Re: Wavelets and Reflection image question

Jerzie.Klenchier@xxxxxxxxx wrote:
Hi all,

I've recently begun trying to understand the fundamentals of
lossy image compression via transforms such as DCT and Wavelets
(CDF9/7).

In a paper I was reading it suggested that prior to applying a
forward transform that a "reflection image" of the original image
be created.

This involves flipping the image vertically and horizontally and
copy those flipped variants above, below and to the left and right
hand-side, ending up with a larger image that is 3xwidth and 3xheight
of the original. then applying the forward transform and then the
inverse transform leads to a much higher PSNR than when the image
itself is forward then inverse transformed.

My questions are:

1. What is this method called? as I can't find anything else in the
literature I have that comments about this

Dependent on how precisely the flipping is done, this is called WSS or HSS (whole sample symmetric resp. half sample symmetric) extensions. For the odd-length wavelets in JPEG2000 (CDF9/7,5/3), you need the WSS.


2. Why does it provide a better result? is this some kind of Gibbs
effect on the border areas? I find that a great deal of the nose
when only using the original image comes from around the borders.

The reason why WSS works so nice with the 9/7 and the 5/3 is the symmetry of the wavelet. That is, the symmetric extension of the wavelet
creates after filtering wavelet coefficients that are symmetric again. You can, thus, on the backwards transformation, just mirror-extend the
wavelet data, and filter it, to go back to the original image, i.e.
mirroring in the wavelet domain and in the image domain are equivalent.
That said, you do not need to keep any reference to data outside of the image, and you get back the *identical* result.

For DCT, for example, you need to keep DCT coefficients at the boundary that belong to "invented" data, namely those belonging to coefficients
outside the image. This is not the case here.

A good reference for this is probably the Marcellin/Taubman book on JPEG2000.

So long,
Thomas
.

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