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The second (expository) paper is pretty readable. I have only the barest grasp of algebraic topology but I believe I have a rough high-level understanding of wh
by jamii 15y ago
The second (expository) paper is pretty readable. I have only the barest grasp of algebraic topology but I believe I have a rough high-level understanding of what it is doing. It would be interesting to implement their barcode program independently to test whether or not I really understand.
- Tloewald 15y agoThe comment is interesting. He? argues that any 2 manifold with no edges would be likely to end up as a Klein bottle. The question is then why a 2 manifold. Well, the thing we're asking about is a 2d picture, right? Maybe that has something to do with it. Let's suppose we tried the same trick using 3x3x3 pixel representations of STL models — might that turn out to be form a simple edge less 3 manifold embedded in 27 dimensional space? (perhaps for simplicity we could use 2x2x2 cubes and look at 8 dimensional space... In essence we're talking about a population of 2d data arbitrarily but consistently mapped into higher dimensional space and we discover it maps to a 2 manifold.