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  • Real Time Face Tracking Using PF MEANSHIFT.pdf
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sc0">r</span><span class="fc1 sc0">ocee</span><span class="fc1 sc0">din</span><span class="fc1 sc0">g</span><span class="fc1 sc0">s</span><span class="_ _0"></span><span class="fc1 sc0"> o</span><span class="fc1 sc0">f</span><span class="fc1 sc0"> th</span><span class="fc1 sc0">e IEEE </span><span class="_"> </span><span class="fc1 sc0"> </span></div><div class="t m0 x6 h5 y7 ff2 fs3 fc0 sc0 ls4 ws3"><span class="fc1 sc0">In</span><span class="fc1 sc0">tern</span><span class="fc1 sc0">atio</span><span class="fc1 sc0">n</span><span class="fc1 sc0">a</span><span class="fc1 sc0">l Co</span><span class="fc1 sc0">n</span><span class="fc1 sc0">f</span><span class="fc1 sc0">ere</span><span class="fc1 sc0">n</span><span class="fc1 sc0">ce o</span><span class="fc1 sc0">n</span><span class="fc1 sc0"> </span><span class="_ _0"></span><span class="fc1 sc0">Au</span><span class="fc1 sc0">to</span><span class="fc1 sc0">m</span><span class="fc1 sc0">a</span><span class="fc1 sc0">t</span><span class="fc1 sc0">i</span><span class="fc1 sc0">o</span><span class="fc1 sc0">n</span><span class="fc1 sc0"> an</span><span class="fc1 sc0">d</span><span class="fc1 sc0"> </span><span class="fc1 sc0">L</span><span class="fc1 sc0">o</span><span class="fc1 sc0">g</span><span class="fc1 sc0">i</span><span class="fc1 sc0">stic</span><span class="fc1 sc0">s</span><span class="fc1 sc0"> </span></div><div class="t m0 x7 h5 y8 ff2 fs3 fc0 sc0 ls5 ws4"><span class="fc1 sc0">Q</span><span class="fc1 sc0">i</span><span class="fc1 sc0">ng</span><span class="fc1 sc0">dao, C</span><span class="_ _0"></span><span class="fc1 sc0">h</span><span class="fc1 sc0">i</span><span class="fc1 sc0">n</span><span class="fc1 sc0">a S</span><span class="fc1 sc0">e</span><span class="fc1 sc0">pt</span><span class="fc1 sc0">e</span><span class="fc1 sc0">m</span><span class="_ _0"></span><span class="fc1 sc0">ber 2008</span><span class="fc1 sc0"> </span></div><div class="t m0 x8 h6 y9 ff3 fs4 fc0 sc0 ls6 ws5">Real Time Face Tracking Using </div><div class="t m0 x9 h6 ya ff3 fs4 fc0 sc0 ls7 ws6">Particle Filtering and Mean Shift </div><div class="t m0 xa h7 yb ff4 fs5 fc0 sc0 ls0 ws0">Fan</div><div class="c xa yc w2 h8"><div class="t m0 xb h7 yd ff4 fs5 fc0 sc0 ls0 ws0">g</div></div><div class="t m0 xc h7 yb ff4 fs5 fc0 sc0 ls8 ws7"> Xu </div><div class="t m0 xd h9 ye ff4 fs6 fc0 sc0 ls9 ws0">[1][2] </div><div class="t m0 xe h7 yb ff4 fs5 fc0 sc0 lsa ws8">and Jun Chen</div><div class="c xe yc w3 h8"><div class="t m0 xf h7 yd ff4 fs5 fc0 sc0 ls0 ws0">g</div></div><div class="t m0 x10 h9 ye ff4 fs6 fc0 sc0 ls9 ws0">[2]</div><div class="t m0 x11 ha yf ff5 fs5 fc0 sc0 ls0 ws0">Chao Wang</div><div class="t m0 x12 hb y10 ff5 fs6 fc0 sc0 lsb ws0">[1]</div><div class="t m0 xf hc y11 ff6 fs7 fc0 sc0 lsc ws9">[1]Depart<span class="_ _0"></span>ment of Sof<span class="_ _0"></span>tware, School of N<span class="_ _0"></span>ankai Univer<span class="_ _0"></span>sity <span class="_ _1"> </span>[1]Depart<span class="_ _0"></span>ment of Sof<span class="_ _0"></span>tware, School of N<span class="_ _0"></span>ankai Univer<span class="_ _0"></span>sity</div><div class="t m0 x13 hd y12 ff5 fs7 fc0 sc0 lsd wsa">[2]Shenzhen<span class="_ _2"></span> Institute of Advanced Integration Technolo<span class="_ _2"></span>gy, </div><div class="t m0 x14 he y13 ff3 fs8 fc0 sc0 lse ws0">wangchao@nankai.<span class="_ _2"></span>edu.cn</div><div class="t m0 xf hc y14 ff6 fs7 fc0 sc0 lsf wsb">Chinese Academy of Sciences/<span class="_ _0"></span>The Chinese University of </div><div class="t m0 xd hd y15 ff5 fs7 fc0 sc0 ls10 wsc">Hong Kong</div><div class="t m0 x1 he y16 ff3 fs8 fc0 sc0 ls11 wsd">{fang.xu, jun.cheng}@siat.ac.cn</div><div class="t m0 x4 hf y17 ff7 fs9 fc0 sc0 ls12 wse">Abstract- Particle fil<span class="_ _0"></span>ter is widely<span class="_ _0"></span> used in ob<span class="_ _0"></span>ject tracking<span class="_ _0"></span>. Howeve<span class="_ _0"></span>r, </div><div class="t m0 x4 hf y18 ff7 fs9 fc0 sc0 ls13 wsf">it has one no<span class="_ _2"></span>table weakn<span class="_ _2"></span>esses that is sam<span class="_ _2"></span>ple degeneracy p<span class="_ _2"></span>roblem. </div><div class="t m0 x4 hf y19 ff7 fs9 fc0 sc0 ls14 ws10">This pape<span class="_ _0"></span>r pro<span class="_ _0"></span>poses a n<span class="_ _0"></span>ovel al<span class="_ _0"></span>gorith<span class="_ _0"></span>m to ove<span class="_ _0"></span>rcome this<span class="_ _0"></span> proble<span class="_ _0"></span>m by </div><div class="t m0 x4 hf y1a ff7 fs9 fc0 sc0 ls15 ws11">incorporatin<span class="_ _0"></span>g mean shif<span class="_ _0"></span>t into pa<span class="_ _0"></span>rticle filtering. Me<span class="_ _0"></span>an shift reacti<span class="_ _0"></span>ng </div><div class="t m0 x4 hf y1b ff7 fs9 fc0 sc0 ls16 ws12">on samp<span class="_ _2"></span>le herds the samp<span class="_ _2"></span>les in the reference m<span class="_ _2"></span>od<span class="_ _2"></span>e area, which </div><div class="t m0 x4 hf y1c ff7 fs9 fc0 sc0 ls17 ws13">could make le<span class="_ _0"></span>ss samples be u<span class="_ _0"></span>sed while trackin<span class="_ _0"></span>g. The propo<span class="_ _0"></span>sed </div><div class="t m0 x4 hf y1d ff7 fs9 fc0 sc0 ls12 ws14">algorithm is<span class="_ _0"></span> used in fac<span class="_ _0"></span>e track<span class="_ _0"></span>ing. Results de<span class="_ _0"></span>monstrate that <span class="_ _0"></span>our </div><div class="t m0 x4 hf y1e ff7 fs9 fc0 sc0 ls18 ws15">approac<span class="_ _0"></span>h has<span class="_ _0"></span> better<span class="_ _0"></span> perfor<span class="_ _0"></span>mance tha<span class="_ _0"></span>n that<span class="_ _0"></span> of the<span class="_ _0"></span> mean<span class="_ _0"></span> shift<span class="_ _0"></span> </div><div