In this lecture (starting from 1:31:00) the professor says that the set of all images of a person lives in a low dimensional surface (compared the the set of all possible images). And he says that the dimension of that surface is 50 and that they get this number by adding the three translations of the body, the three rotations of the head and the independent movements of the face's muscles. He also adds that it may be more than 50 but less than 100. How do we get the number 50 ?
The professor previously said (in the same lecture, 1:29:00) that the set of all the images that we could describe as natural and that we could interpret are in a manifold. I try to understand how the number 50 came up like the following: let's take an image of a person, since it's "natural" then it belongs to that manifold. Hence there is an open set to which this image belongs to and there is a homeomorphic map from this open set to an euclidean space. Let's suppose (I don't know why but it's the only possible thing I could come up with to understand) that all the images of that same person, regardless of his position and expressions..., are in that open space then through the homeomorphic mapping we have the "same points" in an euclidean space, do we get the base of it by decomposing all the possible movements of the person?
I hope someone can clarify things for me, it seems this doesn't only work with images but all types of non-structured types of data.