KLT Tracker. Alignment. 1. Detect Harris corners in the first frame. 2. For each Harris corner compute motion between consecutive frames

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1 KLT Tracker Tracker. Detect Harrs corers the frst frame 2. For each Harrs corer compute moto betwee cosecutve frames (Algmet). 3. Lk moto vectors successve frames to get a track 4. Itroduce ew Harrs pots at every m frames 5. Track ew ad old Harrs pots usg steps 2-4. Algmet

2 Mea-Shft Trackg Lecture-

3 Mea-Shft Trackg

4 Mea-Shft Trackg

5 UCF Computer Vso Lab Mea-Shft Trackg 5

6 Presetatos Comacu et al Alper Ylmaz Afsh Dehgha

7 Mea-Shft Theory ad Its Applcatos Lecture-8 Mea Shft : A robust Approach Toward Feature Space Aalyss, by Comacu, Meer, IEEE PAMI, Volume 24, No 5, May 2002, pages

8 Rego of terest Ceter of mass Objectve : Fd the desest rego Mea Shft vector

9 Rego of terest Ceter of mass Objectve : Fd the desest rego Dstrbuto of detcal bllard balls Mea Shft vector

10 Rego of terest Ceter of mass Objectve : Fd the desest rego Dstrbuto of detcal bllard balls Mea Shft vector

11 Rego of terest Ceter of mass Objectve : Fd the desest rego Dstrbuto of detcal bllard balls Mea Shft vector

12 Rego of terest Ceter of mass Objectve : Fd the desest rego Dstrbuto of detcal bllard balls Mea Shft vector

13 Rego of terest Ceter of mass Objectve : Fd the desest rego Dstrbuto of detcal bllard balls Mea Shft vector

14 Rego of terest Ceter of mass Objectve : Fd the desest rego Dstrbuto of detcal bllard balls Mea Shft vector

15 Rego of terest Ceter of mass Objectve : Fd the desest rego Dstrbuto of detcal bllard balls

16 Mea Shft Vector Gve: Data pots ad approxmate locato of the mea of ths data: Task: Estmate the exact locato of the mea of the data by determg the shft vector from the tal mea. UCF Computer Vso Lab. 6

17 Mea Shft Vector Example M h ( y) x x y x 0 Mea shft vector always pots towards the drecto of the maxmum crease the desty. UCF Computer Vso Lab. 7

18 Mea Shft (Weghted) M h x w ( y 0) x ( y 0) y x w ( y 0) 0 x : umber of pots the kerel y 0 : tal mea locato x : data pots h : kerel radus Weghts are determed usg kerels (masks): Uform, Gaussa or Epaechkov UCF Computer Vso Lab. 8

19 Propertes of Mea Shft Mea shft vector has the drecto of the gradet of the desty estmate. It s computed teratvely for obtag the maxmum desty the local eghborhood. UCF Computer Vso Lab. 9

20 What s Mea-Shft? A tool for fdg modes a set of data samples, mafestg a uderlyg probablty desty fucto (PDF) R N No-parametrc Desty Estmato Dscrete PDF Represetato Data No-parametrc Desty GRADIENT Estmato (Mea Shft) PDF Aalyss

21 No-Parametrc Desty Estmato Assumpto : The data pots are sampled from a uderlyg PDF Data pot desty mples PDF value! Assumed Uderlyg PDF Real Data Samples

22 No-Parametrc Desty Estmato Assumed Uderlyg PDF Real Data Samples

23 No-Parametrc Desty Estmato Assumed Uderlyg PDF Real Data Samples

24 Parametrc Desty Estmato Assumpto : The data pots are sampled from a uderlyg PDF PDF( x) = c e ( x-μ ) Estmate Assumed Uderlyg PDF Real Data Samples

25 Kerel Desty Estmato Varous Kerels P( x) K( x-x ) A fucto of some fte umber of data pots x x Examples: Epaechkov Kerel K E ( x) 2 c x x 0 otherwse Data Uform Kerel K U ( x) c x 0 otherwse Normal Kerel KN ( x) cexp 2 x 2

26 Profle ad Kerel Radally symmetrc Kerel K(x) 2 ck( x ) Profle P( x) K(x-x ) k 2 c ( x-x )

27 Kerel Desty Estmato P( x) ck( x-x P( x) ck ( x-x 2 ) 2 ) P( x) 2c(x-x ) k( x-x 2 )

28 Kerel Desty Estmato 2 ) ( x-x (x-x ) 2c x) ( k P 2 ) ( x-x -x) (x 2c x) ( g P -x ) ( x-x ) ( x-x x ) ( x-x 2c x) ( g g g P 2 2 ) ( x-x x 2c ) ( x-x x 2c x) ( g g P ) ( ) ( x x k g

29 -x ) ( x-x ) ( x-x x ) ( x-x 2c x) ( g g g P -x x 2c x) ( g g g P

30 ( ) g c c P k g g x x x Computg The Mea Shft g P g P c (x) m(x) m(x) c (x)

31 Mea Shft Mode Detecto What happes f we reach a saddle pot? Perturb the mode posto ad check f we retur back Updated Mea Shft Procedure: Fd all modes usg the Smple Mea Shft Procedure Prue modes by perturbg them (fd saddle pots ad plateaus) Prue earby take hghest mode the wdow

32 Mea Shft Propertes Automatc covergece speed mea shft vector sze depeds o gradet. Near maxma, the steps are small ad refed Adaptve Gradet Ascet Covergece s guarateed for ftesmal steps oly, (therefore set a lower boud) For Uform Kerel ( ), covergece s acheved a fte umber of steps Normal Kerel ( ) exhbts a smooth trajectory, but s slower tha Uform Kerel ( ).

