Novel integro-differential equations in image processing and its applications

Prashant Athavale; Eitan Tadmor

doi:10.1117/12.850779

27 January 2010 Novel integro-differential equations in image processing and its applications

Prashant Athavale, Eitan Tadmor

Proceedings Volume 7533, Computational Imaging VIII; 75330S (2010) https://doi.org/10.1117/12.850779
Event: IS&T/SPIE Electronic Imaging, 2010, San Jose, California, United States

Abstract

Motivated by the hierarchical multiscale image representation of Tadmor et al.,¹ we propose a novel integrodifferential 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 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. Finally, we also propose another novel IDE based on the (BV,L¹) decomposition. We present numerical results for this IDE and its variant and examine its properties.

Citation Download Citation

Prashant Athavale and Eitan Tadmor "Novel integro-differential equations in image processing and its applications", Proc. SPIE 7533, Computational Imaging VIII, 75330S (27 January 2010); https://doi.org/10.1117/12.850779

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