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I can see from the literature that PDE-based image processing (especially inpainting) was a "hot topic" at one point. Why does it not seem to be an active area of research anymore, yet it looks like there are many unanswered seemingly important questions to be answered? If it is being done, what are some of the recent works and where can I find them? I cant seem to find so much on GoogleScholar?

Royi
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KaRJ XEN
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  • In Amazon there's plenty of relevant literature searching with 'Image Processing PDE'. You are asking 3 questions in one. How do you tell whether it's and active area of research or not? just by the amount of researchers? just amount of recently published papers? Certainly, even if the amount of researchers has diminished, for those yet involved it is active indeed. Successful research is supposed to do what you mentioned : answer questions. If there's been a reduction of interest It has to be either problem solved, or other tools serve better purpose. – John Bofarull Guix Sep 16 '22 at 18:46

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PDE for image processing had its glory days when we didn't have a good model for images.

Back in those days, PDE's were the best models as they were mathematically understandable and in many times computationally efficient.
This brought the Anisotropic and Isotropic Smoothing, Sharpening filters and even the use of PDE's for image inpainting.
It also brought tools for image analysis (Segmentation) and were popular in medical imaging.

But in the late 2000's we had 2 other concepts which proved to be better:

  1. Statistical Models: We built a lot of priors and modelling for image processing which proved to be better. In some cases extending the methods. For instance, Non Local Means, Weighted Least Squares, etc...
  2. Learned Dictionary Methods: Learning a compact representation of a set of images. Then this compact representation helps do things like smoothing, segmenting, etc... They proved to be a great advancement (See K-SVD for instance).

Then, just before the DL boom the fusion of those 2 approaches created the best results. Like low rank models for dictionaries...

Yet the DL made most of those obsolete for many use cases (Not all) and this is where we are now.

Royi
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