HOe178-04L6

# HOe178-04L6 - Image Quantization Quantization (Jan 22,...

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Quantization (Jan 22, 2004) & Optimal Quantizer & Uniform Quantizer 01/22/04 Quantization 2 Image Quantization u (continuous ) Quantizer u& ε {r 1 ,r 2 ,r 3 ,.... ,r L } u& u t 1 t L+1 t k t k+1 r k 01/22/04 Quantization 3 Decision/Reconstruction Levels u ε [t k ,t k+1 ] r k {t k : k=1,2,. ...,L+1} Transition or decision levels r k k th reconstruction level Example: Uniform quantizer u ε [0,10.0] We want u& ε {0,1,. ....,255} t 1 = 0; t 257 = 10.0; uniformly spaced, t k = (k-1).10/256 k = 1,2,. ....,257) 01/22/04 Quantization 4 Example: quantization rt t qtt r r kk k kkk =+ F H G I K J =− =− = −− 1 2 10 256 5 256 11 Quantization interval Constant Uniform quantizer 01/22/04 Quantization 5 MMSE Quantizer Minimise the mean squared error, MSE = Expected value of (u-u&) 2 given the number of quantization levels L. Assume that the density function p u (u) is known (or can be approximated by a normalised histogram). Note that for images, u==image intensity. p u (u) is the image intensity ditribution. 01/22/04 Quantization 6 Optimum MSE quantizer Ε Ε () , ( ( ) )( )( ) ( )( ) [, ] , ( ) ; uu p u d u M S E uup u d u u d u ur ut t ur pud u u t k i t t i L u

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## This note was uploaded on 12/28/2011 for the course ECE 178 taught by Professor Manjunath during the Fall '08 term at UCSB.

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HOe178-04L6 - Image Quantization Quantization (Jan 22,...

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