Forward-and-backward diffusion processes for adaptive image enhancement and denoising

Guy Gilboa*, Nir Sochen, Yehoshua Y. Zeevi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

350 Scopus citations


Signal and image enhancement is considered in the context of a new type of diffusion process that simultaneously enhances, sharpens, and denoises images. The nonlinear diffusion coefficient is locally adjusted according to image features such as edges, textures, and moments. As such, it can switch the diffusion process from a forward to a backward (inverse) mode according to a given set of criteria. This results in a forward-and-backward (FAB) adaptive diffusion process that enhances features while locally denoising smoother segments of the signal or image. The proposed method, using the FAB process, is applied in a super-resolution scheme. The FAB method is further generalized for color processing via the Beltrami flow, by adaptively modifying the structure tensor that controls the nonlinear diffusion process. The proposed structure tensor is neither positive definite nor negative, and switches between these states according to image features. This results in a forward-and-backward diffusion flow where different regions of the image are either forward or backward diffused according to the local geometry within a neighborhood.

Original languageEnglish
Pages (from-to)689-703
Number of pages15
JournalIEEE Transactions on Image Processing
Issue number7
StatePublished - Jul 2002
Externally publishedYes


FundersFunder number
Fund for the Promotion of Research
Israeli Ministry of Science
Ollendorf Minerva Center
Technion-Israel Institute of Technology


    • Adaptive denoising
    • Anisotropic diffusion
    • Beltrami flow
    • Color processing
    • Image enhancement
    • Inverse diffusion
    • Scale-space


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