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That's an interesting related thought that is not quite the same as the paper. They claim that what we perceive as "color similarity" is not a metric at all. Th

by woopsn 2y ago

That's an interesting related thought that is not quite the same as the paper. They claim that what we perceive as "color similarity" is not a metric at all. That would be required in order to define arclength and geodesy. I agree with others that it is not surprising and is a technicality. If you put that aside then the situation is much closer to your intuition.

Sniffnoy 2y ago
Are you sure it's claiming that? Looking quickly I didn't see anything to indicate that, I didn't see anything claiming triangle inequality violations. (But this is why I wish it had been phrased explicitly in these terms, instead of talking about whether it's specifically Riemannian!)
- mannykannot 2y ago
  At one point, the article says "importantly, [the principle of diminishing returns] holds even along geodesics, making it distinct from and stronger than the triangle inequality." Later, they say "it is not trivial to verify whether any given path through color space is a geodesic. We chose the neutral axis because it is the one path on which all available data agree that it is indeed a geodesic", and go on to argue (if I am following it correctly) that it is unlikely that their principle of diminishing returns is just an artifact from this choice. I do not know if the authors are claiming that what we perceive as color similarity is not a metric at all, but personally, I would not be surprised if it were not. See my other post for how my subjective perception of color differences seems to me.
  - Sniffnoy 2y ago
    > stronger than the triangle inequality That's not a violation -- "stronger than" is the opposite of a violation!
- woopsn 2y ago
  You're right, I misinterpreted. I don't know what they get out of calling the space non-Riemannian if not to say the inner product fails. Good idea, ignoring that term.
  - Sniffnoy 2y ago
    I mean, what they mean by "non-Riemannina" specifically is that it's a metric that can't be realized as the metric on a Riemannian manifold. But while that much is clear, getting beyond that is not. Which is why I'm asking, are they saying it's not a length space...

by woopsn 2y ago

Sniffnoy 2y ago

Are you sure it's claiming that? Looking quickly I didn't see anything to indicate that, I didn't see anything claiming triangle inequality violations. (But this is why I wish it had been phrased explicitly in these terms, instead of talking about whether it's specifically Riemannian!)

mannykannot 2y ago
At one point, the article says "importantly, [the principle of diminishing returns] holds even along geodesics, making it distinct from and stronger than the triangle inequality." Later, they say "it is not trivial to verify whether any given path through color space is a geodesic. We chose the neutral axis because it is the one path on which all available data agree that it is indeed a geodesic", and go on to argue (if I am following it correctly) that it is unlikely that their principle of diminishing returns is just an artifact from this choice. I do not know if the authors are claiming that what we perceive as color similarity is not a metric at all, but personally, I would not be surprised if it were not. See my other post for how my subjective perception of color differences seems to me.
- Sniffnoy 2y ago
  > stronger than the triangle inequality That's not a violation -- "stronger than" is the opposite of a violation!
woopsn 2y ago
You're right, I misinterpreted. I don't know what they get out of calling the space non-Riemannian if not to say the inner product fails. Good idea, ignoring that term.
- Sniffnoy 2y ago
  I mean, what they mean by "non-Riemannina" specifically is that it's a metric that can't be realized as the metric on a Riemannian manifold. But while that much is clear, getting beyond that is not. Which is why I'm asking, are they saying it's not a length space...