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Unformatted text preview: Restoration in the Presence of Noise Only – Spatial Filtering COMP344 COMP344 Restoration in the Presence of Noise Only – Spatial Filtering Restoration in the Presence of Noise Only g ( x , y ) = h ( x , y ) * f ( x , y ) + η ( x , y ) When noise is the only image degradation present in an image g ( x , y ) = f ( x , y ) + η ( x , y ) G ( u , v ) = F ( u , v ) + N ( u , v ) In case of periodic noise , it is usually possible to estimate N ( u , v ) from the spectrum of G ( u , v ) and subtract it to obtain an estimate of the original image f ( x , y ) In general, estimating the noise terms η ( x , y ) is unreasonable, so subtracting them from g ( x , y ) is impossible Spatial filtering is the method of choice in situations when only additive noise is present COMP344 Restoration in the Presence of Noise Only – Spatial Filtering Spatial Filter: Mean Filter Mean filters Arithmetic mean filter Geometric mean filter Harmonic mean filter Contraharmonic mean filter Common to all mean filters is that they operate on a rectangular subimage of size m × n centred at point ( x , y ) COMP344 Restoration in the Presence of Noise Only – Spatial Filtering Arithmetic Mean Filter Arithmetic mean given { a 1 , a 2 , . . . , a n } 1 n ∑ n i =1 a i Arithmetic mean filter computes the average value of the corrupted image g ( x , y ) in the area defined by S xy ˆ f ( x , y ) = 1 mn ∑ ( s , t ) ∈ Sxy g ( s , t ) smooths local variance of the image can also be implemented by using a convolution mask with all the coefficients equal to 1 / ( mn ) COMP344 Restoration in the Presence of Noise Only – Spatial Filtering Geometric Mean Filter Geometric mean Q n i =1 a i 1 / n = n √ a 1 · a 2 . . . a n Example Geometric mean of 2 and 8: 4 Geometric mean filter computes the product of the pixels of the corrupted image g ( x , y ) in the area defined by S xy . Then, it raises the product to the power 1 / ( mn ) ˆ f ( x , y ) = h Q ( s , t ) ∈ Sxy g ( s , t ) i 1 mn achieves smoothing comparable to the arithmetic mean filter, but it tends to lose less image detail in the process...
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 Fall '09
 AlbertK.Wong
 Mean, Sxy, Spatial Filtering

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