Eduardo S. L. Gastal eslgastal@inf.ufrgs.br |
and |
Manuel M. Oliveira oliveira@inf.ufrgs.br |
Computer Graphics Forum.
Volume 34 (2015), Number 2, Proceedings of Eurographics 2015, pp. 81-93.
Honorable Mention at Eurographics 2015 Best Paper Award
Abstract | Downloads | Results | Reference | Acknowledgements |
We present a discrete-time mathematical formulation for applying recursive digital filters to non-uniformly sampled signals. Our solution presents several desirable features: it preserves the stability of the original filters; is well-conditioned for low-pass, high-pass, and band-pass filters alike; its cost is linear in the number of samples and is not affected by the size of the filter support. Our method is general and works with any non-uniformly sampled signal and any recursive digital filter defined by a difference equation. Since our formulation directly uses the filter coefficients, it works out-of-the-box with existing methodologies for digital filter design. We demonstrate the effectiveness of our approach by filtering non-uniformly sampled signals in various image and video processing tasks including edge-preserving color filtering, noise reduction, stylization, and detail enhancement. Our formulation enables, for the first time, edge-aware evaluation of any recursive infinite impulse response digital filter (not only low-pass), producing high-quality filtering results in real time.
Full paper (8 MB, 13 pages) |
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Non-Uniform Filtering julia source code (65 MB) Version 1.2 (November 17, 2015) for Julia v0.4, includes complete IJulia notebook |
Click here to access our IJulia notebook with various examples illustrating some of the possible applications of our mathematical formulation. |
Eduardo S. L. Gastal and Manuel M. Oliveira. "High-Order Recursive Filtering of Non-Uniformly Sampled Signals for Image and Video Processing". Computer Graphics Forum. Volume 34 (2015), Number 2, Proceedings of Eurographics 2015, pp. 81-93.
@article{GastalOliveira2015NonUniformFiltering, author = {Eduardo S. L. Gastal and Manuel M. Oliveira}, title = {High-Order Recursive Filtering of Non-Uniformly Sampled Signals for Image and Video Processing}, journal = {Computer Graphics Forum}, volume = {34}, number = {2}, month = {May}, year = {2015}, pages = {81--93}, note = {Proceedings of Eurographics 2015} }
High-Order Recursive Filtering, Non-Uniformly Sampled Signals, Edge-Aware Image and Video Processing, Edge-Preserving Filtering.
CNPq-Brazil fellowships and grants # 150550/2015-4, 158666/2010-0, 557814/2010-3, 308936/2010-8, and 482271/2012-4. |
Last updated: November 17, 2015.