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Fast Hierarchical Importance Sampling with Blue Noise Properties

Fast Hierarchical Importance Sampling with Blue Noise Properties. Victor Ostromoukhov University of Montreal. Charles Donohue University of Montreal. Pierre-Marc Jodoin University of Montreal. Presented By: Ryan Overbeck. Goal. To QUICKLY generate a GOOD point sample distribution.

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Fast Hierarchical Importance Sampling with Blue Noise Properties

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  1. Fast Hierarchical Importance Sampling with Blue Noise Properties Victor Ostromoukhov University of Montreal Charles Donohue University of Montreal Pierre-Marc Jodoin University of Montreal Presented By: Ryan Overbeck

  2. Goal • To QUICKLY generate a GOOD point sample distribution.

  3. Motivation NPR -- Stippling Environment Map Sampling Image Anti-aliasing [Agarwal et al. 2003] [Kopf et al. 2006] [Taken from CDRinfo: http://www.cdrinfo.com/]

  4. Good == Blue Noise? • In English: • We want a set of samples that are random but regularly spaced! • In Fourier: • Low angular anisotropy • Low energy annulus about the DC spike • High energy annulus • mean distance between samples • Medium energy background

  5. Blue Noise? • Low angular anisotropy => Radially evenly random • Low energy annulus about the DC spike => Aperiodic • High energy annulus => Adjustable mean distance • Medium magnitude background => Spatially evenly random Samples Fourier Images from Dunbar et al. 06

  6. Solution: • Use Penrose Tiling to provide sample distribution • Kinda Random • Aperiodic • Multi-resolution

  7. Penrose Tiling

  8. Penrose Tiling: Subdivision

  9. Penrose Tiling

  10. Stuff I’m Glossing Over • F-codes and Structural Indices • Heuristic for subdivision • Lookup Table-based Relaxation • Improves the spatial distribution of the sampling points.

  11. Example Penrose Tiling

  12. Example Penrose Fourier Analysis Ideal Blue Noise Fourier

  13. Results LightGen Structured Importance Penrose Distributions using 300 Samples 45 minutes 25 Seconds 8 milliseconds Images rendered using above distributions

  14. Conclusion • Penrose Tiling can quickly generate a hierarchical point sample distribution that is “random” and regularly spaced. • Blue Noise == Random and regularly spaced.

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