33 Real Modalty Aalyss Tessellate the space wth wdows Ru the procedure parallel

34 Real Modalty Aalyss The blue data pots were traversed by the wdows towards the mode

35 Mea Shft Applcatos

36 UCF Computer Vso Lab Mea Shft Object Trackg Geeral Framework Target Represetato Choose the model the tal frame Choose a feature space Represet the model the selected feature space Quatzed Color Space PDF 36 The object s beg modeled usg color probablty desty

37 Mea Shft Object Trackg UCF Computer Vso Lab Geeral framework Target Localzato Trackg Select a ROI aroud the target locato curret frame Fd the most smlar caddate based o the smlarty fuc 37

38 UCF Computer Vso Lab Mea Shft Object Trackg PDF Represetato Target Model : color dstrbuto by dscrete m b color hstogram Curret Frame Next Frame Caddate Model : color dstrbuto by dscrete m b color hstogram Smlarty Fuco? The Bhattacharyya Coeffcet 38

39 UCF Computer Vso Lab Mea Shft Object Trackg Covergece Pot Ital Locato 39

40 Target Model for Trackg Features used for trackg clude: Gray level Color Gradet Feature probablty dstrbuto are calculated by usg weghted hstograms. The weghts are derved from Epaechkov profle. UCF Computer Vso Lab. 40

41 Dstrbuto x, x 2, x 3, x 4 have the same feature, such as gray level. p( u) C x S k 2 x [ S x ) u] ( S( x ) s the color at x_ UCF Computer Vso Lab. 4

42 Target Gray Level Feature target 2 target o - target mage hstogram target dstrbuto target 2 dstrbuto o target dstrbuto UCF Computer Vso Lab. 42

43 Smlarty of Target ad Caddate Dstrbutos Target : q u. ^ Caddate : p u. d( y) ( y) ( y) [ pˆ( y), q] pˆ u ( y) q u m u (y) :Bhattacharya coeffcet. UCF Computer Vso Lab. 43

44 Dstace Mmzato Mmzg the dstace correspods to maxmzg Bhattacharya coeffcet. [ pˆ( y), q] pˆ u ( y) q u m u Taylor expaso aroud pˆ ( y 0) [ pˆ( y), q] [ˆ( p y 0), q] 2 m pˆ ( y ) u u pˆ ( y ) u 0 Maxmzg Bhattacharya coeffcet ca be obtaed by maxmzg the blue term. q UCF Computer Vso Lab. 44

45 UCF Computer Vso Lab. 45 Lkelhood Maxmzato ] ), ( ˆ [ ] ), ( ˆ [ 0 q y p q y p m u u u p q p 0 ) ( ˆ ) ( ˆ 2 y y h : radus of sphere C h : ormalzato costat S(x ) : gray level at x y : kerel ceter m : umber of bs h k x y m u u u p q u S 0 ) ( ˆ ] ) ( [ y x lkelhood maxmzato depeds o maxmzg w. x C h 2

46 UCF Computer Vso Lab. 46 Lkelhood Maxmzato Usg Mea Shft Vector 0 ) ( ˆ ] ) ( [ ) ( m u o u u o w where p q u S w y x y Maxmzato of the lkelhood of target ad caddate depeds o the weghts: ) ( ) ( ) ( y y x y y x x h w w M Sce s strctly postve, mea shft vector ca be ( 0 ) y x w wrtte as Thus, ew target ceter s ) ( ˆ 0 y 0 y y h M

47 Algorthm Calculate (q) talze estmated ceter (y =y 0 ) Calculate (p) Calculate ( w) Estmate ew target ceter (y ) false d< update target ceter (y 0 =y ) Repeat utl ed of the sequece UCF Computer Vso Lab. 47

48 Trackg A Sgle Pot

49

50

51

52

53

54 UCF Computer Vso Lab Refereces D. Comacu, V. Ramesh, ad P. Meer. Real-tme trackg of o-rgd objects usg mea shft. I IEEE Proc. o Computer Vso ad Patter Recogto o, pages , D. Comacu, V. Ramesh, ad P. Meer. Mea shft: A robust approach towards feature space aalyss. IEEE Tras. o Patter Aalyss ad Mache Itellgece, 24(5):603 69,

Unsupervised Learning and Other Neural Networks

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