage to fnd the centers of each regon along the lne. To overcome errors due to mperfect color segmentaton, we frst use an over-segmented mage to fnd the frst set of medal as ponts. We then merge neghborng regons wth smlar color and etract addtonal medal as ponts on the new regons. Ths method etracts many medal as ponts effcently. Confdence weght. Each etracted pont s weghted by a confdence measure based on the followng crterons: () the lelhood of the pont beng on the medal as of the leg, () the lelhood of the regon (to whch the pont belongs) beng a subset of the leg, and () the lelhood of the wdth of the regon. In order to compute these lelhoods, we need frst a jont probablty model, learned from tranng data, of the postons of the legs and the poston of the torso. Estmates of the torso poston are provded by headshoulder contour matchng. The confdence measures are used to prune out some of the medal as ponts wth low confdence (Fgure 3.d). We use the remanng ponts and the correspondng weghts to generate the proposal maps for the nees and anles, as descrbed n Secton 3. Fgure 2 shows eamples of proposal maps for lower body jonts. These dstrbutons are generally more dffused, as the observatons are less relable. Because each observaton could be assocated to ether sde of the lmbs, the maps for the left and rght legs are smlar to some etent. Nonetheless, the proposal maps do capture dfferent regons of hgh denstes to ndcate plausble postons of legs and allow for proposal jumps to eplore these regons durng Marov chan teratons. 6. Eperments Database and Ground Truth. We used a set of mages representng varous human actvtes on whch we have generated ground truth by manually locatng jont postons and estmatng ther relatve depths. Among ths set, we chose a subset for tranng (prmarly for learnng the pror dstrbutons of model parameters), and the rest for testng the proposed method. Ths second subset s used for the eperments descrbed n ths secton. The eperments were conducted wthout any manual pre-processng such as bacground removal, scalng and centerng of the person, or model ntalzaton. At the start of the MCMC search, the human model was ntalzed n a standard uprght pose n the center of the mage. Pose Estmaton. Fgure 4 shows the obtaned 3D pose estmaton on varous mages from the test set after 1000 Marov chan teratons. The estmated human model and ts pose (the MAP soluton) are projected onto the mage and a 3D renderng from a sdeward vew s also shown to llustrate the depth estmaton. Some small errors are observed and dscussed n the fgure capton; these are mostly due to the lac of mage observable or features. The overall 3D pose estmaton s good on ths challengng set of mages. The estmated jont postons were compared wth the ground truth data, and a RMS error was computed usng all body jonts. Snce the depth has a hgher uncertanty, we have computed two separate RMS errors: one for the 2D poston and the other for the depth. We computed the average of these errors over all test mages (average RMS error); the result (based on 20 mages) s gven n Table 1. As the posteror dstrbuton s mult-modal, the MAP soluton may be nsuffcent. As an alternatve measure, we appromated the posteror dstrbuton as a mture model by clusterng the samples usng -mean algorthm (we used =20). (An alternatve technque s the greedy K-adventurers algorthm [12] whch updates the mture model after each teraton.).

7 A B C D E F Fgure 4: Pose Estmaton. 1st Row: Orgnal mages, 2nd row: estmated poses, 3rd row: sde vew. Due to space lmtaton, the mages were cropped for dsplay. Errors nclude: (1) the person s left lower leg n mage A, as t s mostly hdden, (2) the left arm n B, where the elbow s hghly bent, (3) the left foot n C whch s dar and smlar to bacground, (4) the feet n E s wrongly estmated to be tp-toed. In addton, there are errors n depth estmates such as the rght elbow n B, the tltng of the torso n B, the left feet n C, and the rght arm n D. The clusters were raned by ther sample szes. Usng the estmated cluster means, average RMS errors were computed based on Ran 5, 10, 15 crterons. (For eample, Ran 5 result was obtaned by fndng the lowest error among the fve hghest raned cluster means.) These results, presented n Table 1, show that the mture model captures better estmates of the pose, especally the depth estmates. Good pose estmates are usually found wthn the 5 hghest raned components. Average RMS Error (pel) (mage poston) (depth) MAP Soluton Mture Ran Model Ran Soluton Ran Table 1. Average RMS errors n mage poston and depth, usng MAP solutons and mture model soluton. To eamne the spread of the RMS errors among test mages, Fgure 5 shows a hstogram of these errors usng Ran 5 results. Convergence Analyss. Fgure 6 shows the RMS errors wth respect to the MCMC teratons. The error for the 2D mage poston decreases rapdly from the start of the MCMC process; ths s due largely to the observaton-drven proposal dynamcs. For the depth estmate, the nematcs flp dynamc s helpful for fndng good depth estmates, but t requres a longer tme for eploraton. In the current mplementaton, 1000 teratons were consdered and t too, on average, 8 mnutes. 7. Concluson We have presented a data-drven MCMC framewor for estmatng 3D human pose n statc mages. Image observatons of dfferent cues provde nferences on the mage postons of body jonts. We ntroduce the use of proposal map as an effectve mechansm to consoldate these nferences and generate 3D pose canddates for MCMC. As the results show, the technque s effectve on a wde varety of mages.

