Definition of Tracking

Transcription

1 Trckng

2 Defnton of Trckng Trckng: Generte some conclusons bout the moton of the scene, objects, or the cmer, gven sequence of mges. Knowng ths moton, predct where thngs re gong to project n the net mge, so tht we don t hve so much work lookng for them.

3 Why Trck? Detecton nd recognton re epensve If we get n de of where n object s n the mge becuse we hve n de of the moton from prevous mges, we need less work detectng or recognzng the object. A B Detecton + recognton A B Scene Trckng (less detecton, no recognton C Imge Sequence New person C

4 Trckng Slhouette by Mesurng Edge ostons Observtons re postons of edges long normls to trcked contour

5 Why not Wt nd rocess the Set of Imges s Btch? In cr system, detectng nd trckng pedestrns n rel tme s mportnt. Recursve methods requre less computng

6 Implct Assumptons of Trckng hyscl cmers do not move nstntly from vewpont to nother Object do not teleport between plces round the scene Reltve poston between cmer nd scene chnges ncrementlly We cn model moton

7 Relted Felds Sgnl Detecton nd Estmton Rdr technology

8 The roblem: Sgnl Estmton We hve system wth prmeters Scene structure, cmer moton, utomtc zoom System stte s unknown ( hdden We hve mesurements Components of stble feture ponts n the mges. Observtons, projectons of the stte. We wnt to recover the stte components from the observtons

9 Necessry Models We use models to descrbe pror knowledge bout the world (ncludng eternl prmeters of cmer the mgng projecton process System Dynmcs revous Stte Model Net Stte Stte Mesurement Model (projecton (u, v Mesurement

10 A Smple Emple of Estmton by Lest Squre Method Gol: Fnd estmte â of stte such tht the lest squre error between mesurements nd the stte s mnmum C C ˆ 2 n 0 n n ( n ( 2 ˆ n Stte vrble n ˆ - Mesurement t t

11 Recursve Lest Squre Estmton We don t wnt to wt untl ll dt hve been collected to get n estmte â of the depth We don t wnt to reprocess old dt when we mke new mesurement Recursve method: dt t step re obtned from dt t step - Stte vrble ˆ â Mesurement t

12 Recursve Lest Squre Estmton 2 Recursve method: dt t step re obtned from dt t step - t ˆ ( ˆ ˆ + k k k k ˆ + ˆ k k ˆ ˆ +

13 Recursve Lest Squre Estmton 3 ˆ ˆ + ( ˆ Estmte t step Gn Actul mesure Gn specfes how much do we py ttenton to the dfference between wht we epected nd wht we ctully get Innovton redcted mesure

14 Lest Squre Estmton of the Stte Vector of Sttc System. Btch method H mesurement equton H 2... n H H... H 2 n H H Fnd estmte â tht mnmzes C 2 (X H T (X H 2 H 2 We fnd ˆ (H T H H T X

15 Lest Squre Estmton of the Stte Vector of Sttc System 2 H H 2. Recursve method Clculton s smlr to clculton of runnng verge We hd: ˆ ˆ ( ˆ + redcted mesure Now we fnd: wth 2 ˆ ˆ + K (X H ˆ - - K ( H Gn mtr Innovton H H T T H 2

16 Dynmc System A V X w A A t A V V t V X X w A V X t t A V X Stte of rocket Mesurement w - + Φ [ ] V A V X V + H Stte equton for rocket Mesurement equton Nose Twek fctor

17 ˆ Φ Recursve Lest Squre Estmton for Dynmc System Stte equton Φ + ˆ - Mesurement equton H + K ' - - T (Klmn Flter n redcton for (I - K + - w - K ( T H - Q - ' w n - H T ~ N(0, Q ~ Φ N(0, ˆ - - ' H ( H ' H + R Φ Φ + Twek fctor for model R Mesurement nose Gn Covrnce mtr for predcton error redcton for Covrnce for estmton error

18 Stte equton ˆ K ' - Estmton when System Model f ( ˆ ' f - H T - ( I K + ( H - K ( f s Nonlner (Etended Klmn Flter f + ( w H + v - - H T - ' ' H H - T Mesurement equton f( ˆ + R - - Dfferences compred to + Q regulr Klmn flter re - crcled n red Jcobn Mtr

19 Trckng Steps redct net stte s Φ â - usng prevous step nd dynmc model redct regons N( H Φ ˆ, ' - of net mesurements usng mesurement model nd uncertntes Mke new mesurements n predcted regons Compute best estmte of net stte ˆ Φ ˆ - + K ( H Φ Mesurement ˆ - Correcton of predcted stte redcton regon (u, v

20 Recursve Lest Squre Estmton for Dynmc System (Klmn Flter Mesurement Stte vector Estmton â t

21 Trckng s robblstc Inference roblem Fnd dstrbutons for stte vector nd for mesurement vector. Then we re ble to compute the epecttons â nd ˆ Smplfyng ssumptons (sme s for HMM (, 2, L, - ( - (Only mmedte pst mtters (, j, K, ( ( j K( k (Condtonl ndependence of mesurements gven stte

22 Trckng s Inference redcton Correcton roduces sme results s lest squre pproch f dstrbutons re Gussns: Klmn flter See Forsyth nd once, Ch d,, ( (,, ( L L - - d,, ( (,, ( (,, ( L L L

23 Klmn Flter for D Sgnls Stte equton f + h + w - - Mesurement equton v w ~ N(0,q ~ N(0,r v ˆ f ˆ + K ( h f ˆ - - K p' p - redcton for ( pror estmte p' f 2 ( h( h p K 2 + p' q + h p' r - - Twek fctor for model Gn Stndrd devton for predcton error Mesurement nose redcton for St.d. for estmton error

24 Applctons: Structure from Moton Mesurement vector components: Coordntes of corners, slent ponts Stte vector components: Cmer moton prmeters Scene structure Is there enough equtons? N corners, 2N mesurements N unknown stte components from structure (dstnces from frst center of projecton to 3D ponts 6 unknown stte components from moton (trnslton nd rotton More mesurements thn unknowns for every frme f N>6 (2N > N + 6 Btch methods Recursve methods (Klmn flter

25 roblems wth Trckng Intl detecton If t s too slow we wll never ctch up If t s fst, why not do detecton t every frme? Even f rw detecton cn be done n rel tme, trckng sves processng cycles compred to rw detecton. The CU hs other thngs to do. Detecton s needed gn f you lose trckng Most vson trckng prototypes use ntl detecton done by hnd (see Forsyth nd once for dscusson

26 References Klmn, R.E., A New Approch to Lner redcton roblems, Trnsctons of the ASME--Journl of Bsc Engneerng, pp , Mrch 960. Sorenson, H.W., Lest Squres Estmton: from Guss to Klmn, IEEE Spectrum, vol. 7, pp , July D. Forsyth nd J. once. Computer Vson: A Modern Approch, Chpter 9. O. Fugers.. Three-Dmensonl Computer Vson. MIT ress. Ch. 8, Trckng Tokens over Tme.