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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 thi
by 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 agoAt 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 agoYou'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 agoI 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...