class="t m0 x4 hf y1f ff7 fs9 fc0 sc0 ls19 ws16">tracker and t<span class="_ _0"></span>he conventiona<span class="_ _0"></span>l particle filter. Moreove<span class="_ _0"></span>r, the </div><div class="t m0 x4 hf y20 ff7 fs9 fc0 sc0 ls1a ws17">computation<span class="_ _0"></span> time in each fr<span class="_ _0"></span>ame is less than <span class="_ _0"></span>that of the<span class="_ _0"></span> mean shift </div><div class="t m0 x4 hf y21 ff7 fs9 fc0 sc0 ls1b ws18">tracker or the c<span class="_ _0"></span>onventional p<span class="_ _0"></span>article filter. </div><div class="t m0 x4 h10 y22 ff8 fs9 fc0 sc0 ls1c ws19">Keywords<span class="_ _0"></span>- particle filte<span class="_ _0"></span>r mean s<span class="_ _0"></span>hift embed s<span class="_ _0"></span>amples </div><div class="t m0 x15 h11 y23 ff3 fs7 fc0 sc0 ls1d ws0">I.<span class="_ _3"> </span>I<span class="fsa ls1e">NTRODUCTION</span></div><div class="t m0 x16 h11 y24 ff3 fs7 fc0 sc0 ls1f ws1a">With the rapid enhancement of computational power, </div><div class="t m0 x4 h11 y25 ff3 fs7 fc0 sc0 ls1f ws1b">object tracking h<span class="_ _0"></span>as been an active research area in the </div><div class="t m0 x4 h11 y26 ff3 fs7 fc0 sc0 ls20 ws1c">computer vision in recen<span class="_ _0"></span>t <span class="_ _2"></span>years. It plays<span class="_ _0"></span> an important role in </div><div class="t m0 x4 h11 y27 ff3 fs7 fc0 sc0 ls20 ws1d">robot tracking<span class="_ _0"></span>, monitoring and surveillance systems, virtual </div><div class="t m0 x4 h11 y28 ff3 fs7 fc0 sc0 ls21 ws1e">sport, hum<span class="_ _0"></span>an-computer interfaces, and etc. </div><div class="t m0 x16 h11 y29 ff3 fs7 fc0 sc0 ls22 ws1f">Three comm<span class="_ _0"></span>on approaches are widely used in<span class="_ _0"></span> object </div><div class="t m0 x4 h11 y2a ff3 fs7 fc0 sc0 ls1f ws20">tracking. One is based on Kalman f<span class="_ _0"></span>ilter or extended Kalman </div><div class="t m0 x4 h11 y2b ff3 fs7 fc0 sc0 ls1f ws1a">filter [13,14]. Som<span class="_ _0"></span>e researchers use mean shift tracker or </div><div class="t m0 x4 h11 y2c ff3 fs7 fc0 sc0 ls23 ws21">snake as the comparison model. Kal<span class="_ _2"></span>man filter assumes that the </div><div class="t m0 x4 h11 y2d ff3 fs7 fc0 sc0 ls24 ws22">probabilit<span class="_ _2"></span>y distributions of the states are Gaussian. However, </div><div class="t m0 x4 h11 y2e ff3 fs7 fc0 sc0 ls25 ws23">in real tracking, many<span class="_ _0"></span> factors lead the tracking states to </div><div class="t m0 x4 h11 y2f ff3 fs7 fc0 sc0 ls26 ws24">distribu<span class="_ _0"></span>te non-Gaussi<span class="_ _0"></span>an and non-lineari<span class="_ _0"></span>ty. Another is mean </div><div class="t m0 x4 h11 y30 ff3 fs7 fc0 sc0 ls20 ws25">shift [2, 4, 16] w<span class="_ _0"></span>hich is a robust non-parametric m<span class="_ _0"></span>ethod for </div><div class="t m0 x4 h11 y31 ff3 fs7 fc0 sc0 ls27 ws26">climbi<span