HP Labs Technical Reports

An Accurate Operator Splitting Scheme for Nonlinear Diffusion Filtering

Barash, Danny; Kimmel, Ronny

HPL-2000-48R1

Keyword(s): nonlinear diffusion filtering; operator-splitting schemes; bilateral filtering

Abstract: Efficient numerical schemes for nonlinear diffusion filtering based on additive operator splitting (AOS) were introduced in [15]. AOS schemes are efficient and unconditionally stable, yet their accuracy is limited. Future applications of nonlinear diffusion filtering may require better accuracy at the expense of a relatively modest cost in computations and complexity. In this report we explore second order operator- splitting schemes for nonlinear diffusion filters. An accurate extension of the AOS schemes is suggested, which belongs to the alternating direction implicit (ADI) type methods, coupled with a symmetric splitting. The splitting is both additive and multiplicative, and preserves the accuracy of propagating with the Crank-Nicolson scheme in each dimension.

20 Pages

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