ADVANCED TOPICS ON VIDEO PROCESSING Image Spatial Processing Image - PowerPoint PPT Presentation

ADVANCED TOPICS ON VIDEO PROCESSING Image Spatial Processing Image Spatial Processing

FILTERING EXAMPLES FILTERING EXAMPLES

FOURIER INTERPRETATION FOURIER INTERPRETATION

FILTERING EXAMPLES FILTERING EXAMPLES

FOURIER INTERPRETATION FOURIER INTERPRETATION

FILTERING EXAMPLES FILTERING EXAMPLES

FILTERING EXAMPLES FILTERING EXAMPLES

FOURIER INTERPRETATION FOURIER INTERPRETATION

FILTERING EXAMPLES FILTERING EXAMPLES

FOURIER INTERPRETATION FOURIER INTERPRETATION

LINEAR AND NON LINEAR OPERATIONS LINEAR AND NON LINEAR OPERATIONS Median Filter: (6 8 9 9 10 11 12 13 15) = 10 Median Filter: (6, 8, 9, 9, 10 , 11, 12, 13, 15) 10 Minimum = 6; Maximum: 15 Average of nearest neighbours: Average of nearest neighbours:

LOW PASS GAUSSIAN FILTER LOW PASS GAUSSIAN FILTER

MEDIAN FILTERING MEDIAN FILTERING

HI PASS FILTERING FOR HIGH FREQUENCIES

EXAMPLE EXAMPLE

1D DERIVATIVES 1D DERIVATIVES

GRADIENT METHODS GRADIENT METHODS  1D example  1D example Si ye s Yes Yes >Thres- Thres hold? No No No edge No edge

2D CASE 2D CASE  The first derivative is substituted by the gradient Th fi d i i i b i d b h di       f x y , f x y ,        f x y , i i   x y x y  Omnidirectional detector  Based on|  ƒ(x,y)|: isotropic behaviour |  ƒ( B d )| i t i b h i  Directional detector  Based on an oriented derivative:  ex.: a possible horizontal edge detector is |  y|

2D APPROACH 2D APPROACH

EDGE THINNING EDGE THINNING 1) if  f  has a local horizontal max but not a vertical one in ( (x 0 ,y 0 ), then, that point is an edge point if ) then that point is an edge point if   f f    K K K K 2( 2( typical typical value) value)   x y ( x y ) ( x y , ) 0, 0 0 0 2) if  f  has a local vertical max but not a horizontal one in   (x 0 ,y 0 ), then, that point is an edge point if   f f   K K 2(typical value)     y y x x ( x y ) ( x y ) 0, 0 0, o

DIRECTIONAL CASE DIRECTIONAL CASE .

EXAMPLE: ISOTROPIC CASE EXAMPLE: ISOTROPIC CASE .

DISCRETIZATION DISCRETIZATION The gradient operator can be discretized as: The gradient operator can be discretized as:     2 2         f f ( ( x , , y y ) ) f f x , , y y             f f ( ( x , y ) )       x y        2 2 f ( n , n ) f ( n , n ) f ( n , n ) 1 2 x 1 2 y 1 2 Which is based on a discretization of directional derivatives: derivatives:    f ( n , n ) f ( n , n ) f ( n , n ) 1 2 x 1 2 y 1 2

FINITE IMPULSE RESPONSE MODEL FINITE IMPULSE RESPONSE MODEL Discrete operators for derivative estimation can be estimated as sc ete ope ato s o de at e est at o ca be est ated as FIR filters.  f ( n , n ) f ( n , n ) * h ( n , n ) y 1 2 1 2 y 1 2   f f ( ( n n , n n ) ) f f ( ( n n , n n ) ) * h h ( ( n n , n n ) ) x 1 2 1 2 x 1 2 f f ( ( n n 1 n , n ) ) f x f ( ( n n 1 n , n ) ) 2 2 h x ( n 1 n , ) 2