class="_ _2"></span>ng den<span class="_ _2"></span>sity gr<span class="_ _2"></span>adients t<span class="_ _2"></span>o find<span class="_ _2"></span> the pea<span class="_ _2"></span>k of pr<span class="_ _2"></span>obabilit<span class="_ _2"></span>y </div><div class="t m0 x4 h11 y32 ff3 fs7 fc0 sc0 ls28 ws27">model. Mean-Shif<span class="_ _0"></span>t tracker is a real-time algorithm that </div><div class="t m0 x4 h11 y33 ff3 fs7 fc0 sc0 ls1f ws28">endeavors to m<span class="_ _0"></span>aximize the correlation between two st<span class="_ _0"></span>atistical </div><div class="t m0 x4 h11 y34 ff3 fs7 fc0 sc0 lsf ws29">distributions<span class="_ _0"></span>. The correlation, <span class="ls29 ws2a">or sim<span class="_ _0"></span>ilarity between two </span></div><div class="t m0 x4 h11 y35 ff3 fs7 fc0 sc0 ls2a ws2b">distributions<span class="_ _0"></span> is expressed as a measurement deriv<span class="_ _0"></span>ed from the </div><div class="t m0 x4 h11 y36 ff3 fs7 fc0 sc0 ls2b ws2c">Bhattacharyya coefficient. Gen<span class="_ _0"></span>eral distributions may u<span class="_ _0"></span>se </div><div class="t m0 x4 h11 y37 ff3 fs7 fc0 sc0 ls2c ws2d">color, or texture or combine both. But sometimes it falls into </div><div class="t m0 x4 h11 y38 ff3 fs7 fc0 sc0 ls2d ws2e">local extrem<span class="_ _0"></span>e value so w<span class="_ _0"></span>e can n<span class="_ _0"></span>ot find what w<span class="_ _0"></span>e need. Third, </div><div class="t m0 x4 h11 y39 ff3 fs7 fc0 sc0 ls20 ws2f">particle filter [1, 3, 5, 8],<span class="_ _0"></span> as a widely used approach in<span class="_ _0"></span> object </div><div class="t m0 x4 h11 y3a ff3 fs7 fc0 sc0 ls28 ws30">tracking, is well suited to estimate state<span class="_ _2"></span> of non-linear, non-</div><div class="t m0 x4 h11 y3b ff3 fs7 fc0 sc0 ls2e ws31">Gaussian dy<span class="_ _0"></span>namic systems<span class="_ _0"></span>. A common problem<span class="_ _0"></span> with particl<span class="_ _0"></span>e </div><div class="t m0 x4 h11 y3c ff3 fs7 fc0 sc0 ls20 ws32">filtering techniques is the degeneracy problem [3], wh<span class="_ _0"></span>ich </div><div class="t m0 x4 h11 y3d ff3 fs7 fc0 sc0 ls2f ws33">cause the distribution concentrating on a relatively small </div><div class="t m0 x4 h11 y3e ff3 fs7 fc0 sc0 ls30 ws34">subset of sa<span class="_ _2"></span>mple<span class="_ _2"></span>s, thus <span class="_ _2"></span>making t<span class="_ _2"></span>he use<span class="_ _2"></span>ful info<span class="_ _2"></span>rmatio<span class="_ _2"></span>n to be </div><div class="t m0 x4 h11 y3f ff3 fs7 fc0 sc0 ls2a ws35">carried by<span class="_ _0"></span> only a sm<span class="_ _0"></span>all subset of<span class="_ _0"></span> samples wi<span class="_ _0"></span>th significant </div><div class="t m0 x4 h11 y40 ff3 fs7 fc0 sc0 ls2b ws36">weights. To solve this prob<span class="_ _0"></span>lem, there are three k<span class="_ _0"></span>inds of </div><div class="t m0 x4 h11 