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lecture5_filtering

lecture5_filtering - Spatial Domain Linear Spatial Domain...

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patial Domain Linear Spatial Domain Linear Filtering Yao Wang Polytechnic University, Brooklyn, NY 11201 With contribution from Zhu Liu, Onur Guleryuz, and Gonzalez/Woods, Digital Image Processing, 2ed
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Outline Introduction oise remo al sing lo ass filters • Noise removal using low-pass filters • Sharpening by edge enhancement Edge detection using high-pass filters Edge enhancement by high emphasis filters Edge detection First order gradient g Second order gradient ummary Yao Wang, NYU-Poly EL5123: Spatial Filtering 2 Summary
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Problems Smoothing oise removal Noise removal Detail preserving image smoothing Sharpening Edge enhancement Detail focusing Edge detection Yao Wang, NYU-Poly EL5123: Spatial Filtering 3
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Approaches Spatial domain operation or filtering (the rocessed value for the current pixel processed value for the current pixel depends on both itself and surrounding ixels) pixels) Linear filtering on ear filtering Non-linear filtering Rank order filtering including median orphological filtering Morphological filtering Adaptive filtering Yao Wang, NYU-Poly EL5123: Spatial Filtering 4
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Noise Removal (Image Smoothing) An image may be “dirty” (with dots, speckles,stains) Noise removal: To remove speckles/dots on an image Dots can be modeled as impulses (salt-and-pepper or speckle) r continuously varying (Gaussian noise) or continuously varying (Gaussian noise) Can be removed by taking mean or median values of neighboring pixels (e.g. 3x3 window) quivalent to low ass filtering Equivalent to low-pass filtering Problem with low-pass filtering May blur edges More advanced techniques: adaptive, edge preserving Yao Wang, NYU-Poly EL5123: Spatial Filtering 5
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Example Yao Wang, NYU-Poly EL5123: Spatial Filtering 6
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Averaging Filter: An Intuitive Approach Replace each pixel by the average of ixels in a square window surrounding this pixels in a square window surrounding this pixel ) 1 , 1 ( ) , 1 ( ) 1 , 1 ( ( 1 ) , ( n m f n m f n m f n m g )) 1 , 1 ( ) , 1 ( ) 1 , 1 ( ) 1 , ( ) , ( ) 1 , ( 9 n m f n m f n m f n m f n m f n m f Trade-off between noise removal and etail preserving: detail preserving: Larger window -> can remove noise more effectively, but also blur the details/edges Yao Wang, NYU-Poly EL5123: Spatial Filtering 7 y, g
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Example: 3x3 average 100 100 100 100 100 100 200 205 203 100 100 195 200 200 100 100 200 205 195 100 100 100 100 100 100 100 100 100 100 100 100 144 167 145 100 100 167 200 168 100 100 144 166 144 100 100 100 100 100 100 Yao Wang, NYU-Poly EL5123: Spatial Filtering 8
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Example Yao Wang, NYU-Poly EL5123: Spatial Filtering 9
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Weighted Averaging Filter Instead of averaging all the pixel values in the indow, give the closer- y pixels higher window, give the closer by pixels higher weighting, and far-away pixels lower weighting.
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