
PDE-Based Image Compression - ingve
http://www.mia.uni-saarland.de/Research/IP_Compress.shtml
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saturncoleus
New compression algorithms are always interesting because they reveal a new
way of describing a photograph in a succinct way. The overlap between image
compression and image searching is surprisingly high because the same
techniques are used to derive the most important part of the picture data.
Even if a new compression isn't ideal for image transmission, it is pretty
much always a new avenue to look at for image matching/searching.

Coming from the other side, corners and edges are great ways to describe an
image when doing process. It's a natural step to use this data for
compression, which is what the authors have done here.

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bwindels
> It's a natural step to use this data for compression, which is what the
> authors have done here.

I understood the pixels for compression were chosen randomly, not by how much
they define the main features of the picture. Or you meant the selected pixels
are assumed to be defining features when reconstructing the image?

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Sanddancer
I feel very much a sense of uncanny valley looking at the PDE-based images.
The extreme jpeg images /look/ mechanically compressed, whereas the PDE images
seem to be almost but not quite natural in the results. I'm curious as to what
the results would be with an image compressed to say 1:10th its original size

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lifthrasiir
The goal is to provide a similar _enough_ image to base any residual coding.
Xiph.org folks have a good example of exploiting such redundancy in the video
compression format [1].

[1]
[https://people.xiph.org/~jm/daala/paint_demo/](https://people.xiph.org/~jm/daala/paint_demo/)
(was later abandoned due to the high cost, and now we have
[https://people.xiph.org/~jm/daala/deringing_demo/](https://people.xiph.org/~jm/daala/deringing_demo/)
)

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dogmatix
The jagged edges on straight lines is interesting, it looks to me like this
could get closer to the input image with a little bit of intelligent anti-
aliasing.

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speps
Could this be used in graphics rendering? You output only a few pixels and
then fill the rest using this algorithm.

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Keyframe
Sampling is already an integral (ha!) part of rendering. Not exactly in a way
you're describing, apart from maybe sparse lighting passes like global
illumination. Even then, it's more about random distribution and probability
density functions than anything else.

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FreeFull
I wonder how suitable this technique would be for compressing video, since it
seems to work on volumetric data.

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amelius
I'm wondering how well deep learning would work for compressing video. For
example, the face of an actor, when it has been exposed from different angles
in the first 5 minutes of the movie, need not be fully coded for the remainder
of the movie. At least, that is what intuition says.

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street
Comparing to JPEG seems somewhat dishonest (or thoughtless), considering the
large parts of one color in some of the images. PNG and other algorithms not
designed for detailed pictures would probably do better.

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tlarkworthy
No. PNG is lossless, it will do a really bad job at compression. Even those
uniform colors won't actually be uniform because they are from image sensors.

JPEG is the appropriate comparison, as the authors are solving the same
problem as JPEG tries to solve (i.e. a good enough lossy compression for
natural images).

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Houshalter
PNG doesn't need to be lossless. You can identify the pixels that are
requiring more bits to compress, and change their values to make them easier.
It's not as good as JPEG, but I suspect it'd be comparable to this for the
same level of quality.

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amelius
How do they choose the interpolation points?

What PDE are they using?

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d33
Is it just me or is the article a bit lacking? I couldn't for example see a
comparison of file sizes or a reference implementation.

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azinman2
The captions showed images for the same compression ratios. It seems that,
like jpg, you set some slider for how much compression you want. Since they
select some % of source pixels it's a bit more easily calculated than jpeg
"quality".

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defen
Is this technique related to compressed sensing?

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kxyvr
From what I can tell skimming their papers, no. Their technique really is
based on solving a PDE to fill in the gaps in the image. Neat idea and I'm a
little surprised that it works so well. Compressed sensing relies on an
equivalence between a discrete and a continuous optimization problem under
very specific assumptions, which allows the sparsest possible solution to an
underdetermined linear system to be found. In this work, there's no
optimization, so no compressed sensing.

