lecture7_median_morph

lecture7_median_morph - Median Filtering and Median...

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edian Filtering and Median Filtering and Morphological 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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Lecture Outline Median filter ank order filter Rank order filter Bilevel Morphological filters Dilation and erosion Opening and closing Grayscale Morphological filters Yao Wang, NYU-Poly EL5123: Non-linear Filtering 2
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Median Filter Problem with Averaging Filter lur edges and details an image Blur edges and details in an image Not effective for impulse noise (Salt-and-pepper) Median filter: Taking the median value instead of the average or weighted average of pixels in the window Sort all the pixels in an increasing order, take the middle one The window shape does not need to be a square pecial shapes an preserve line structures – Special shapes can preserve line structures Yao Wang, NYU-Poly EL5123: Non-linear Filtering 3
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Median Filter: 3x3 Square Window 100 100 100 100 100 00 00 05 03 00 100 200 205 203 100 100 195 200 200 100 100 200 205 195 100 Window shape 100 100 100 100 100 100 100 100 100 100 100 100 200 100 100 100 200 200 200 100 100 100 195 100 100 100 100 100 100 100 Yao Wang, NYU-Poly EL5123: Non-linear Filtering 4 Matlab command: medfilt2(A,[3 3])
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Median Filter: 3x3 Cross Window 100 100 100 100 100 00 00 05 03 00 100 200 205 203 100 100 195 200 200 100 100 200 205 195 100 Window shape 100 100 100 100 100 100 100 100 100 100 100 195 200 200 100 100 200 200 200 100 100 195 200 195 100 100 100 100 100 100 Yao Wang, NYU-Poly EL5123: Non-linear Filtering 5 Note that the edges of the center square are better reserved
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Example Yao Wang, NYU-Poly EL5123: Non-linear Filtering 6
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Matlab Demo: nrfiltdemo Original Image Corrupted Image Filtered Image Yao Wang, NYU-Poly EL5123: Non-linear Filtering 7 Can choose between mean, median and adaptive (Wiener) filter with different window size
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Rank order filters Rank order filters stead of taking the mean rank all pixel Instead of taking the mean, rank all pixel values in the window, take the n-th order alue. value. E.g. max or min or median roperties Properties Non-linear T(f 1 + f 2 ) T(f 1 ) + T(f 2 ) Yao Wang, NYU-Poly EL5123: Non-linear Filtering 8
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Multi-level Median Filtering To reduce the computation, one can concatenate several small median filters to realize a large window operation. When the small windows are designed properly, this approach can also help reserve edges better. Median Yao Wang, NYU-Poly EL5123: Non-linear Filtering 9
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Hybrid Linear/Median Filter One can combine median filters with linear r rank order filters or rank order filters. MED1 MIN r MED2 Or MAX Or MEAN MED3 Yao Wang, NYU-Poly EL5123: Non-linear Filtering 10
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Morphological Processing Morphological operations are originally developed for bilevel images for shape and structural manipulations . Basic functions are dilation and erosion .
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lecture7_median_morph - Median Filtering and Median...

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