ADVANCED TOPICS ON VIDEO PROCESSING

Size: px

Start display at page:

Download "ADVANCED TOPICS ON VIDEO PROCESSING"

Antony Rich
5 years ago
Views:

1 ADVANCED TOPICS ON VIDEO PROCESSING Image Spatial Processig

2 FILTERING EXAMPLES

3 FOURIER INTERPRETATION

4 FILTERING EXAMPLES

5 FOURIER INTERPRETATION

6 FILTERING EXAMPLES

7 FILTERING EXAMPLES

8 FOURIER INTERPRETATION

9 FILTERING EXAMPLES

10 FOURIER INTERPRETATION

11 LINEAR AND NON LINEAR OPERATIONS Media Filter: (6899 (6, 8, 9, 9,,,, 3, 5) = Miimum = 6; Maximum: 5 Average o earest eighbours:

12 LOW PASS GAUSSIAN FILTER

13 MEDIAN FILTERING

14 HI PASS FILTERING FOR HIGH FREQUENCIES

15 EXAMPLE

16 D DERIVATIVES

17 GRADIENT METHODS D example >ThresThres hold? ye Si s Yes No No edge Yes No No edge

18 D CASE The irst derivative is substituted by the gradiet x y x, y i x x Omidirectioal detector, x, y y Based o ƒ(x,y) : isotropic i behaviour Directioal detector Based o a orieted derivative: ex.: a possible horizotal edge detector is y i y

19 D APPROACH

20 EDGE THINNING ) i has a local horizotal max but ot a vertical oe i ( ) the that poit is a edge poit i (x,y ), the, that poit is a edge poit i x K K ( typical value) y ( x y ) ( x, y ), ) i has a local vertical max but ot a horizotal oe i (x,y ), the, that poit is a edge poit i y K x ( ) ( ) x, y x, y o K(typical value)

21 DIRECTIONAL CASE.

22 EXAMPLE: ISOTROPIC CASE.

23 DISCRETIZATION DISCRETIZATION The gradiet operator ca be discretized as: The gradiet operator ca be discretized as:, ), ( ) ( y x y x, ), ( ), ( y y x y y x ), ( ), ( ), ( y x Which is based o a discretizatio o directioal derivatives: derivatives: ), ( ), ( ), ( y x

24 FINITE IMPULSE RESPONSE MODEL Discrete sc ete operators ope ato s or o derivative de at e estimatio est at o ca ca be estimated est ated as FIR ilters. y (, ) (, ) * hy (, ) x (, ) (, ) * hx (, ) (, ) hx (, ) x (, )

25 DISCRETE DIFFERENTIAL OPERATORS Pixel dierece: lumiace dierece betwee to eighbour pixels alog orthogoal directios. x y Separable ilters ( j, k) ( j, k) ( j, k ) ( j, k) ( j, k) ( j, k) h x h y

26 EXAMPLE: PIXEL DIFFERENCE

27 SEPARATED PIXEL DIFFERENCE I arther pixels are chose there is a higher oise rejectio, ad there is o phase traslatio i edge deiitio. x ( j, k) ( j, k ) ( j, k ) ( j, k ) ( j, k ) ( j, k ) y h x h y

28 EX.: SEPARATED PIXEL DIFFERENCE

29 ROBERTS EDGE EXTRACTION ROBERTS EDGE EXTRACTION ), ( ), ( ), ( k j k j k j x ), ( ), ( ), ( k j k j k j y h h h x h y

30 EX.: ROBERTS METHOD

31 PREWITT METHOD PREWITT METHOD Estimatio ca be improved ivolvig more samples or te Estimatio ca be improved ivolvig more samples or te gradiet operator 3x3,, * x K = vertical low pass* horizotal high pass,,,, vertical low pass horizotal high pass,, * K,,,, y = vertical high pass* horizotal low pass