8 Occurence RM S Er ror (pe l) Image Poston Depth RMS Error (pel) Image Poston Depth Iteratons Fgure 5: Hstogram of Average RMS Error (usng Ran 5 result). Fgure 6: Convergence Analyss (usng Ran 5 result). Note that the relatve depth estmate has no global offset and therefore has smaller error at the start of teraton compared to mage poston. The system currently has two man lmtatons. Frstly, the technque requres a good face detecton algorthm. The face detecton method used s relable only for frontal faces. Secondly, the computatonal cost s stll qute hgh, even wth the use of data-drven proposal. As future wor, we are eplorng better technques to detect non-frontal faces. In addton, we are desgnng technques based on gradent-based dffuson and Gbbs samplng to mprove the effcency of the MCMC algorthm. Acnowledgment Ths research was partally funded by the Integrated Meda Systems Center, a Natonal Scence Foundaton Engneerng Research Center, under Cooperatve Agreement No. EEC , and by the Advanced Research and Development Actvty of the U.S. Government under contract: MDA C References [1] K. Choo, D.J. Fleet. People tracng wth hybrd Monte Carlo, ICCV 2001, pp [2] W. Gls, S. Rchardson, D. Spegelhalter. Marov Chan Monte Carlo n Practce. Chapman and Hall, [3] S. Ioffe and D.A. Forsyth. Probablstc methods for fndng people, IJCV 43(1), pp.45-68, June [4] M. Lee, I. Cohen. Human Upper Body Pose Estmaton n Statc Images. ECCV [5] G. Mor, J. Mal. Estmatng Human Body Confguratons usng Shape Contet Matchng. ECCV 2002, pp [6] R. Ronfard, C. Schmd, and B. Trggs. Learnng to parse pctures of people. ECCV 2002, vol. 4, pp [7] Rosales, R.; Sclaroff, S. Inferrng body pose wthout tracng body parts, CVPR 2000, pp [8] G. Shahnarovch, P. Vola, and T. Darrell. Fast Pose Estmaton wth Parameter Senstve Hashng, ICCV 2003, pp [9] C. Smnchsescu, B. Trggs. Covarance Scaled Samplng for Monocular 3D Body Tracng, CVPR 2001, [10] C. Smnchsescu, B. Trggs. Knematc Jump Processes for Monocular Human Tracng, CVPR 2003, pp [11] C.J. Taylor. Reconstructon of artculated objects from pont correspondences n a sngle uncalbrated mage. CVIU 80(3): , December [12] Z. Tu and S. Zhu, Image Segmentaton by Data-Drven Marov Chan Monte Carlo, PAMI 24(5), pp , [13] P. Vola, M. Jones. Rapd object detecton usng a boosted cascade of smple features, CVPR 2001, pp [14] S. Zhu, R. Zhang, Z. Tu. Integratng bottom-up/top-down for object recognton by data drven Marov chan Monte Carlo, CVPR 2000, pp [15] T. Zhao, R. Nevata. Bayesan Human Segmentaton n Crowded Stuatons, CVPR 2003, pp