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 .
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.
(11) Inter-subject registration was achieved with Diffeomorphic
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 , the Diffeomorphic
Morphons (DM) method  was used to register the end-expiration phase to all others in each 4DCT dataset.