32 GRADIENT ESTIMATION Gradiet modulus = the value o the higher g directioal derivative Gradiet phase = orietatio o the higher directioal derivative Squared lattice =eight possible directios h, E h, NE h, N h, NW

33 GRADIENT ESTIMATION h, W h, SW h, h, S SE

34 EX.: PREWITT METHOD 3X3 3

35 SOBEL METHOD Same dimesios o Prewitt ilter Dieret weight or cetral poit i dieret directios. h r h c Sobel or exagoal grids. h

36 EX.: SOBEL METHOD

37 COMPARISON Roberts Sobel Prewitt

38 FREI-CHEN OPERATOR Isotropic operator similar il to Prewitt dieret weight or the cetral poit i the 4 directios. The gradiet has the same value or horizotal, vertical ad diagoal edges. h r h c

39 EX.: METODO O DI FREI-CHEN

40 EXTENDED OPERATORS EXTENDED OPERATORS A li it th ti d th d i th i k i A limit or the aoremetioed methods is their weakess i accurate edge detectio whe SNR is very low. A possible solutio i to exted their size: the result will be a A possible solutio i to exted their size: the result will be a less accurate edge positioig but oise rejectio will be higher. higher. PREWITT METHOD 7X7 Extesio o Prewitt 3X3 Extesio o Prewitt 3X3 Normalized impulse respose: h r r

41 EX.: PREWITT 7X7 METHOD

42 ABDOU 7X7 METHOD ABDOU 7X7 METHOD I ilt k th t i li d i l i ht Is a ilter mask that gives a liear decreasig sample weight as they are arther rom the edge. Its behaviour is close to a trucated pyramid trucated pyramid. The ormalized impulse respose is: h r 3 3 r

43 EX.: ABDOU 7X7 METHOD

44 FURTHER EXTENDED OPERATORS It tspossbetoobta is possible to obtai exteded etededgadet gradiet ilters teso or low SNR coditios covolvig a 3x3 operator with a low-pass ilter. h( j, k) h ( j, k)* h ( j, k) G H G (j,k) is oe o the previously cosidered ilters, H PB (j,k) is the impulse respose or a low-pass ilter. PG

45 EXAMPLE Prewitt 3X3 covoled with: h * 9...ad we get the Smoothed Prewitt 5X5 h

46 LAPLACIAN BASED METHODS D Case Fi d i g th d d i ti di g t Fid zero-crossig o the secod derivative, correspodig to ilectio poits.

47 LAPLACIAN For the D case the d order dieretial operator is the Laplacia ( x, y) ( x, y) ( x, y) ( ( x, y)) x y Isotropic operator More sesible to oise with respect to gradiet False edges ca be geerated due to oise. Thier edges are produced.

48 ALGORITHM: CASE D Gradiet estimatio O( x, y) ( xy, ) ( x, y) =? Yes O ( x, y ) Yes threshold edge No No

49 ZERO-CROSSING WITHOUT THRESHOLD Sobel vs. Laplacia

50 LAPLACIAN DISCRETIZATION Ca be see as the covolutio o (, ) with the impulse respose h(, ) o a liear system.

51 4 NEIGHBOURS METHOD 4 NEIGHBOURS METHOD S bl li d ilt Separable ormalized ilter Uit gai or cotiuous compoet The sig o h( ) ca be chaged itho t chages i The sig o h(, ) ca be chaged without chages i the ial result (sice we are lookig or zeros o laplacia) 4 4 ), ( h

52 EX.: 4 NEIGHBOURS METHOD

53 LAPLACIAN DISCRETIZATION LAPLACIAN DISCRETIZATION The laplacia ca be approximated with iite diereces ), ( ), ( ), ( ), ( k j k j y x y x diereces ), ( ), ( ), ( k j k j y x x x ) ( ), ( ), ( ), ( ), ( k j k j k j x y x x x xx ), ( ), ( ), ( k j k j k j