y41 ff3 fs7 fc0 sc0 ls31 ws37">methods to ov<span class="_ _0"></span>ercome the degen<span class="_ _0"></span>eracy problem: the first is </div><div class="t m0 x4 h11 y42 ff3 fs7 fc0 sc0 ls32 ws38">resampling which is widely used [6, 12<span class="_ _0"></span>]. It selects the large </div><div class="t m0 x17 h11 y43 ff3 fs7 fc0 sc0 ls25 ws39">weights samples and eliminates the small weights ones. It can </div><div class="t m0 x17 h11 y44 ff3 fs7 fc0 sc0 ls21 ws3a">reduce the ef<span class="_ _0"></span>fects of degen<span class="_ _0"></span>erac<span class="_ _2"></span>y phen<span class="_ _0"></span>omenon but introduces </div><div class="t m0 x17 h11 y45 ff3 fs7 fc0 sc0 ls21 ws3b">the samples poor pro<span class="_ _0"></span>blems as well. The s<span class="_ _0"></span>econd one is choice </div><div class="t m0 x17 h11 y46 ff3 fs7 fc0 sc0 ls22 ws3c">of importance dens<span class="_ _0"></span>ity. The importance density is proposed as<span class="_ _0"></span> </div><div class="t m0 x17 h11 y47 ff3 fs7 fc0 sc0 ls33 ws3d">a mixture den<span class="_ _0"></span>sity that depends upon th<span class="_ _0"></span>e past state and the </div><div class="t m0 x17 h11 y48 ff3 fs7 fc0 sc0 ls34 ws3e">most<span class="_ _0"></span> recent observations<span class="_ _0"></span> [17]. Third, em<span class="_ _0"></span>bedding mean sh<span class="_ _0"></span>ift or </div><div class="t m0 x17 h11 y49 ff3 fs7 fc0 sc0 ls33 ws3f">camshift in the particle filter is proposed by Shen and Wei [6]. </div><div class="t m0 x17 h11 y4a ff3 fs7 fc0 sc0 ls2d ws40">They advanced MSEPF(Mean Shift Embedded Particle Filter) </div><div class="t m0 x17 h11 y4b ff3 fs7 fc0 sc0 ls20 ws41">to herd sam<span class="_ _0"></span>ples <span class="_ _2"></span>using mean shift s<span class="_ _0"></span>earch, so it can concentrates </div><div class="t m0 x17 h11 y4c ff3 fs7 fc0 sc0 ls35 ws42">on samples with large weights. The MSEPF can eff<span class="_ _0"></span>icientl<span class="_ _2"></span>y </div><div class="t m0 x17 h11 y4d ff3 fs7 fc0 sc0 ls36 ws43">maintain multiple <span class="_ _2"></span>modes in the posterio<span class="_ _2"></span>r density. </div><div class="t m0 x18 h11 y4e ff3 fs7 fc0 sc0 ls22 ws44">The proposed algorithm<span class="_ _0"></span> is also based on the mean sh<span class="_ _0"></span>ift </div><div class="t m0 x17 h11 y4f ff3 fs7 fc0 sc0 ls37 ws45">and particle filter which ov<span class="_ _0"></span>erco<span class="_ _2"></span>mes the degen<span class="_ _0"></span>eracy problem </div><div class="t m0 x17 h11 y50 ff3 fs7 fc0 sc0 ls1f ws46">effectively. This alg<span class="_ _0"></span>orithm absorbs th<span class="_ _0"></span>e advantages of th<span class="_ _0"></span>e mean </div><div class="t m0 x17 h11 y51 ff3 fs7 fc0 sc0 ls24 ws47">shift and particle filter. In this algorithm, samples are </div><div class="t m0 x17 h11 y52 ff3 fs7 fc0 sc0 ls2c ws48">distributed based o<span class="_ _2"></span>n the po<span class="_ _2"></span>sterior