A closed-form Hilbert distance on the matrix box {0 ≺ X ≺ I} (the extended Gaussian parameter space) is derived, plus a claimed full isometry classification: orthogonal conjugation and complement X → I−X.
Log-Euclidean metrics for fast and simple calculus on diffusion tensors
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Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family
A closed-form Hilbert distance on the matrix box {0 ≺ X ≺ I} (the extended Gaussian parameter space) is derived, plus a claimed full isometry classification: orthogonal conjugation and complement X → I−X.