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spline wavelets & WaveLab
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Josep Monés i Teixidorq (jmones (at) puntbarra (dot) net)
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PostPosted: Mon Nov 03, 2003 4:32 pm    
Subject: spline wavelets & WaveLab
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Hi,

I'm trying to implement a paper on video compression and it says that they use "biorthogonal 9-7 spline wavelets" for spatial decomposition. I'm using WaveLab in GNU Octave and I'm afraid it doesn't contain those wavelets.

I'm a newbie in wavelets and I miss a lot of things, so please sorry if I've overlooked something and my questions are too obvious.

* Where can I find the definition of those wavelets?
*Can anybody tell me what does that 9-7 mean?
* Does it refer to the N and Ñ coefficients of this explanation: http://documents.wolfram.com/applications/wavelet/FundamentalsofWavelets/1.6.3.html ?
* Do CDF filters in WaveLab802 refer to these filters? In that case, could anybody tell me the coefficients for the 9-7 filters, which are missing in WaveLab?

Thanks very much,

Josep
Sumit Kumar (snath@site.uottawa.ca)
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PostPosted: Mon Nov 03, 2003 6:04 pm    
Subject: Re: spline wavelets
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Hi Joseph

Well you got that partially right.. 9-7 indeed refer to the coefficients, but in some literature they also refer to the "vanishing moments" of the signal.
If you are interested in the actual coefficient values, then here they are

ad1[0] = 0.85269867900888996D;
ad1[1] = 0.37740285561282999D;
ad1[2] = -0.11062440441844D;
ad1[3] = -0.02384946501956D;
ad1[4] = 0.037828455507260002D;
----and apply a symmetry after this to get the other filter coefficients (the 9 coefficient filter)

ad2[0] = 0.78848561640637005D;
ad2[1] = -0.41809227322204001D;
ad2[2] = -0.040689417609200002D;
ad2[3] = 0.064538882628759994D;
(The 7 coefficient filter)

If you are looking for the definition of these filters, go back to Pg. 273 of "10 Lectures on Wavelets - I Daubechies"... There she explains how to obtain these wavelets.

May I ask you what aspect in video compression you are trying to accomplish, as I am also involved with (3-D) video compression and coding
Josep Monés i Teixidor (jmones (at) puntbarra (dot) net)
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PostPosted: Mon Nov 03, 2003 10:53 pm    
Subject: Low bandwith video compression
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Hi Sumit,

Thanks very much for your answer. As I understand then 9-7 filter corresponds to splines with N=4 and Ñ=4.

Am I wrong or the 7-th coeff filter you typed had ad2[1] and ad2[3] negated? Shouldn't it be:

ad2[0] = 0.78848561640637005D;
ad2[1] = 0.41809227322204001D;
ad2[2] = -0.040689417609200002D;
ad2[3] = -0.064538882628759994D;
(The 7 coefficient filter)

In Wavelab sources I found that Villasenor filter with param=1 is just the same filter but with both functions swapped. In the sources there's a comment that calls that the 7-9 filter. So I guess this is the 9-7... ;P

To answer your question about what I'm trying to do: it's just a project for an undergraduate course on image compression. It consists on chosing a paper which describes an algorithm and implement it (only implement it, no design involved). I've chosen a video compression codec based on wavelets (J.Y.Tham et al. "Highly Scalable Wavelet-Based Video Codec for Very Low Bit-Rate Environment". IEEE Journal on selected areas in communications. Vol 16 pp. 12-27, Jan 1998). It uses a simple motion compensation, Daubechies orthogonal wavelet for temporal decomposition, biorthogonal spline wavelet for spatial decomposition which then uses to build a TRI-ZTR, which the paper defines as an extension of Shapiro's zerotree from 2D to 3D.

As I'm a complete newbie on the subject (my knowledge is just from a few classes) I'm a little bit lost here... ;)
Sumit Kumar (snath@site.uottawa.ca)
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PostPosted: Tue Nov 04, 2003 12:04 am    
Subject: Re: spline wavelets
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Whoa, Joseph
Thank you for pointing out my mistake ! You are right there.. the symmetry should be applied from ad[0] in both cases ! Now you have talked abt the words "highly-scalable" video compression... What kind of scalability are you trying to achieve ? Spatial, Temporal, Spatio-temporal, SNR , Content or all of the above ?.. I am working with most of them anyways...
Sumit Kumar (snath@site.uottawa.ca)
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PostPosted: Tue Nov 04, 2003 12:14 am    
Subject: Re: spline wavelets
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Joseph,
My mistake again; I was right the first time....

Let me present all the coefficients (from MATLAB ) and not my Java source code :)

h0o =

0.02674875741081
-0.01686411844287
-0.07822326652899
0.26686411844287
0.60294901823636 -> point of symmetry
0.26686411844288
-0.07822326652899
-0.01686411844288
0.02674875741081

(Low-pass filter)

h1o =

0.04563588155713
-0.02877176311425
-0.29563588155713
0.55754352622850 -> point of symmetry
-0.29563588155712
-0.02877176311425
0.04563588155713

(High-Pass filter)

These are the analysis filters...Use the lifting steps, outlined in the paper by Sweldens and Daubechies to get the sythensis filters (rather the synthesis part of the wavelet transform)... Do not use a simple convolution to generate your wavelet transform
carolmincy (carolmincy@gawab.com)
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Subject: Hi everyone
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Subject: Payday Loans - Pros & Cons
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PostPosted: Fri Nov 30, 2012 7:49 am    
Subject: Re: spline wavelets
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PostPosted: Thu Dec 27, 2012 5:00 am    
Subject: Re: spline wavelets
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