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eee508_Enhancement_Part3

# eee508_Enhancement_Part3 - Nonlinear Filtering for Noise S...

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Nonlinear Filtering for Noise Smoothing Frequency Domain Method for Noise Smoothing ¾ Example: Picture with lines on it. Can we get rid of lines? Think of the image as desired image + noise (lines). ¾ Consider working in transformed domain: take DTFT or DFT. ¾ Exploit separability of noise and image. EEE 508 1

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Nonlinear Filtering for Noise Smoothing ¾ Consider DTFT of noise image: Ȧ 2 ʌ d ( n 1 , n 2 )= d ( n 2 )·1 D ( Ȧ 1 , Ȧ 2 )=2 ʌ į ( Ȧ 1 ) D ( Ȧ 2 ) Ȧ (1) ( constant along n 1 ) 1 ʌ - ʌ ¾ DTFT of the desired image: - ʌ ʌ Ȧ 1 ʌ - ʌ (2) EEE 508 2
Nonlinear Filtering for Noise Smoothing ¾ DTFT of original (noisy) image: Ȧ 2 ʌ Ȧ 1 ʌ - ʌ (1)+(2) ¾ In the frequency domain, the signal and noise are separable ( i t l ) ll t i t b i d t i - ʌ (approximately) null out noise component by removing dots in frequency domain, then take inverse transform the noise is gone or significantly reduced. EEE 508 3

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Nonlinear Filtering for Noise Smoothing ¾ DTFT of filtered image: Ȧ 2 ʌ Ȧ 1 ʌ - ʌ (1)+(2) - ʌ EEE 508 4
Edge Enhancement Motivation: Edges are very important for intelligibility, segmentation, analysis, and identification. Transform Compression 1. Root Filtering x ( n 1 n 2 ) l X ( K 1 , K 2 ) = Transform (such as DFT) ± ² ± ² ± ² 1 0 ; , , , 2 1 1 2 1 2 1 d d ³ D D K K X K K X K K X ± ² ± ² 1 0 ; , 2 1 , 2 1 d d D T D K K j o e K K X ¾ Note : Since 0 D 1 | X ( K 1 , K 2 )| D = D root of magnitude of X ( K 1 , K 2 ). EEE 508 5

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Edge Enhancement ¾ Observation : (about behavior) y = a y 0 < D < 1 y = a D ¾ Eff f i b l li d a 0 Effect of D -rooting: boosts low-amplitude components or coefficients and de-emphasizes high–amplitude components or coefficients. EEE 508 6
Edge Enhancement ¾ For natural or common images, high-frequency components, which correspond to edges, tend to have low amplitudes, and low- frequency components tend to have high amplitudes. D – rooting boosts high–frequency components which correspond to edges to edges. ¾ D – rooting can be done in any transform domain: DFT, DCT, or Hadamard domain. ¾ Note: Blur is associated with loss in high-frequency region: Note: Blur is associated with loss in high frequency region: boosting the high-frequency components can help in improving the blurred image.

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eee508_Enhancement_Part3 - Nonlinear Filtering for Noise S...

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