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  2. Diffeomorphometry - Wikipedia

    en.wikipedia.org/wiki/Diffeomorphometry

    Diffeomorphometry is the metric study of imagery, shape and form in the discipline of computational anatomy (CA) in medical imaging.The study of images in computational anatomy rely on high-dimensional diffeomorphism groups which generate orbits of the form {}, in which images can be dense scalar magnetic resonance or computed axial tomography images.

  3. Large deformation diffeomorphic metric mapping - Wikipedia

    en.wikipedia.org/wiki/Large_deformation...

    A diffeomorphic mapping system is a system designed to map, manipulate, and transfer information which is stored in many types of spatially distributed medical imagery. Diffeomorphic mapping is the underlying technology for mapping and analyzing information measured in human anatomical coordinate systems which have been measured via Medical ...

  4. Diffeomorphism - Wikipedia

    en.wikipedia.org/wiki/Diffeomorphism

    Testing whether a differentiable map is a diffeomorphism can be made locally under some mild restrictions. This is the Hadamard-Caccioppoli theorem: [1] If , are connected open subsets of such that is simply connected, a differentiable map : is a diffeomorphism if it is proper and if the differential: is bijective (and hence a linear isomorphism) at each point in .

  5. Diffeology - Wikipedia

    en.wikipedia.org/wiki/Diffeology

    Recall that a topological manifold is a topological space which is locally homeomorphic to . Differentiable manifolds generalize the notion of smoothness on in the following sense: a differentiable manifold is a topological manifold with a differentiable atlas, i.e. a collection of maps from open subsets of to the manifold which are used to "pull back" the differential structure from to the ...

  6. Local diffeomorphism - Wikipedia

    en.wikipedia.org/wiki/Local_diffeomorphism

    A map is a local diffeomorphism if and only if it is a smooth immersion (smooth local embedding) and an open map.. The inverse function theorem implies that a smooth map : is a local diffeomorphism if and only if the derivative: is a linear isomorphism for all points .

  7. Head of key Japan opposition party admits to extra-marital affair

    www.aol.com/news/head-key-japan-opposition-party...

    By Satoshi Sugiyama. TOKYO (Reuters) -Yuichiro Tamaki, the head of the Japanese opposition party that has emerged as kingmaker as lawmakers select the next prime minister on Monday, said a tabloid ...

  8. 10 Overrated Foods People Are Pretending to Enjoy - AOL

    www.aol.com/finance/10-overrated-foods-people...

    3. Foie Gras. Foie gras is probably the ultimate starter-pack item for acting like a rich person, and the one food item that chefs love to cook to appeal to said rich people.Redditors on the other ...

  9. Exotic sphere - Wikipedia

    en.wikipedia.org/wiki/Exotic_sphere

    In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar one (hence the name ...