A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing, and the Nonlinear Diffusion Equation

Authors:
Danny Barash
Affiliations:
New York Univ., and the Howard Hughes Medical Institute, New York
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
2002

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Abstract

In this paper, the relationship between bilateral filtering and anisotropic diffusion is examined. The bilateral filtering approach represents a large class of nonlinear digital image filters. We first explore the connection between anisotropic diffusion and adaptive smoothing, and then the connection between adaptive smoothing and bilateral filtering. Previously, adaptive smoothing was considered an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates between nonlinear digital image filters and the nonlinear diffusion equation.