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eee508_Enhancement_Part2

eee508_Enhancement_Part2 - Homomorphic Processing o o o p c...

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Homomorphic Processing Motivation: Image with a large dynamic range, e.g. natural scene on a bright sunny day, recorded on a medium with a small dynamic range, e.g. a film image contrast significantly reduced especially in the dark and bright regions. One Approach: Enhance image by reducing its dynamic range and increase its local contrast prior to recording it on medium with a small dynamic range. use a homomorphic processing t hi h t i l i t it d i system which operates in log intensity domain. 1 EEE 508
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Homomorphic Processing ¾ Strategy based on: x ( n 1 , n 2 ) = i ( n 1 , n 2 ) · r ( n 1 , n 2 ) Image formed by Illumination: Reflectance Image formed by recording light reflected from objects which are illuminated by li ht Illumination: assumed to be slow varying and main contributor to dynamic range Reflectance component: represents details of objects and assumed to very rapidly and some light source the primary contributor to local contrast 9 To decrease dynamic range, decrease i ( n 1 , n 2 ) 9 To increase local contrast, increase r ( n 1 , n 2 ) 2 EEE 508
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Homomorphic Processing ¾ To separate the two components i ( n 1 , n 2 ) and r ( n 1 , n 2 ) , apply a logarithmic operation log x ( n 1 , n 2 ) = log [ i ( n 1 , n 2 )] + log [ r ( n 1 , n 2 )] low frequency usually high/mid frequency y 1 ( n 1 , n 2 ) assumed to remain slowly varying assumed to remain rapidly varying J <1 LPF log [ i ( n 1 , n 2 )] u y 1 1 y 2 log HPF u log [ r ( n 1 , n 2 )] x ( n 1 , n 2 ) exp + x 0 ( n 1, , n 2 ) 3 EEE 508 J 2 >1 H ( Ȧ 1 , Ȧ 2 )
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Homomorphic Processing y ( n n ) y ( n n ) J 2 H ( Ȧ 1 , Ȧ 2 ) log x ( n 1 , n 2 ) 1 n 1 , n 2 exp x 0 ( n 1, , n 2 ) 2 n 1 , n 2 J 1 2 2 2 1 Z Z ± y 2 ( n 1 , n 2 ) | J 1 log [ i ( n 1 , n 2 )] + J 2 log [ r ( n 1, n 2 )] x 0 ( n 1 , n 2 ) = [ i ( n 1 , n 2 )] J 1 [ r ( n 1 , n 2 )] J 2 J 1 and J 2 allow for control over illumination and contrast. Note : System with log operation followed by a linear operation followed by exponentiation operation is called a “homomorphic system for multiplication” or “multiplicative homomorphic processing”.
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