Comments on: The face manifold
https://ldtopology.wordpress.com/2010/07/14/the-face-manifold/
Recent Progress and Open ProblemsSun, 12 Apr 2020 06:46:11 +0000
hourly
1 http://wordpress.com/
By: Robert Osborne
https://ldtopology.wordpress.com/2010/07/14/the-face-manifold/#comment-27099
Sun, 12 Apr 2020 06:46:11 +0000http://ldtopology.wordpress.com/?p=1269#comment-27099Really great written post.
]]>
By: luysii
https://ldtopology.wordpress.com/2010/07/14/the-face-manifold/#comment-1073
Sun, 18 Jul 2010 18:42:34 +0000http://ldtopology.wordpress.com/?p=1269#comment-1073I have no idea why wordPress put one of my posts (Linear Algebra Survival Guide for Quantum Mechanics — III) as possibly related to this one. Clearly this group knows a lot more math than I ever will. If any of you see anything wrong with any of the posts (there are 9 in the series), please post a comment over there. The point of the series was to make some of the arcane phenomena of linear algebra (the rules for matrix multiplication and the complex inner product, along with why anyone (particularly a physicist ) should be interested in hermitian matrices) seem more natural and plausible.

Luysii

]]>
By: Jesse Johnson
https://ldtopology.wordpress.com/2010/07/14/the-face-manifold/#comment-1069
Thu, 15 Jul 2010 17:56:22 +0000http://ldtopology.wordpress.com/?p=1269#comment-1069That’s a good point, Pierre. I was thinking of the face manifold as having positive co-dimension, like an algebraic variety. But if it’s an open set then it would be a manifold. There is a BBC documentary on the human face, hosted by John Cleese, that shows some pictures of faces that aren’t recognizable as faces because of medical conditions that went untreated. I wonder if those would be included in the face manifold (or face space, though I’m not sure I get the pun.)
]]>
By: Pierre
https://ldtopology.wordpress.com/2010/07/14/the-face-manifold/#comment-1068
Thu, 15 Jul 2010 10:44:01 +0000http://ldtopology.wordpress.com/?p=1269#comment-1068Wouldn’t it be a manifold? My gut feeling is that this thing is open in that big euclidean space. Small enough changes in a picture of a face should still look like a face, right?
]]>
By: Ian
https://ldtopology.wordpress.com/2010/07/14/the-face-manifold/#comment-1067
Wed, 14 Jul 2010 18:39:16 +0000http://ldtopology.wordpress.com/?p=1269#comment-1067I think a more appropriate term would be “face space”, but maybe the pun would be lost on most people.
]]>
By: Cristina Valle
https://ldtopology.wordpress.com/2010/07/14/the-face-manifold/#comment-1066
Wed, 14 Jul 2010 18:28:46 +0000http://ldtopology.wordpress.com/?p=1269#comment-1066Very interesting idea, it may have many applications besides social networks.
I wonder what kind of topology you have to define on such a vector space in order to have a manifold with the desired properties on the continuos functions. I think I’m going to read Carlsson’s article next.
]]>