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The following question refers to a dissertation in Bishop's book (see the attachment)

Can someone give me an intuition about the fact that a set of images will live on a three dimensional manifold? I've understood the general context and that each point in the space corresponds to an image. But how does the author come up with the notion of three dimensional manifold?

(Bishop's book - pag. 38)

nbro
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tech_1994
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    Could you please put your **specific** question in the title? "Curse of Dimentionality - Manifold" is not a question and it's also not specific. Thanks. – nbro Jun 27 '22 at 17:44
  • Maybe it is like a fiber bundle with image valued model fibers. With projections onto a 3d base space (x,y,angle)? Plus some kind of mapping from high dimensional fiber bundle to low dimensional fiber bundle. – Emil Jun 28 '22 at 17:05
  • Perhaps the mapping/embedding from high dimensions to low dimensions discards some model parameter, like using bounding boxes instead of a mask or something. – Emil Jun 28 '22 at 17:20
  • I am guessing the total space is maybe [0,255]^(WxHxC). Don't really understand how the projection to (x,y,angle) would look. Perhaps some kind of rotated crop from each possible image. And not sure what the fibers would be, perhaps some kind of feature. – Emil Jun 28 '22 at 18:20
  • On second thought, a fiber might be all the image crops stacked on top of eachother, or something similar. And (x,y,angle) would be some kind of tag identifying the region. – Emil Jun 28 '22 at 19:14
  • Perhaps you could alternatively think of it as a volumetric grid that can have different intensities in it, that way strange paths like "moving towards a red circle" might make more sense. – Emil Jun 28 '22 at 23:18

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