Foundations and Trends® in Computer Graphics and Vision > Vol 8 > Issue 1

A Fresh Look at Generalized Sampling

Diego Nehab, IMPA, Rio de Janeiro, Brazil, diego@impa.br Hugues Hoppe, Mircrosoft Research, USA, hhoppe@microsoft.com
 
Suggested Citation
Diego Nehab and Hugues Hoppe (2014), "A Fresh Look at Generalized Sampling", Foundations and Trends® in Computer Graphics and Vision: Vol. 8: No. 1, pp 1-84. http://dx.doi.org/10.1561/0600000053

Published: 12 Mar 2014
© 2014 D. Nehab and H. Hoppe
 
Subjects
Image and video processing,  Sampling,  Signal reconstruction
 

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In this article:
1. Introduction
2. Background
3. Basic Notation, Definitions, and Properties
4. Fundamental Algorithms
5. Translation and Scaling
6. Approximation of Derivatives
7. Generalized Prefiltering and its Variance
8. Theoretical Considerations
9. Practical Considerations
10. Experiments and Analyses
11. Conclusions
Appendix A. Source-code
References

Abstract

Discretization and reconstruction are fundamental operations in computer graphics, enabling the conversion between sampled and continuous representations. Major advances in signal-processing research have shown that these operations can often be performed more efficiently by decomposing a filter into two parts: a compactly supported continuous-domain function and a digital filter. This strategy of “generalized sampling” has appeared in a few graphics papers, but is largely unexplored in our community. This paper broadly summarizes the key aspects of the framework, and delves into specific applications in graphics. Using new notation, we concisely present and extend several key techniques. In addition, we demonstrate benefits for prefiltering in image downscaling and supersample-based rendering, and present an analysis of the associated variance reduction. We conclude with a qualitative and quantitative comparison of traditional and generalized filters.

DOI:10.1561/0600000053
ISBN: 978-1-60198-728-0
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ISBN: 978-1-60198-729-7
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Table of contents:
1. Introduction
2. Background
3. Basic Notation, Definitions, and Properties
4. Fundamental Algorithms
5. Translation and Scaling
6. Approximation of Derivatives
7. Generalized Prefiltering and its Variance
8. Theoretical Considerations
9. Practical Considerations
10. Experiments and Analyses
11. Conclusions
Appendix A. Source-code
References

A Fresh Look at Generalized Sampling

Discretization and reconstruction are fundamental operations in computer graphics, enabling the conversion between sampled and continuous representations. Major advances in signal processing research have shown that such operations can often be performed more efficiently by decomposing a filter into two parts: a compactly-supported continuous-domain function and a digital filter. This strategy of “generalized sampling” has appeared in a few graphics papers, but is largely unexplored within the computer graphics community.

A Fresh Look at Generalized Sampling broadly summarizes the key aspects of generalized sampling, and delves into specific applications in graphics. Using new notation, it concisely presents and extends several key techniques. In addition, it demonstrates benefits for prefiltering in image downscaling and supersample-based rendering, and presents an analysis of the associated variance reduction. It concludes with a qualitative and quantitative comparison of traditional and generalized filters.

A Fresh Look at Generalized Sampling is an ideal primer for graphics researchers interested in generalized sampling methods and how they might apply them.

 
CGV-053