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a b 1 b [ i ] 0 i 1 5 / 1 5 / a [ j ] j 0 j 0 = = a - - PowerPoint PPT Presentation
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 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 1 5 / a [ j ] j 0 = a [ j ] b [ i j ] 0
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Σ
0 0 1 4 6 4 1 0 0 …
…
b a = a b
×
1 16
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1 1 0.6
1 5
/
1 5
/
1 5
/
.2 .2 .2 .2 .2 .2 .2 .2 b[i] a[j] a[j]b[i – j] a[j] a[j]b[i – j] (a b)[i]
× = × = = ×
Σ Σ Σ
6 –7 i i j j j
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x t t x x1 x2 area area g(x) f(t) f(t)g(x – t) (f g)(x)
× × = =
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–½ 0 ½ ½ f(x) f(t) f(t)f(x – t) (f f)(x) x x t t –½
3
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2.1 1.4 2.9 2.1 2.1 1.4 1.4 2.9 2.9 f(x) δ(t) δ(t)f(x – t) (δ f )(x) x x t t t
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- riginal
linear blur box blur Gaussian blur
Isharp = (1 − ↵)I + ↵(I ? fg,σ)
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Isharp = (1 + ↵)I − ↵(I ? fg,σ)
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box tent B-spline
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reconstruct sample smooth (f
r
f
s
) fr fs
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upsample
× 3
downsample
× 3
radius 1 radius 2 radius 3
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1 1 2 2 3 4 4 sin πu πu 3
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1 1 1 –1 1 –1 x u ftent(x) fB(x) sinc2(u) fbox(x) sinc(u) 1 1 1 1 –1 x x x u –4 4 –4 4 u u sinc4(u) 1 –4 4 1 1 –1 fg(x) 1 –4 4
2 3 1 √2π
√2π fg(2πu)
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1 x s1(x) x s1/2(x) u s1(u) u s2(u) 1 1 1
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x u aliasing aliasing
- riginal
sampled reconstructed T T 1
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- riginal
sampled sampled × 2 sampled × 4 T T 1 T T 1 T T 1 aliasing aliasing minimal aliasing x u
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1
- riginal
mild blur strong blur x u filter filter 1
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- riginal
samp.: no filter samp.: mild blur samp.: strong blur x u severe aliasing some aliasing minimal aliasing
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- riginal
sampled sampled × 2 sampled × 4 T T 1 T T 1 T T 1 aliasing aliasing minimal aliasing x u
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- riginal