The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation
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 to be an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation.
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Citations
Cites
Bilateral Filtering for Gray and Color Images
Tomasi, C., & Manduchi, R. (2002) · Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271) · doi:10.1109/iccv.1998.710815 · Cited by 8,177 · cited 9×
“Bilateral filtering was introduced [ 9 ] as a nonlinear filter which combines domain and range filtering.”
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Cited by
Bilateral Filtering: Theory and Applications
Paris, S., Kornprobst, P., Tumblin, J., & Durand, F. (2009) · Foundations and Trends in Computer Graphics and Vision · doi:10.1561/0600000020 · Cited by 586
Automatic Estimation and Removal of Noise from a Single Image
Liu, C., Szeliski, R., Kang, S. B., Zitnick, C. L., & Freeman, W. T. (2008) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2007.1176 · Cited by 486
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
Elmoataz, A., Lezoray, O., & Bougleux, S. (2008) · IEEE Transactions on Image Processing · doi:10.1109/tip.2008.924284 · Cited by 466
Adaptive Bilateral Filter for Sharpness Enhancement and Noise Removal
Zhang, B., & Allebach, J. P. (2008) · IEEE Transactions on Image Processing · doi:10.1109/tip.2008.919949 · Cited by 403
Metadata
- Authors
- Barash, D.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2002-06
- Volume
- 24
- Issue
- 6
- Pages
- 844-847
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2168896212
- Cited by
- 514
- References
- 1
- FWCI
- 16.10
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
