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ezw_rmf - RMFBasedEZW Algorithm June1,2000 Organization...

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    RMF Based EZW  Algorithm School of Computer Science,  University of Central Florida, VLSI and M-5 Research Group June 1, 2000
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    Organization The EZW algorithm Basic concept Introduction of the algorithm An example A brief introduction of RMF 1-D RMF example 2-D RMF example The RMF based EZW algorithm Basic Idea Band_max construction algorithm An example Experimental results Conclusions
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    EZW – basic concepts(1) E  – The EZW encoder is based on progressive  encoding. Progressive encoding is also known as  embedded encoding Z  – A data structure called zero-tree  is used in EZW  algorithm to encode the data W  – The EZW encoder is specially designed to use  with wavelet transform . It was originally designed to  operate on images (2-D signals)
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    A Multi-resolution Analysis Example EZW – basic concepts(2) Lower octave has higher resolution and contains higher frequency information
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    The EZW algorithm is based on two  observations: Natural images in general have a low  pass spectrum. When an image is  wavelet transformed,  the energy in the  sub-bands decreases with the scale  goes lower (low scale means high  resolution), so the wavelet coefficient  will, on average, be smaller in the  lower levels than in the higher levels. Large wavelet coefficients are more  important than small wavelet  coefficients. 631 544    86  10   -7   29   55 -54  730 655   -13  30  -12  44   41  32     19  23   37  17   -4  –13  -13  39     25 -49   32  -4     9  -23  -17 -35    32 -10   56 -22  -7  -25   40 -10      6  34  -44   4  13  -12   21  24   -12  -2    -8 -24 -42    9  -21  45    13  -3   -16 -15  31  -11 -10 -17 typical wavelet coefficients  for a 8*8 block in a real image EZW – basic concepts(3)
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    EZW – basic concepts(4) The observations give rise to the basic progressive coding idea: 1. We can set a threshold T, if the wavelet coefficient is larger than T,  then encode it as 1, otherwise we code it as 0. 2. ‘1’ will be reconstructed as T (or a number larger than T) and ‘0’  will be reconstructed as 0. 3. We then decrease T to a lower value, repeat 1 and 2. So we get  finer and finer reconstructed data. The actual implementation of EZA algorithm should consider : 1. What should we do to the sign of the coefficients. (positive  or negative) ? – answer: use POS and NEG 2.
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