Some time ago we were investigating image metrics for texture compression. We already knew PSNR(RMSE) was a poor metric but, IIRC, it seemed SSIM wasn't ideal either. A team member did produce what appeared to be a better metric (based on public databases) but ...
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..we ran out of time/resources to verify it. The ideal would be to use a quality metric inside the actual compressor to influence the pixel/mode choices (not just be squared-error guided) but I can't currently see a feasible strategy. Guess it's a https://stoutsandstilettos.files.wordpress.com/2012/06/holy-grail.jpg …
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