Re: Wavelet based compression for not squared images

Rafael wrote:

for wavelet based image compression they always use a dyadic DWT.
You mean, the Mallat basis? Not necessarely. The FBI fingerprint
algorithm uses a different basis. JPEG2000-2 can use a different
basis.

With dyadic DWT I mean that width and height of successive subbands
are always have the size of their predecessor subband. At least for
EZW and SPIHT algorithm this is quite a basic feature because this
ensures that every coefficient has 4 descendants.

Some special rules have to be invented to work around this necessity, which means the boundary handling has to be specified. For EZW, for example, it seems quite natural to say that a coefficient has significant "parents" if the intersection of the 2x2 neighbourhood in the parent band with the image rectangle (which then might be smaller than 2x2) is significant.

So does dyadic mean the same than Mallat basis (didn't find much
information in the internet about it!) ? If I consider the example you
gave, the answer is probably no!

Probably no.

You are misinformed! ...
At this page: http://jj2000.epfl.ch/jj_tutorials/jpeg2000_720_540/28.html
they say JPEG2000-1 uses only dyadic decomposition, this implies that
the tiles have to be of size 2^k otherwise a further dyadic
decomposition is not possible anymore at a certain point.

The decomposition is "as dyadic as possible".

Lets take
your example with 3x3 tiles. A further dyadic decomposition won't be
possible any more (1,5x1,5 ????)!

Of course it is possible! With the tile origin at 0x0, we have for the first level that the band sizes are 2x2,2x1,1x2 and 1x1.

HTHH,
Thomas

Fuer was steht HTHH??? :)

Hope to have helped.

Greetings,
Thomas
.

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