Journal
JOURNAL OF MATHEMATICAL IMAGING AND VISION
Volume 20, Issue 3, Pages 267-298Publisher
SPRINGER
DOI: 10.1023/B:JMIV.0000024043.96722.aa
Keywords
Gaussian scale space; Poisson scale space; alpha scale spaces; scale space axiomatics; semigroup 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 {(x, s) is an element of R-d x 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.
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