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I'd appreciate some references/literature on the applications of manifold-valued random variables, i.e., random variables $X:\Omega\to M$, where M is a manifold (could be even infinite dimensional), and $\Omega$ is the sample space. I'm looking for refernces that more particularly deal with medical imaging applications. Introductory or beginners' level literature will be more appropriate for me.

To be precise, I'm looking to see how one can collect the raw data from medical imaging, assume some appropriate probability models, and then fit them into a suitable manifold framework. I'm interested to see what kind of manifold will naturally arise in these contexts.

I've advanced mathematics and basic statistics backgrounds, just in case this helps to answer.

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    $\begingroup$ Saw a talk from www.cacs.louisiana.edu/~mjin/ that might be apropos; it was to do with compression of colonoscopy data using Teichmüller theory. I think SUNY SB has a group that deals with medical imaging. Maybe look there? $\endgroup$ – isomorphismes Mar 21 '15 at 4:49
  • $\begingroup$ Also "any manifold" is like so general, as you say it could be infinite-dimensional so all of time series is included by default. I think as stated it's too vague. $\endgroup$ – isomorphismes Mar 21 '15 at 4:50

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