On the Axioms of Scale Space Theory

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We consider alternative scale space representations beyond the well-established Gaussian case that satisfy all “reasonable” axioms. One of these turns out to be subject to a first order pseudo partial differential equation equivalent to the Laplace equation on the upper half plane {(xs) ∈ 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 fractional power of (minus) the spatial Laplace operator.
Original languageEnglish
Pages (from-to)267-298
Number of pages32
JournalJournal of Mathematical Imaging and Vision
Issue number3
Publication statusPublished - 2004


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