Interpolating Rotations with Non-abelian Kuramoto Model on the 3-Sphere

Kapić, Zinaid; Crnkić, Aladin

doi:10.1007/978-3-030-90055-7_48

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…where 𝜑 𝑗 ∈ [0,2𝜋) and 𝜔 𝑗 are a phase and an intrinsic frequency of oscillator 𝑗 respectively, and 𝐾 is global coupling strength. The model (1) and its generalizations have found wide applications in studying synchronization phenomena across various systems, including complex networks, power grids, and interpolation problems [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Averaging data on the unit hypersphere

Crnkić,

Kapić,

Jusić

et al. 2023

IOP Conf. Ser.: Mater. Sci. Eng.

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Averaging data on the unit sphere S d (also called a unit hypersphere) is a common problem in computer vision, robotics and other fields, with applications ranging from motion planning to DNA modelling. In this paper, we introduce a new method for averaging data represented as points on the unit sphere S d−1 using the d-dimensional generalized Kuramoto model. Our method is verified on a range of benchmark data sets and compared with common data averaging algorithms. Also, we showcase the applicability of this method for solving rotation averaging problem.

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Section: Introductionmentioning

confidence: 99%

Averaging data on the unit hypersphere

Crnkić,

Kapić,

Jusić

et al. 2023

IOP Conf. Ser.: Mater. Sci. Eng.

Self Cite

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“…The Kuramoto model and its variations have been used to study synchronization phenomena in a variety of systems [7][8][9]. It has also been used to understand synchronization in complex networks [10], power grids [11], clustering of static and stream data [12,13], as well for solving rotation averaging and interpolation problems [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Interpolation on the unit hypersphere using the n-dimensional generalized Kuramoto model

Kapić,

Crnkić

2023

IOP Conf. Ser.: Mater. Sci. Eng.

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Computer graphics, robotics, and physics are one of the many domains where interpolation on the unit sphere S n (often called a unit hypersphere or unit n-sphere) plays a crucial role. In this paper, we introduce a novel approach for achieving smooth and precise interpolation on the unit sphere S n−1 using the n-dimensional generalized Kuramoto model. The proposed algorithm finds the shortest and most direct path between two points on that non-Euclidean manifold. Our simulation results demonstrate that it achieves performance comparable to that of a Spherical Linear Interpolation algorithm. Also, the paper proposes the application of our algorithm in the interpolation of rotations that are presented in the form of four-dimensional data.

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Spline Interpolation on the Special Orthogonal Group SO(n)

Adouani,

Samir

2024

Regression and Fitting on Manifold-Valued Data

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Interpolating Rotations with Non-abelian Kuramoto Model on the 3-Sphere

Cited by 5 publications

References 19 publications

Averaging data on the unit hypersphere

Averaging data on the unit hypersphere

Interpolation on the unit hypersphere using the n-dimensional generalized Kuramoto model

Spline Interpolation on the Special Orthogonal Group SO(n)

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