Multiscale image representation using novel integro-differential equations

Eitan Tadmor; Prashant Athavale

doi:10.3934/ipi.2009.3.693

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2009, Volume 3, Issue 4: 693-710. Doi: 10.3934/ipi.2009.3.693

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Multiscale image representation using novel integro-differential equations

Eitan Tadmor^1, and
Prashant Athavale^2,

1.
Department of Mathematics, Institute for Physical Science & Technology and Center of Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD 20742
2.
Applied Mathematics and Scientific Computation (AMSC) and Center of Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD 20742

Received: June 30, 2009

Revised: July 31, 2009

Published: October 2009

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Abstract

Motivated by the hierarchical multiscale image representation of Tadmor et. al., [25], we propose a novel integro-differential equation (IDE) for a multiscale image representation. To this end, one integrates in inverse scale space a succession of refined, recursive 'slices' of the image, which are balanced by a typical curvature term at the finer scale. Although the original motivation came from a variational approach, the resulting IDE can be extended using standard techniques from PDE-based image processing. We use filtering, edge preserving and tangential smoothing to yield a family of modified IDE models with applications to image denoising and image deblurring problems. The IDE models depend on a user scaling function which is shown to dictate the BV^∗ properties of the residual error. Numerical experiments demonstrate application of the IDE approach to denoising and deblurring.

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Mathematics Subject Classification: 26B30,65C20,68U10.

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