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e178-L9

e178-L9 - Image Sampling Lecture Slide#10 Week 5 Sampling...

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Image Sampling Lecture Slide #10 Week 5 Sampling 2 Sampling and Quantization Spatial Resolution (Sampling) Determines the smallest perceivable image detail. What is the best sampling rate? Gray-level resolution (Quantization) Smallest discernible change in the gray level value. Is there an optimal quantizer?

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Sampling 3 Image sampling and quantization In 2-D f(x,y) (Continuous image) Sampler f s (m,n) Quantizer u(m,n) To Computer Sampling 4 1-D 1 D x(t) Time domain X(u) Frequency T s(t) x s (t) = x(t) s(t) = Σ x(kt) δ (t-kT) s(f ) 1/T 1/T X s (f)
Sampling 5 2-D: Comb function y comb(x,y; Δ x , Δ y ) x Δ x Δ y Comb( , ; , ) ( , ) x y x y x m x y n y n m Δ Δ Δ Δ = −∞ = −∞ δ Sampling 6 Sampled Image f x y f x y x y x y f m x n y x m x y n y x y x y u v x y u v x y s n m ( , ) ( , ) ( , ; , ) ( , ) ( , ) ( , ; , ) ( , ) , ; , ) = = ← → = = −∞ = −∞ comb comb COMB comb( Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ δ 1 1 1

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Sampling 7 Sampled Spectrum F s ( u , v ) = F ( u , v ) COMB ( u , v ) = 1 Δ x Δ y F ( u , v ) k , l = −∞
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