a b 1 b [ i ] 0 i 1 5 / 1 5 / a [ j ] j 0 j 0 = = a - PowerPoint PPT Presentation

b … 0 0 1 4 6 4 1 0 0 … 1 × a = 16 Σ a b

1 b [ i ] 0 i × × 1 5 / 1 5 / a [ j ] j 0 j 0 = = a [ j ] b [ i – j ] 0 0 0 0 0 0 0 0 .2 .2 .2 .2 .2 0 × Σ Σ 1 5 / a [ j ] j 0 = a [ j ] b [ i – j ] 0 0 0 .2 .2 .2 0 Σ 1 0.6 0 ( a b )[ i ] – 7 0 i 6

g ( x ) 0 x × × f ( t ) t 0 t 0 = = f ( t ) g ( x – t ) area area ( f g )( x ) 0 x 1 x x 2

f ( x ) – ½ 0 ½ x f ( t ) t 0 t 0 f ( t ) f ( x – t ) ( f f )( x ) – ½ 3 0 ½ x

2.9 2.1 1.4 f ( x ) x δ ( t ) t t t 2.9 2.1 δ ( t ) f ( x – t ) 1.4 2.9 2.1 1.4 ( δ f )(x) x

original box blur linear blur Gaussian blur I sharp = (1 − ↵ ) I + ↵ ( I ? f g, σ )

I sharp = (1 + ↵ ) I − ↵ ( I ? f g, σ )

box tent B-spline

reconstruct f r smooth f s ( f f r ) s sample

downsample × 3 radius 1 radius 2 radius 3 upsample × 3

sin π u π u 1 4 2 3 1 2 3 4

1 1 f box ( x ) sinc( u ) –1 1 –4 4 x u sinc 2 ( u ) 1 1 f tent ( x ) –1 1 –4 4 x u 1 f B ( x ) sinc 4 ( u ) 1 2 3 –1 1 –4 4 u x 1 f g ( x ) √ 2 π f g (2 π u ) 1 1 √ 2 π –1 1 –4 4 x u

s 1 ( x ) s 1 ( u ) u x 0 1 0 1 s 1/2 ( x ) s 2 ( u ) x u 0 1 0 1

reconstructed sampled original T x T 1 0 aliasing u aliasing

sampled × 4 sampled × 2 sampled original T T T x T 1 T 1 T 1 0 aliasing u aliasing minimal aliasing

strong blur mild blur original x filter filter 0 1 1 u

samp.: strong blur samp.: mild blur samp.: no filter original x 0 aliasing minimal aliasing aliasing severe some u

sampled × 4 sampled × 2 sampled original T T T x T 1 T 1 T 1 0 aliasing u minimal aliasing aliasing

resampled reconstructed original x 0 u