e178-04L6

e178-04L6 - Quantization (Jan 22, 2004) Optimal Quantizer...

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Quantization (Jan 22, 2004) & Optimal Quantizer & Uniform Quantizer
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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
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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)
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Example: quantization rt t qt t r r kk k k k k =+ F H G I K J =− = −− 1 2 10 256 5 256 11 Quantization interval Constant Uniform quantizer
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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.
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Optimum MSE quantizer Ε Ε () ,( ( ) ) ( ) ( ) ( ) ( ) [, ] , ( ) ; uu p u d u MSE u u u u p udu ur ut t p u d u rt u t kk k i t t i L u L i i = =− =∈ == + = z zz z + + Expected value of u = Since if
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e178-04L6 - Quantization (Jan 22, 2004) Optimal Quantizer...

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