Variety of high-order recursive filters illustrating the versatility of our Non-Uniform Filtering formulation.
High-Order Recursive Filtering of Non-Uniformly Sampled Signals for Image and Video Processing
Eduardo S. L. Gastal
eslgastal@inf.ufrgs.br
and Manuel M. Oliveira
oliveira@inf.ufrgs.br

Instituto de Informática, UFRGS

Logo INF Logo UFRGS

Computer Graphics Forum.
Volume 34 (2015), Number 2, Proceedings of Eurographics 2015, pp. 81-93.

Honorable Mention at Eurographics 2015 Best Paper Award


Contents

Abstract Downloads Results Reference Acknowledgements

Abstract

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.

Downloads

Paper

Full paper (8 MB, 13 pages)

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Source Code (Updated)

Non-Uniform Filtering julia source code (65 MB)
Version 1.2 (November 17, 2015) for Julia v0.4, includes complete IJulia notebook

Results

Click here to access our IJulia notebook with various examples illustrating some of the possible applications of our mathematical formulation.

Reference

Citation

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.

BibTeX

@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}
}
  

Keywords

High-Order Recursive Filtering, Non-Uniformly Sampled Signals, Edge-Aware Image and Video Processing, Edge-Preserving Filtering.

Acknowledgements

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.