EECE253_16_MedianFilters

# EECE253_16_MedianFilters - EECE\CS 253 Image Processing...

This preview shows pages 1–11. Sign up to view the full content.

EECE\CS 253 Image Processing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester 2007 Lecture Notes Lecture Notes on Mathematical Morphology: The Median Filter This work is licensed under the Creative Commons Attribution-Noncommercial 2.5 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/2.5/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
27 April 2008 2 27 April 2008 2 1999-2007 by Richard Alan Peters II The Median Filter O Returns the median value of the pixels in a neighborhood O Is non-linear O Is a morphological filter O Is similar to a uniform blurring filter which returns the mean value of the pixels in a neighborhood of a pixel O Unlike a mean value filter the median tends to preserve step edges original median filtered
27 April 2008 3 27 April 2008 3 1999-2007 by Richard Alan Peters II This can be computed as follows: 1. Let I be a monochrome (1-band) image. 2. Let Z define a neighborhood of arbitrary shape. 3. At each pixel location, p = ( r , c ), in I 4. … select the n pixels in the Z -neighborhood of p , 5. … sort the n pixels in the neighborhood of p, by 6. The output value at p is L ( m ), where m = n / 2 +1. value, into a list L ( j ) for j = 1,…, n . Median Filter: General Definition { } () { } supp med , median Z IZ I ∈+ = qp pq

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
27 April 2008 4 27 April 2008 4 1999-2007 by Richard Alan Peters II Median Filter: General Definition sorted intensity values from neighborhood of p . 131 133 133 136 140 143 147 152 154 157 160 162 163 164 165 171 p p median assigned to pixel loc p in output image.
27 April 2008 5 27 April 2008 5 1999-2007 by Richard Alan Peters II A Noisy Step Edge ( ) = + 33 25 . 1 32 25 . 0 25 . 0 5 . 32 n n n H for for ( ) ( ) ( ) ( ) 25 . 0 , 25 . 0 unif 5 . 32 = + where n u n u n H

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
27 April 2008 6 27 April 2008 6 1999-2007 by Richard Alan Peters II Blurred Noisy 1D Step Edge ( ) ( ) = + = 4 4 9 1 k k n h n h
27 April 2008 7 27 April 2008 7 1999-2007 by Richard Alan Peters II Blurred Noisy 1D Step Edge J(32-4:32+4)= 0.1920 0.3416 0.0464 0.0177 0.3062 1.3043 1.0079 1.0082 1.0950 J(33-4:33+4)= 0.3416 0.0464 0.0177 0.3062 1.3043 1.0079 1.0082 1.0950 1.2935 0.5910 0.7134 mean mean

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
27 April 2008 8 27 April 2008 8 1999-2007 by Richard Alan Peters II Median Filtered Noisy 1D Step Edge ( ) ( ) {} 4 4 med = + = k k n h n h
27 April 2008 9 27 April 2008 9 1999-2007 by Richard Alan Peters II Median Filtered Noisy 1D Step Edge J(32-4:32+4)= 0.1920 0.3416 0.0464 0.0177 0.3062 1.3043 1.0079 1.0082 1.0950 0.0177 0.0464 0.1920 0.3062 0.3416 1.0079 1.0082 1.0950 1.3043 J(33-4:33+4)= 0.3416 0.0464 0.0177 0.3062 1.3043 1.0079 1.0082 1.0950 1.2935 0.0177 0.0464 0.3062 0.3416 1.0079 1.0082 1.0950 1.2935 1.3043 sorted sorted median median

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
27 April 2008 10 27 April 2008 10 1999-2007 by Richard Alan Peters II Median vs. Blurred step noisy blurred median The median filter preserves the step edge better than the blurring filter.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 43

EECE253_16_MedianFilters - EECE\CS 253 Image Processing...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online