You mentioned hexagonal filters in passing so I just wanted to plug this (seemingly unknown) paper by @sigfpe which generalizes fast box filtering by prefix sums to polygons (and n-dimensional polytopes):https://www.researchgate.net/publication/269699690_Fast_and_Exact_Convolution_with_Polygonal_Filters …
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Yes, it's an excellent technique, especially for CPUs/DSPs! (Less so for GPUs, where data dependence of prefix sum is painful) Three more interesting additional links: https://arxiv.org/abs/1806.04171 Google Pixel Portrait Mode uses this method, but with circular bokeh. 1/2
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This was a great article, keep em coming please! The thing about it decreasing noise is interesting. It seems like a more generalized version of approximating data by taking a DFT, keeping only the top N amplitude frequencies and then doing an IDFT.
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Thanks! Yes, there are many similarities between those transforms! :) Btw as an alternative to keeping only the highest buckets (“hard thresholding”), check out the Wiener filter guaranteeing minimum squared error if you know the noise strength/spectrum https://en.wikipedia.org/wiki/Wiener_filter …
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Super cool! And double-points for using something else than Matlab or Mathematica :]
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Thanks! :) I was “lucky” to study at a poor college that had no money for Matlab licenses so I never learned it.;) I still personally use Mathematica quite a bit, but it’s price.. and numpy is so ubiquitous and accessible (Jupyter, colaboratory) that it feels wrong not to use it.
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Enlightening article, thanks! One thing that got me a bit confused: To get a MxN matrix we multiply a M-column by an N-row. Shouldn’t the initial SVD explanation show column*energy*row? The Python example supports that by taking the 1st column of U and 1st row of V.
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Yeah, you are right; It’s not very strict on my side, apologies if it caused any confusion. But it also doesn’t really matter “in practice” since we could make it work with such an alternative formulation…
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This net can learn the noise so you might not need fake blurring, haze, fog. http://openaccess.thecvf.com/content_CVPR_2019/html/Gandelsman_Double-DIP_Unsupervised_Image_Decomposition_via_Coupled_Deep-Image-Priors_CVPR_2019_paper.html …
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