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- W3115442687 abstract "Filtration of quantifiable objects by smoothing kernels on Riemannian manifolds for visualisation is an ongoing research. However, using common filters created for linear domains on manifolds with non-Euclidean topologies can yield misleading results. While there is a lot of ongoing research on convolution of quantifiable functions with smoothing kernels on the lower dimensional manifolds, higher-dimensional problems particularly pose a challenge. One important generalization of lower dimensional compact Riemannian manifolds is the unit hypersphere. In this paper, we derive explicit forms of convolution formulae for Gegenbauer kernel filtration on the surface of unit hypersphere. We prove that the Gegebauer filtration is the limit of a sequence of finite linear combinations of the hyperspherical Legendre harmonics, among other results." @default.
- W3115442687 created "2021-01-05" @default.
- W3115442687 creator A5036430105 @default.
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- W3115442687 date "2020-12-12" @default.
- W3115442687 modified "2023-09-27" @default.
- W3115442687 title "Gegenbauer kernel filtration on the unit hypersphere." @default.
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- W3115442687 hasPublicationYear "2020" @default.
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