prob<span class="_ _2"></span>ability density, this </div><div class="t m0 x17 h11 y53 ff3 fs7 fc0 sc0 ls38 ws49">means so<span class="_ _2"></span>me sa<span class="_ _2"></span>mples <span class="_ _2"></span>which <span class="_ _2"></span>ma<span class="_ _2"></span>y have a long d<span class="_ _2"></span>istance<span class="_ _2"></span> fro<span class="_ _2"></span>m the<span class="_ _2"></span> </div><div class="t m0 x17 h11 y54 ff3 fs7 fc0 sc0 ls37 ws45">reference m<span class="_ _0"></span>ode area. We use mean shift to s<span class="_ _0"></span>earch the most </div><div class="t m0 x17 h11 y55 ff3 fs7 fc0 sc0 ls25 ws4a">similar area in each s<span class="_ _0"></span>amples and renew each samples center </div><div class="t m0 x17 h11 y56 ff3 fs7 fc0 sc0 ls39 ws4b">with mean shift search. Most sa<span class="_ _2"></span>mples in this algorithm gat<span class="_ _2"></span>her </div><div class="t m0 x17 h11 y57 ff3 fs7 fc0 sc0 ls3a ws4c">to modes of ob<span class="_ _2"></span>servation, so<span class="_ _2"></span> most sa<span class="_ _2"></span>mples have lar<span class="_ _2"></span>ge weights.<span class="_ _2"></span> </div><div class="t m0 x17 h11 y58 ff3 fs7 fc0 sc0 ls3b ws4d">It solves the problems of particle filtering and mean shift </div><div class="t m0 x17 h11 y59 ff3 fs7 fc0 sc0 ls2d ws4e">effectively. <span class="_ _0"></span>Because most s<span class="_ _0"></span>amples have large w<span class="_ _0"></span>eight, it can </div><div class="t m0 x17 h11 y5a ff3 fs7 fc0 sc0 lsc ws4f">hold m<span class="_ _0"></span>odes divers<span class="_ _0"></span>iform in the poste<span class="_ _0"></span>rior density<span class="_ _0"></span> using<span class="_ _0"></span> fewer </div><div class="t m0 x17 h11 y5b ff3 fs7 fc0 sc0 ls2c ws50">samples, resultin<span class="_ _2"></span>g in low computa<span class="_ _2"></span>tional cost. Gao and Y<span class="_ _2"></span>ang </div><div class="t m0 x17 h11 y5c ff3 fs7 fc0 sc0 ls31 ws51">[7] proposed th<span class="_ _0"></span>at using mean shift to find the roug<span class="_ _0"></span>hly area in </div><div class="t m0 x17 h11 y5d ff3 fs7 fc0 sc0 ls2d ws52">the frame, using particle filter in this area. However, the </div><div class="t m0 x17 h11 y5e ff3 fs7 fc0 sc0 ls35 ws53">searching area is large so that it need much ti<span class="_ _2"></span>me. Thus this </div><div class="t m0 x17 h11 y5f ff3 fs7 fc0 sc0 ls20 ws54">approach can n<span class="_ _0"></span>ot solve the dra<span class="_ _2"></span>wback<span class="_ _0"></span> of mean shift, it also </div><div class="t m0 x17 h11 y60 ff3 fs7 fc0 sc0 ls2b ws55">involved in local extreme<span class="_ _0"></span> valu<span class="_ _2"></span>e. </div><div class="t m0 x18 h11 y61 ff3 fs7 fc0 sc0 ls33 ws56">The paper is organ<span class="_ _0"></span>ized as follows. S<span class="_ _0"></span>ection 2 introduces </div><div class="t m0 x17 h11 y62 ff3 fs7 fc0 sc0 ls25 ws57">the particle filter, m<span class="_ _0"></span>ean