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SCALESPACE
2005
Springer

Regularity and Scale-Space Properties of Fractional High Order Linear Filtering

12 years 1 months ago
Regularity and Scale-Space Properties of Fractional High Order Linear Filtering
We investigate the use of fractional powers of the Laplacian for signal and image simplification. We focus both on their corresponding variational techniques and parabolic pseudodifferential equations. We perform a detailed study of the regularisation properties of energy functionals, where the smoothness term consists of various linear combinations of fractional derivatives. The associated parabolic pseudodifferential equations with constant coefficients are providing the link to linear scale-space theory. These encompass the well-known α-scale-spaces, even those with parameter values α > 1 known to violate common maximumminimum principles. Nevertheless, we show that it is possible to construct positivity-preserving combinations of high and low-order filters. Numerical experiments in this direction indicate that non-integral orders play an essential role in this construction. The paper reveals the close relation between continuous and semi-discrete filters, and by that helps...
Stephan Didas, Bernhard Burgeth, Atsushi Imiya, Jo
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where SCALESPACE
Authors Stephan Didas, Bernhard Burgeth, Atsushi Imiya, Joachim Weickert
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