03-2 - Histogram processing

03-2 - Histogram processing - 4/28/2008 Histogram processing

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4/28/2008 1 Histogram processing Spring 2008 ELEN 4304/5365 DIP 1 by Gleb V. Tcheslavski: gleb@ee.lamar.edu Preliminaries The histogram of a digital image with intensity levels in the range [0, L 1] is a discrete function ( ) kk hr n = k th intensity value Number of pixels in the image with intensity r k Histograms are frequently normalized by the total number of pixels in the image. Assuming a M x N image, a normalized histogram Spring 2008 ELEN 4304/5365 DIP 2 () ,0 , 1 , . . . 1 k k n pr k L MN = = is related to probability of occurrence of r k in the image
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4/28/2008 2 Preliminaries Components are concentrated on the low (dark) side Components are concentrated on the high (light) side Narrow histogram typically concentrated around the middle Components cover a wide range of intensities – high contrast Spring 2008 ELEN 4304/5365 DIP 3 Histogram equalization Assuming that r represents the intensity of an input image in the range [0, L-1] (black to white), we consider the intensity mapping () 1 TL 0 ≤ ≤ sT rr L = such that a) T ( r ) is monotonically increasing in [0, L-1] – to prevent reversal intensity artifacts; b) T ( r ) being in [0, L-1] for r in [0, L-1] – to ensure the range of output intensity being the same as for input intensity. Spring 2008 ELEN 4304/5365 DIP 4 For example:
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4/28/2008 3 Histogram equalization The image intensity levels can be viewed as random variables in [0, L-1]. Let p r ( r ) and p s ( s ) represent pdfs of r and s We need a transformation that would produce the and s. We need a transformation that would produce the output image with uniform p s ( s
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This note was uploaded on 12/08/2010 for the course ELEN 4304 taught by Professor Staff during the Spring '08 term at Lamar University.

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03-2 - Histogram processing - 4/28/2008 Histogram processing

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