shift and new<span class="_ _0"></span> algorithm. In section 3, </div><div class="t m0 x17 h11 y63 ff3 fs7 fc0 sc0 lsf ws58">we apply<span class="_ _0"></span> ne<span class="_ _2"></span>w algorithm to face track<span class="_ _0"></span>ing, respectively </div><div class="t m0 x17 h11 y64 ff3 fs7 fc0 sc0 ls27 ws59">discus<span class="_ _2"></span>sing d<span class="_ _2"></span>yna<span class="_ _2"></span>mical <span class="_ _2"></span>model,<span class="_ _2"></span> obser<span class="_ _2"></span>vation <span class="_ _2"></span>model, etc<span class="_ _2"></span>. In </div><div class="t m0 x17 h11 y65 ff3 fs7 fc0 sc0 ls3c ws5a">section 4, we dis<span class="_ _0"></span>cuss our experim<span class="_ _0"></span>ent and compare propos<span class="_ _0"></span>ed </div><div class="t m0 x17 h11 y66 ff3 fs7 fc0 sc0 ls35 ws5b">algorithm with mean shift and conventional particle filter. </div><div class="t m0 x17 h11 y67 ff3 fs7 fc0 sc0 ls27 ws5c">Concl<span class="_ _2"></span>usion a<span class="_ _2"></span>nd fut<span class="_ _2"></span>ure <span class="_ _2"></span>works wi<span class="_ _2"></span>ll be gi<span class="_ _2"></span>ven i<span class="_ _2"></span>n sectio<span class="_ _2"></span>n 5. </div><div class="t m0 x19 h11 y68 ff3 fs7 fc0 sc0 ls1d ws0">II.</div><div class="t m0 x1a h12 y69 ff4 fs7 fc0 sc0 ls0 ws0">P</div><div class="t m0 x1b h12 y6a ff4 fsa fc0 sc0 ls3d ws0">ARTICLE<span class="fs7 ls3e"> F</span><span class="ls3f">ILTER<span class="fs7 ls3e"> W</span>ITH<span class="fs7 ls3e"> M</span><span class="ls40">EAN<span class="fs7 ls3e"> S</span><span class="ls41">HIFT<span class="_ _2"></span> </span></span></span></div><div class="t m0 x17 hd y6b ff5 fs7 fc0 sc0 ls32 ws5d">A. Particle Filter </div><div class="t m0 x18 h11 y6c ff3 fs7 fc0 sc0 ls42 ws5e">Particle filters are a sample-<span class="_ _0"></span>based variant of Bayes fi<span class="_ _0"></span>lters. </div><div class="t m0 x17 h11 y6d ff3 fs7 fc0 sc0 ls43 ws5f">The aim of particle filter estimation is to evaluate the posterior </div><div class="t m0 x17 h11 y6e ff3 fs7 fc0 sc0 ls44 ws60">probabilit<span class="_ _2"></span>y density function, </div><div class="t m0 x1c h13 y6f ff3 fsb fc0 sc0 ls0 ws0">)<span class="_ _4"></span>|<span class="_ _5"></span>(</div><div class="t m0 x1d h14 y70 ff6 fsc fc0 sc0 ls0 ws0">k<span class="_ _6"></span>k</div><div class="t m0 x1e h15 y6f ff6 fsb fc0 sc0 ls0 ws0">z<span class="_ _7"></span>x<span class="_ _8"></span>p</div><div class="t m0 x1f h11 y71 ff3 fs7 fc0 sc0 ls1f ws61"> <span class="_ _9"></span>of th<span class="_ _0"></span>e state vector </div><div class="t m0 x20 h16 y72 ff3 fsd fc0 sc0 ls0 ws0">2252</div><div class="t m0 x21 h17 y73 ff9 fse fc0 sc0 ls0 ws0">Authorized licensed use limited to: TIANJIN UNIVERSITY OF TECHNOLOGY. Downloaded on November 10, 2008 at 21:02 from IEEE Xplore. Restrictions apply.</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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