[theora-dev] What sort of math i required?

[Martin Jeppesen]

> http://datacompression.info/index.shtml has links to most everything
> useful on the web. Most of it is introductory, but as I said, Theora
> doesn't get that sophisticated. Just Huffman and RLE, for the most part.
> This is, however, something that can be addressed without losing the
> ability to losslessly transcode. Of course, you may also run into patent
> issues.

Thanks for the link. I have been trying out the Adaptive Huffman. I
remember from Amiga days, the Crunch Mania used Huffman along some sliding
window.

Why are people still using Huffman? Haven't there come better algorithms
since?

> A general knowledge of wavelets is certainly useful, but not directly
> applicable. Tarkin was supposed to be Xiph's foray into a wavelet-based
> video codec, but it has been mostly dormant for the past year or more.
> Also, not everyone believes that wavelets are the way to go.

Does there excist a wavelet codec today?

> Wavelets could almost certainly provide better compression than the
> vanilla DCT Theora uses, but also carry an increased computational cost.
> They'd also break backwards compatibility.

Interesting indeed! It seams to me, that wavelets are the state of the
art.

>  > An advanced linear algebra course sounds interesting indeed! Can you
>  > give an example where linear algebra is heavily used in Theora?
>
> I recently developed a border padding algorithm that uses a Cholesky
> decomposition to extract a well-behaved set of DCT basis functions that
> are linearly independent over the domain of pixels inside the border,
> which can then be used to select pixel values for pixels outside the
> image border that introduce as many zero coefficients as possible into
> the DCT transform of the block. A very similar process is behind Monty's
> declipping algorithm in postfix, though he does it with a QR decomposition.

How is it preforming? Will it be used?

> The DCT is just a linear transformation. As is the discrete Fourier
> transform. The usefulness of a more abstract view of linear algebra is
> when you realize that the continuous Fourier transform is, too.

Neat!!

> >>>        However, there is also more math involved in encoding when you
> >>> cover topics such as data rate control and psycho-visual models.
> > Have this been documented yet?
>
> Not outside my (reasonably well-commented) source code for my
> experimental encoder. It's also nowhere near ready for prime time yet.

I would love it read it when it is ready!!

<p>> Specialized topics include, but are not limited to, rate control (and
> rate/distortion optimization), motion compensation, quantization (vector
> and otherwise), postprocessing (deblocking and deringing), video
> standards (color spaces, pixel formats, interlacing, etc.).
>
> Don't be put off by the wide variety of topics. You can certainly
> contribute and be useful before you've mastered all of these, and
> hands-on experience is often the best kind.

I surdenly hope so=)

Thanks.

Martin

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