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A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing, and the Nonlinear Diffusion Equation
June 2002 (vol. 24 no. 6)
pp. 844-847

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.

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Index Terms:
Bilateral filtering, anisotropic diffusion, adaptive smoothing, denoising.
Citation:
Danny Barash, "A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing, and the Nonlinear Diffusion Equation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 6, pp. 844-847, June 2002, doi:10.1109/TPAMI.2002.1008390
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