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Frank Nielsen

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Information Geometry, Information Theory, Geometric Science of Information GSI, machine learning, AI, visual computing, HPC, pyBregMan @SonyCSL

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$Voronoi diagram (black points) computed by projecting vertically lower envelope of n 3D graphs of functions {(x,y_i(x))} with y_i(x)=D(x_i,x) (pink). When distance D(x,x')=‖x-x'‖^2, graphs of y_i are paraboloids and Voronoi cell borders are linear$

Voronoi diagram (black points) computed by projecting vertically lower envelope of n 3D graphs of functions {(x,y_i(x))} with y_i(x)=D(x_i,x) (pink). When distance D(x,x')=‖x-x'‖^2, graphs of y_i are paraboloids and Voronoi cell borders are linear

98,307 Aufrufe • vor 7 Monaten

Euclidean Voronoi diagrams are affine diagrams: bisectors are hyperplanes (red 1d lines). Compute Voronoi diagrams as minimization diagrams of paraboloids: square distance functions from sites. Extend to Bregman Voronoi diagrams by using convex potential functions. Duality.

Euclidean Voronoi diagrams are affine diagrams: bisectors are hyperplanes (red 1d lines). Compute Voronoi diagrams as minimization diagrams of paraboloids: square distance functions from sites. Extend to Bregman Voronoi diagrams by using convex potential functions. Duality.

32,117 Aufrufe • vor 1 Jahr

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