DISCRETE DIFFERENTIAL OPERATORS DISCRETE DIFFERENTIAL OPERATORS  Pixel difference: luminance difference between to neighbour pixels along orthogonal directions. neighbour pixels along orthogonal directions.    f x ( j , k ) f ( j , k ) f ( j , k 1 )    f y ( j , k ) f ( j , k ) f ( j 1 , k )  Separable filters  Separable filters          0 0 0 0 0 0 0 0 1 1 0 0        h 0 1 1 h 0 1 0         x y         0 0 0 0 0 0    

EXAMPLE: PIXEL DIFFERENCE C

SEPARATED PIXEL DIFFERENCE SEPARATED PIXEL DIFFERENCE •If farther pixels are chosen there is a higher noise rejection, and there is no phase translation in edge definition.     f x ( j , k ) f ( j , k 1 ) f ( j , k 1 )      f y f ( ( j j , k k ) ) f f ( ( j j 1 1 , k k ) ) f f ( ( j j 1 1 , k k ) )    0 0 0   0 1 0            h 1 0 1 h 0 0 0     x y         0 0 0 0 0 0 0 0 1 1 0 0        

EX.: SEPARATED PIXEL DIFFERENCE S C

ROBERTS EDGE EXTRACTION ROBERTS EDGE EXTRACTION     f x ( j , k ) f ( j , k ) f ( j 1 , k 1 )     f y ( j , k ) f ( j , k 1 ) f ( j 1 , k )      0 0 1 1 0 0         h h 0 0 1 1 0 0 h h 0 0 1 1 0 0         y x     0 0 0 0 0 0    

EX.: ROBERTS METHOD O S O

PREWITT METHOD PREWITT METHOD Estimation can be improved involving more samples for te Estimation can be improved involving more samples for te gradient operator 3x3       f f                        K * f n 1 , n 1 f n 1 , n 1   1 2 1 2  x                                         f f n 1 1 , n f f n 1 1 , n f f n 1 1 , n 1 1 f f n 1 1 , n 1 1 1 2 1 2 1 2 1 2 = vertical low pass* horizontal high pass vertical low pass horizontal high pass    f                      K * f n 1 , n 1 f n 1 , n 1     1 2 1 2   y                           f n , n 1 f n , n 1 f n 1 , n 1 f n 1 , n 1 1 2 1 2 1 2 1 2 = vertical high pass* horizontal low pass

GRADIENT ESTIMATION GRADIENT ESTIMATION • Gradient modulus = the value of the higher directional derivative g • Gradient phase = orientation of the higher directional derivative Squared lattice =eight possible directions     1 0 1 0 1 1                 h n 1 n , 1 0 1 h n 1 n , 1 0 1     2 2        1 0 1 1 1 0        E NE         1 1 1 1 1 0            h n 1 n , 0 0 0 h n 1 n , 1 0 1     2 2              1 1 1 1 1 1 0 0 1 1 1 1         N NW

GRADIENT ESTIMATION GRADIENT ESTIMATION       0 0 1 1 1 1      1 0 1           h n 1 n , 1 0 1   h n 1 n , 1 0 1       2 2     1 1 0    1   1 0   W SW       1 1 0        1 1 1 1 1 1           h n 1 n , 1 0 1  h n 1 n , 0 0 0     2 2     0 0 1 1 1 1         1 1 1 1 1 1     S SE

EX.: PREWITT METHOD 3X3 O 3 3

SOBEL METHOD SOBEL METHOD  Same dimensions of Prewitt filter S di i f P i fil  Different weight for central point in different directions.      1 2 1  1     1 0        h 0 0 0   h 2 0 2     c r   1 2 1          1 1 0 0 1 1      Sobel for exagonal grids.    1 1     h 2 0 2        1 1  

EX.: SOBEL METHOD SO O

COMPARISON COMPARISON Roberts Sobel Sobel Prewitt Prewitt