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

Christoph Lampert chl at math.uni-bonn.de
Thu Dec 11 07:49:40 PST 2003

On 11 Dec 2003, David Kuehling wrote:

> >>>>> "Christoph" == Christoph Lampert <chl at math.uni-bonn.de> writes:
> > the (main) problem with wavelet based codecs is that wavelets aren't
> > localized in the image space, so you cannot just use the very
> > successful block-based motion estimation as for all DCT-based codecs.
> I actually do not know much about all this but why shouldn't a simple
> wavlet-based codec be based on blocks?  What I've seen so far was an
> example using 8x8 wavlets gained via PCA.  Isn't DCT just a special case
> of a wavelet transform with the advantage of high speeds due to
> symmetries that allow speed optimizations analogous to FFT?

DCT is a rather good approximation of PCA (principle component analysis) 
over a wide range of video signals. 
PCA would be optimal from the theoretical point, but there basis functions
depend on input material, which of course you don't have when decoding. 

Advantages of wavelets is in particular scalability. JPEG2000 isn't that
much superior at low compression, but provides a much better picture as
high compression ratios.
IANAL, but my idea of things is that for just coding 8x8 blocks,
wavelets are not superior to DCT. 


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