R. Duits, L.M.J. Florack, J. de Graaf, and B.M. ter Haar Romeny (The Netherlands)

Gaussian Scale Space, Poisson Scale Space, Scale Space Axiomatics, Holomorphic Semigroups

We consider alternative scale space representations beyond the well-established Gaussian case that satisfy all “reason able” axioms. One of these turns out to be subject to a ﬁrst order pseudo partial differential equation equivalent to the Dirichlet problem on the upper half plane {(x, s) ∈ Rd × R | s > 0}. We investigate this so-called Poisson scale space and show that it is indeed a viable alternative to Gaussian scale space. Poisson and Gaussian scale space are related via a one-parameter class of operationally well deﬁned intermediate representations generated by a frac tional power of (minus) the spatial Laplace operator.

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