Seite - 417 - in Differential Geometrical Theory of Statistics

Entropy2016,18, 425 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure5.MinimizingnormalMPPsbetweentwofixedpoints (red/cyan). Fromisotropiccovariance (top row, (a)) to anisotropic (top row, (c)) onS2. ComparewithminimizingRiemanniangeodesic (blackcurve). TheMPPtravels longer in thedirectionsofhighvariance. Familiesofcurves (middle row, (d–f)) andcorrespondinganti-development (bottomrow, (g–i))onthe threesurfaces inFigure4. The familyof curves isgeneratedby rotating the covariancematrix as inFigure4. Noticehowthe varyinganisotropyaffects theresultingminimizingcurves,andhowtheanti-developedcurvesendat differentpoints inR2. (a) (b) (c) Figure6.Cont. 417