diffeomorphism

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diffeomorphism

[‚dif·ē·ə′mȯr·fiz·əm]
(mathematics)
A bijective function, with domain and range in the same or different Euclidean spaces, such that both the function and its inverse have continuous mixed partial derivatives of all orders in neighborhoods of each point of their respective domains.
References in periodicals archive ?
Pietikainen, "Video texture synthesis with multi-frame LBP-TOP and diffeomorphic growth model," IEEE Transactions on Image Processing, vol.
If the singular set S(f) off is not empty, then f is umbilic-free, co-orientable, [M.sup.2] is diffeomorphic to [S.sup.1] x R, and f is given by (1.1).
The manifold Mt is diffeomorphic to M, and thefastflow on [M.sub.[epsilon]] is close to the flow of the reduced equation on M.
In 2008, symmetric log-domain diffeomorphic demons algorithm was proposed, and log Euclidean was used in order to avoid time-consuming computations of log spatial transformations [6].
Segmentation and normalization procedure were carried out using Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) [6, 18].
[tau](L[intersection]M) = ([tau]min, [tau]max) in any proper time parametrization [tau]: L[right arrow]M diffeomorphic to the real line and oriented from past to the future.
White and gray matter were co-registered across participants using the DARTEL (Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra) algorithm (Ashburner & Friston, 2000; Ashburner, 2007) to improve registration.
The coherence condition is checked by noticing that the following two manifolds are diffeomorphic:
It is worth mentioning a qualitative aspect that the diffeomorphic transformations commonly known in the realm of general relativity do not necessarily apply even when [[alpha].sub.0] [right arrow] 0.
The general Brouwer fixed-point theorem states that if a bounded closed subset in [R.sup.n] is diffeomorphic to the closed unit ball, then any continuous self-mapping in it has a fixed point.
Based on a previous DIR selection study [18], the Diffeomorphic Morphons (DM) method [19] was used to register the end-expiration phase to all others in each 4DCT dataset.