431 citations · 1.2k across the 62 of their papers we have counts for
6 papers · 1 filter
Fast -approximation of the Löwner extremal matrices of high-dimensional symmetric matrices
Frank Nielsen, Richard Nock
Matrix data sets are common nowadays like in biomedical imaging where the Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) modality produces data sets of 3D symmetric positive…
Further results on the hyperbolic Voronoi diagrams
Frank Nielsen, Richard Nock
In Euclidean geometry, it is well-known that the -order Voronoi diagram in can be computed from the vertical projection of the -level of an arrangement of hype…
The hyperbolic Voronoi diagram in arbitrary dimension
Frank Nielsen, Richard Nock
We show that in the Klein projective ball model of hyperbolic space, the hyperbolic Voronoi diagram is affine and amounts to clip a corresponding power diagram, requiring however a…
Hyperbolic Voronoi diagrams made easy
Frank Nielsen, Richard Nock
We present a simple framework to compute hyperbolic Voronoi diagrams of finite point sets as affine diagrams. We prove that bisectors in Klein's non-conformal disk model are hyperp…
On the Centroids of Symmetrized Bregman Divergences
Frank Nielsen, Richard Nock
In this paper, we generalize the notions of centroids and barycenters to the broad class of information-theoretic distortion measures called Bregman divergences. Bregman divergence…
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
Frank Nielsen, Jean-Daniel Boissonnat, Richard Nock
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are…