Scale Space Axioms Critically Revisited

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.

Important Links:

Go Back