In the paper Johannes Kopf, Ariel Shamir, Pieter Peers - Content Adaptive Image Downscaling, the authors apply the Expectation-Maximization algorithm to solve an image downscaling problem. I've never done Bayesian statistics, so I find some parts a bit hard to understand. Here's the key part, the calculation of Gaussian kernels in the expectation stage. I'm trying to understand how does one come up with the formulas f and g, highlighted in red and green, and what associated reading do I need to do to understand them further. Thanks!
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Digging through, it looks like the red area looks like squared Mahalanobis distance (multiplied by -0.5), but it's not mentioned at all in the paper... – Babis Apr 17 '23 at 19:14
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Digging through a bit more, I found out that these functions represent multivariate and univariate probability density functions. But for some reason, the f/g functions don't include the scalars multiplied by the exponents – Babis Apr 18 '23 at 06:39
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At the Project Page they have a paper dedicated to implementation details. – Royi Jul 02 '24 at 19:36