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Pareidolia, but underwater: What is under the green paint?
- Pareidolia, but underwater: What is under the green paint?
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RE: Pareidolia, but underwater: What is under the green paint?
oshfdk > Yesterday, 06:32 PM
(Yesterday, 03:18 PM)Jorge_Stolfi Wrote: You are not allowed to view links. Register or Login to view.The report I just posted shows the results of that basic analysis. What do you think of them?
Is it this one? You are not allowed to view links. Register or Login to view.
I'm not sure I understand how it works exactly, I generally fail to understand Bayesian approach (I know the formula and can work the math, but I often struggle with the why part).
(Yesterday, 03:18 PM)Jorge_Stolfi Wrote: You are not allowed to view links. Register or Login to view.where Pr(p∈S) is the prior probabiliy of pixel p belonging to province S -- that is, the probability we assign to that fact before we are given its color C
Where do we get this prior probability, is it just by estimating the proportion of the pixels representing paint, ink or vellum? I think these may vary wildly depending on which part of the book or the folio we are dealing with.
(Yesterday, 03:18 PM)Jorge_Stolfi Wrote: You are not allowed to view links. Register or Login to view.To make the images more intuitive, the image for parch is shown as computed (probability 1 = white) while the others are inverted (probability 1 = black).
Made it counterintuitive for me, to be honest
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RE: Pareidolia, but underwater: What is under the green paint?
Jorge_Stolfi > Yesterday, 07:04 PM
(Yesterday, 06:32 PM)oshfdk Wrote: You are not allowed to view links. Register or Login to view.Where do we get this prior probability, is it just by estimating the proportion of the pixels representing paint, ink or vellum?
That is the fundamental limitation of Bayesian inference: it does not give the probabilities of each possible cause, it only tell us how to change out a priori probabilities. So you must specify those priors in order to use the formula.
When the evidence is strong enough, the results do not depend much on the priors. These matter only when the evidence is ambiguous. In the worst case, when the evidence carries no information about the cause, the results will be the same as the priors.
When it rains at night, streets are usually wet by the next morning. If you have no special information about the night's weather, and you see the street wet in the morning, it is reasonable to assume that it rained. Bayes's formula will say so, whether your prior for "it rained" is 1% or 99%.
That's because P(Wet|NoRain) is very small; say, 0.0001 (but not zero, because there may have been a flood or a street washing truck mat have showed up. While P(Wet|Rain) is basically 1. Therefore P(Rain)P(Wet|Rain) is still much bigger than P(NoRain)P(Wet|NoRain) in any case, and these numbers will become ~1 and ~0 after normalization.
But if you are sure that it did not rain, because you have been out stargazing in the garden all night, the wet street should not make you change your belief. That's because your P(Rain) will be essentially zero, and then P(Rain)P(Wet|Rain) will become much smaller than P(NoRain)P(Wet|NoRain), even if P(Wet|NoRain) is only 0.00001.
In the analysis reported in that document, the prior probability of "OTHER" was set arbitrarily at 0.05, and that of each of the three other classes was set to 0.95/3 = ~0.32.
All the best, --stolfi -
RE: Pareidolia, but underwater: What is under the green paint?
Jorge_Stolfi > Yesterday, 08:18 PM
This image (a clip of You are not allowed to view links. Register or Login to view. magnified 400%) shows some of the challenges on the way to uncovering drawings that have been painted over.
There are some ink traces, like (A), that were quite dark to begin with and suffered little from being painted over, apart from their color getting mixed with the paint color.
But there are some ink traces, like (B), that are very faint, almost invisible. Would we be able to recover them if they were painted over? I think that smudges at ( C) look like they were the original outline of the nymph's left foot which was incorrectly retraced as the thick dark stroke a bit further to the NW. Those smudges are only a little fainter than the toes of that same foot, which almost certainly were there.
To make things worse, when ink strokes were painted over, sometimes the ink would dissolve and either would spread around, or would be pushed by the brush for a small distance; as seems to have happened at (D). Presumably, some strokes were completely washed away and spread over a larger area, mixed with the green paint.
At (E) there are some smudges which look like those at ( C) or at the nymph's toes, and they seem to form a rounded shape that does not seem to be just a random stain or vellum defects. Will we be able to determine if it was indeed painted-over ink, and, if so, recover enough of it to tell what it is?
All the best, --stolfi