54 DISCRETIZATION EXAMPLES DISCRETIZATION EXAMPLES Prewitt method Not separable ilter h (, ) Neighbours method ( ) 8 8 Neighbours method Similar to Prewitt but with a separable ormulatio 4 ) ( h ), ( h

55 EX.: 8 NEIGHBOURS METHOD

56 EX.: PREWITT NOT SEPARABLE

57 NOISE PRESENCE Whe oise is sigiicat these ilters could ot be accurate or diagoal edges. The Prewitt ilter ca work eve i regios with high desity o edges. h(, ) 4 8 Sice ege are directioal ad oise ca geerate lumiace variatios, zero-crossig or laplacia could id o-correct edges.

58 EX.: LAPLACIAN FOR DIAGONAL EDGES

59 SUPER-RESOLUTION RESOLUTION (LAPLACIAN) First method. Give two eighbour pixels, mark as possible edge poit the itrapixels poits i the laplacia values i the two pixels have dieret sigs. Assume as eective edge the poit, amog them, with the largest gradiet. Apply this aalysis to all the pixels couples. LAPLACIAN I 4 I3 I I5 I I I 6 I7 I8 Sig aalysis Magitude compariso

60 Fˆ SUPERRESOLUTION Secod method: aalytical approach Approximate the cotiuous orm o uctio (, ) with a D polyomial i order to describe the laplacia i a aalytical way. Polyomial example: ( r, c) K Kr K3c K4r K5rc K6c K7r c K8rc K9r c where K i are the weights obtaied rom the discrete image. r ad c the become cotiuous variables associtated to a discrete image matrix. ( W ) Polyomial ormulatio ca be oud with small eorts. rc, ( W )

61 SUPERRESOLUTION Method d3: edge ittig Based o the compariso with a edge model based o the image correlatio. sx ( ) a per x < x a+h per x x x L Exemple: compariso with a step uctio E ( x) s( x) the edge is accepted i the MSE is below a threshold. x L dx

62 SUPERRESOLUTION sxy (, ) Case D a or (x cos +y si )< a+h or (x cos +y si ) Compare (x,y) with a D step, where ad speciy the distace ad the agle, i polar coordiates o the edge poit rom the ceter o the cosidered circular regio. The edge is accepted i the MSE is below a Threshold MSE ( x, y) s( x, y) dxdy circle

63 GAUSSIAN FILTERING Why we should use a gaussia uctio? Sice the Fourier trasorm o a Gaussia is still e gaussia, g, The cut-o requecy ca be expressed as a uctio o the width o the impulse respose It has a low aliasig The ilter is separable ad isotropic at the same time h( x, y ) h ( x)h ( y ) h ( x) e x / The oise sesitivityy ((umerous zero crossig) g) decrease as the ilter stregth (width) icrease.

64 LOG OPERATOR The low pass gaussia ilter has a variable cut-o requecy. x y h( x, y) exp H ( x, y ) exp ( x y ) It ollows that the stadard deviatio is iversely proportioal to the ilter width.

65 LOG LOG operator g ( x, y ) ( x, y ) * h ( x, y ) Laplacia ad ilterig are iterchageable sice both o them are liear g ( x, y ) ( x, y ) * h ( x, y ) x y x y exp h ( x, y ) 4 x y h( x, y ) exp x y

66 DIFFERENCE OF GAUSSIANS Thee LOG, OG, Laplacia ap ac a oo a Gaussia Gauss a co correspods espo ds to o thee derivative o a gaussia with respect to The laplacia ca be approximated with the dierece o two gaussia ilters with dieret.

67 DOG APPLICATION

FIR Filter Design: Part I

FIR Filter Design: Part I EEL3: Discrete-Time Sigals ad Systems FIR Filter Desig: Part I. Itroductio FIR Filter Desig: Part I I this set o otes, we cotiue our exploratio o the requecy respose o FIR ilters. First, we cosider some