PDE-Based Image Compression

> 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?

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

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.

I also wondered about video.

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.

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).

For me, it looks like the PDE format is well suited for photographic images with abrupt color changes like the Svalbard picture. The sky is a gradient, it is not just one color, PNG would compress very bad on this one.

You're right that PNG does well on pictures with only few colors like diagrams but who knows how the edge-detecting PDE format would do, it might compress just as well with the same quality.

As with any graphics format, different formats have strong points. One wouldn't use PNG for a portrait and a JPEG for a block of text.

So I look at PDE and notice that its few points and colour contours bear a lot of similarity to a basic vector format. I wonder if a simplified vector format that utilises tracing combined with blurring effects would best PDE.

JPEG is the go-to format for showing your compression is better at high compression rates because once you get past a certain point you don't have enough data for coefficients and JPEG ends up storing most of it as flat 8x8 blocks.

It's not representative of the performance of JPEG becasue You typically don't encode JPEGs at that bit rate.

It's basically taking advantage of the fact that JPEG dips first. http://article.sapub.org/image/10.5923.j.ajsp.20120205.04_01...

Also be wary of things that report compression rates rather than bits-per-pixel. You can get the same image quality at 200:1 if you start with 48 bit colour, The bits per pixel would be the same but if your original data is excessively precise you can throw a lot of it away at no perceptible cost.

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".

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.