Global Diffeomorphic Phase Alignment of Time-Series from Resting-State fMRI Data

Lee, David S.; Sahib, Ashish; Narr, Katherine L.; Nunez, Elvis; Joshi, Shantanu H.

doi:10.1007/978-3-030-59728-3_51

Cited by 3 publications

(2 citation statements)

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“…As increasingly real-world applications have to deal with non-vector data, a great number of algorithms for manifold embedding and manifold learning have been introduced. Recently, many efforts have been made to develop important geometric and statistical tools: Riemannian exponential map and its inverse, means, distributions, geodesic [6,9,25].…”

Section: Introductionmentioning

confidence: 99%

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Bézier Splines Interpolation on Stiefel and Grassmann Manifolds

Samir

2023

JCM

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We propose a new method for smoothly interpolating a given set of data points on Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm. To that end, we reduce interpolation problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox of spline interpolation. The interpolated curve enjoy a number of nice properties: The solution exists and is optimal in many common situations. For applications, the structures with respect to chosen Riemannian metrics are detailed resulting in additional computational advantages.

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Section: Introductionmentioning

confidence: 99%

“…In this context and due to logistic and time constraints, it is very common to store few discrete moments only. Then at each time instant, we have a data point that is represented as an element of a manifold [25]. So there is a need to estimate missing data points on such manifold at non observed time instants.…”

Section: Introductionmentioning

confidence: 99%