[MPlayer-dev-eng] New opensourced video codec NODAEMON

[Shachar Raindel]

Thx, excellent tutorial. There are more details about it are available
in THE book about image processing - Digital Image Processing by
Gonzalez and Woods -  http://www.imageprocessingbook.com/default.htm ,
and in the advanced image processing course in the university close to
you....


     Cheers,
     Shachar

On Sun, 25 Jul 2004 22:45:30 +0200, Roberto Ragusa
<mail at robertoragusa.it> wrote:
> On Thu, 22 Jul 2004 22:06:33 +0900
> Attila Kinali <attila at kinali.ch> wrote:
> 
> > On Tue, May 11, 2004 at 02:57:16PM +0200, Tomas Mraz wrote:
> > > http://sourceforge.net/projects/dirac
> > Has someone had a look at this ?
> 
> It's a work in progress.
> At the moment the quality is good (similar to divx, I'd say), but
> the speed is very low because the algorithm is complex and the code
> not optimized (less than 1fps in my tests).
> Very promising, nonetheless.
> In a few words: divx is motion compensation+DCT, dirac is
> motion compensation+wavelet (a better motion compensation, indeed).
> 
> > And while we are at this, does someone know a good
> > (meaning easy to understand but complete) introduction to
> > wavelet based auido/video coding ?
> 
> I've some experience on the matter.
> What I've found is that the wavelet theory can be approached
> either in a purely mathematical style (talking about "mother wavelet"
> and "infinite series") or in a digital signal processing style
> (talking about "filters" and "resampling").
> 
> More documentation can be found on the first approach, but the
> second approach is IMNSHO easier to understand for people with
> a dsp background (that is, with knowledge on band-limited signals,
> sampling, filters, frequency domain).
> 
> I don't have a link to a good introduction, but the idea is extremely
> simple.
> 
> 1) Consider a sampled monodimensional signal (e.g. audio); you have
> N numbers.
> 
> 2) Apply a low pass filter (let's call it L1) and a high pass filter (H1);
> you have two sequences of N numbers.
> 
> 3) As these two sequences are oversampled, discard every second sample;
> you have two sequences of N/2 numbers (so N numbers again, overall).
> 
> Now the important part: the two sequences of N/2 numbers are equivalent
> to the original sequence, because you can:
> 
> 4) Oversample them inserting a zero after each of the samples;
> you have two sequences of N numbers.
> 
> 5) Apply a low pass filter (L2) to the first one, a high pass filter (H2)
> to the second one; you have two sequences of N numbers.
> 
> 6) Add the two sequences; you have N numbers.
> 
> The final result is identical to the original sequence if some conditions
> are met by L1, H1, L2, H2 (this is were some reasoning in frequency domain
> is necessary).
> 
> Step 1-3 are a wavelet transform, step 4-6 are an inverse wavelet transform.
> 
> But why is this useful for compression? Because:
> a) the two N/2 sequences have different statistics (so custom entropy
> coders can take advantage of that)
> b) the first one is an approximation of the signal, while the second one
> contains the extra details; you can heavily quantize the second without
> much degradation
> 
> You usually apply the transformation again to the first N/2 sequence,
> obtaining two N/4 sequences. So you have (N/4+N/4)+N/2 samples (brutal
> approximation, big details, small details), and so on.
> 
> Example: we will use x0+x1 as low pass filter and x0-x1 as high pass filter.
> A sequence of eight numbers:
>   s= a b c d e f g h (8 samples)
> After ome step of transformation:
>   sl= a+b c+d e+f g+h (4 samples)
>   sh= a-b c-d e-f g-h (4 samples)
> After a second step transform:
>   sll= a+b+c+d e+f+g+h (2 samples)
>   slh= a+b-c-d e+f-g-h (2 samples)
>   sh= a-b c-d e-f g-h (4 samples)
> It is not difficult to understand that you can reverse
> the calculation and find s.
> 
> This has been a very crude simplification, in real world we have
> to consider that:
> 
> - the lenght of the filters is greater than 2 and the filters are
> accurately designed
> - for bidimension signals (images) you split a N*N into four N/2*N/2
> (approximation, horizontal detail, vertical detail, diagonal detail);
> this is usually done by filtering along x and then along y
> - the number of steps can be higher (you could reduce the first
> sequence to one sample only, if you want)
> - you have to be careful when working near the edges because
> longer filters may need samples number -1, -2 or N+1, N+2..., which
> you don't have
> 
> The detail extraction strategy works very well on pictures, because
> all smooth areas have almost zero details.
> 
> In conclusion you split the signal into particular sub bands and
> quantize/encode each of them at your desire.
> The real power of the wavelet approach is that you don't have
> to choose a fixed number upon everything depends (such as size of
> DCT blocks) and that you have no blocking artifacts at all.
> The first thing means that you have no intrinsic limit in your
> compression factor (a 8x8 DCT approach has a sort of 64:1 limit).
> The second thing means that heavy compression just blurs the image
> (DCT needs postprocessing to smooth block edges).
> 
> The whole process is a sort of DCT with adaptive block size
> (e.g. 64x64 on the sky, 2x2 on the grass) and with partially
> overlapped blocks.
> 
> I hope this tutorial was simple enough.
> 
> --
>    Roberto Ragusa    mail at robertoragusa.it
> 
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