Re: few technical questions

>>The cool thing is that you can sort the coefficients by size, take as
>>many of the largest ones as you want, and you are guaranteed that you
>>have picked the right ones.
> 
> Really, I know the principles of wavelet transform, and it can by expressed
> (the principle) in warious ways. One of them is:

I already understood your 1.1-2.2 stuff this way - I did not want to 
urge you to retype all this :) .

> ...and the key word is: "in that direction" ;-)
> 
> Now, when you'll perform a wavelet transform on your favourite graphics tool
> you'll see that in part 2.2) there is large signal strength in diagonal
> axes. Try to perform a 1D wavelet transform on 2.2) part in diagonal
> direction (left-top->right-bottom, followed by right-top->left-bottom), and
> witness the energy compaction -).
> 
> I agree, the red-black wavelet transform would do the trick. In fact i'm
> inwestigating it roght now. But red-black transform is hard to perform in
> parallel, due to it's checkboard-interaved nature. The locality, and
> isgnal-gathering properties are far superior than separable (orthogonal)
> wavelet transform.

I have just read the red-black wavelet paper. The two images of the 
wavelet transforms (Fig. 7) are very illustrating, esp. the tensor 
product case.

> This is no problem. Width and height have different lengths on 99% of
> images, and that's no problem, isn't it ?

You are right, if you are doing only one step. (We PDE people always 
think in 2^J...)

>>I am positively curios how your method performs quality-wise against a
>>three-level (or full) wavelet transform which also gets you 16 (or more)
>>bands (and should be about equally fast) where you strictly go for
>>coefficient size. Maybe better for diagonally dominant pictures and
>>worse for vert/horiz symmetry (-> test examples)?
>>
> This approach would work good in wavelet transforms that shoud be performed
> in parallel, but does not offer the perfect locality of red-black transform.
> My current research focusses on building an adaptive red-black wavelet trans
> form (look-up the adaprive wavelet transform (reduces ringing, better
> preservation of shap features), and red-black trees), with different sizes
> of "detail" kernel and fixed "averages" kernel. It's easily extendable into
> 3D wavelets (possibly motion-corrected).

In the end, we want to do compression - what happens in all three cases 
(full tensor product, your diagonal add-on and red-black) if you simply 
pick the N largest pixels after either method for several choices of N 
and some popular images, set all others to zero and transform back? The 
isotropy properties indicate where in the transformed image you will 
find the bigger coefficients, but not how important they are. Can you 
give some pictures?

Carsten


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