Splitting image into periodic lattice of fractals instead of squares.
dud...@gmail.com
In image compressors (like JPEG, JPEG 2000) the image is splitted into
lattice of squares to be processed faster.
So in lossy compression, we can see recognizable lattice of lines of
discontinuity.
Splitting into periodic lattice of fractal-like shapes shouldn't have
this problem.
We can do it very easily and quickly, using complex base systems:
http://arxiv.org/pdf/0712.1309
To encode inside such shape - we can use wavelet transform
threating it as it was just usual one dimensional binary system.
Phil Carmody
Do you have any evidence that images have a coherence over filigree-
shaped regions that is stronger than their coherence over a small
square region; if so please explain the nature of this coherence?
Or are you just heading slowly and steadily into the crank file?
Phil
--
Dear aunt, let's set so double the killer delete select all.
-- Microsoft voice recognition live demonstration
Marco Al
> To encode inside such shape - we can use wavelet transform
> threating it as it was just usual one dimensional binary system.
Unfortunately the correlation between a sample and it's neighbors in
that one dimensional space is less than the correlation of a pixel with
it's 2D neighborhood. Without some way to make use of correlation in 2D
it's performance will be limited.
Even as a scan pattern for predictive coding space filling curves aren't
useful ... they increase the average distance from a pixel to be coded
to it's already coded neighbors, as such they again reduce correlation.
A new form of spacefilling curves is very cool, but they aren't very
useful for compression.
Marco
Thomas Richter
> Hi all
>
> In image compressors (like JPEG, JPEG 2000) the image is splitted into
> lattice of squares to be processed faster.
Since when does JPEG2000 split images into lattices of squares?
> So in lossy compression, we can see recognizable lattice of lines of
> discontinuity.
Not for JPEG2000 - have you looked at the images?
So long,
Thomas
dud...@gmail.com
I'm sorry I'm new in this field, but I would gladly think about it, if
You could recommend some available papers.
>Unfortunately the correlation between a sample and it's neighbors in
>that one dimensional space is less than the correlation of a pixel with
>it's 2D neighborhood.
I don't see the problem - blocks of each size (supports of wavelets)
creates standard 2 dimensional lattice - we can use 2 dimensional
correlation methods.
>Since when does JPEG2000 split images into lattices of squares?
http://en.wikipedia.org/wiki/Jpeg_2000
for example "Using many tiles can create a blocking effect similar to
the older JPEG 1992 standard."
If You encode blocks lossy separately, You will always have
disconitiniouses - I think if they they will be less recognizable if
they won't create straight pixel lines.
Jarek
Thomas Richter
>> Since when does JPEG2000 split images into lattices of squares?
> http://en.wikipedia.org/wiki/Jpeg_2000
> for example "Using many tiles can create a blocking effect similar to
> the older JPEG 1992 standard."
Which implies that you can use no tiles at all - and this is in fact
what I highly recommend to do. *Do not use tiles*. This doesn't make any
sense.
> If You encode blocks lossy separately, You will always have
> disconitiniouses - I think if they they will be less recognizable if
> they won't create straight pixel lines.
And they continue even less distraction if there are no tiles at all. (-:
So long,
Thomas
dud...@gmail.com
I agree that will look much better, but it seems very time consuming,
especially if we would need hardware compressor/decompressor. Fractal
covering could be used for example in digital cameras.
dud...@gmail.com
we have to increase dimensions to a power of 2.
dud...@gmail.com
wavelets with the largest supports.
Aleks Jakulin
> Splitting into periodic lattice of fractal-like shapes shouldn't have
> this problem.
> We can do it very easily and quickly, using complex base systems:http://arxiv.org/pdf/0712.1309
>
> To encode inside such shape - we can use wavelet transform
> threating it as it was just usual one dimensional binary system.
Interesting mathematics in the paper, but performance results would be
even more persuasive. Yes, you fix some artifacts, but you're giving
up the benefits of 2D transforms with your 1D transform, and you're
introducing the "fractal" artifacts.
Image compression with space-filling curves has been done before, for
example theory.stanford.edu/~matias/papers/eg2000.pdf
Speaking of 2D vs 1D - one problem with JPEG2000 that has preferential
treatment of LH and HL vs HH is that there are those weird
horizontally and vertically aligned ringing artifacts. I wonder if one
should really do that.
--
Aleks Jakulin, PhD
Research Scholar, Department of Statistics,
Columbia University.
home http://stat.columbia.edu/~jakulin/
blog http://stat.columbia.edu/~cook/movabletype/mlm/
Thomas Richter
>
> Image compression with space-filling curves has been done before, for
> example theory.stanford.edu/~matias/papers/eg2000.pdf
We've tried that internally, namely scanning wavelet HH bands with the
Peano curve. Result: Too complex and doesn't pay.
> Speaking of 2D vs 1D - one problem with JPEG2000 that has preferential
> treatment of LH and HL vs HH is that there are those weird
> horizontally and vertically aligned ringing artifacts. I wonder if one
> should really do that.
On the other hand, it is known that the eye has an increased sensibility
to horizontal and vertical structures, so after all this might be not so
bad.
So long,
Thomas
dud...@gmail.com
it has long jumps everywhere.
Instead of being 1D it has nice 2D behavior - larger blocks are
created of neighboring smaller ones.
How it can be used...
Assume that we have encoded coefficients for larger blocks.
Now go line by line with current block size (they create periodic 2D
lattice) and predict the probability using
- neighboring (3 (instead of standard 2) closest neighbors are already
set) blocks and
- larger blocks we are in.
Jarek
dud...@gmail.com
more significant - we should get better compression rates.