CSCAMM Day 2010

Multiscale representation of images using novel integro-differential equations

Eitan Tadmor

University of Maryland

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 `slices' of the image, which are balanced by a typical curvature term at the finer scale. The original motivation came from a variational-based hierarchical decomposition of images. We then use standard techniques from PDE-based image processing --- filtering, edge preserving and tangential smoothing, to yield a family of modified IDE models with applications to image denoising and 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 applications of our new IDE approach (joint work with Prashant Athavale).