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Structured Importance Sampling of Environment Maps

Structured Importance Sampling of Environment Maps. Agarwal, S., R. Ramamoorthi, S. Belongie, and H. W. Jensen. Outline. Monte Carlo Sampling and Importance metric Variance Analysis for Visibility Hierarchical Environment Map Stratification Rendering Optimizations.

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Structured Importance Sampling of Environment Maps

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  1. Structured Importance Sampling of Environment Maps Agarwal, S., R. Ramamoorthi, S. Belongie, and H. W. Jensen

  2. Outline • Monte Carlo Sampling and Importance metric • Variance Analysis for Visibility • Hierarchical Environment Map Stratification • Rendering Optimizations

  3. Monte Carlo Sampling and Importance • Area based stratified sampling • Illumination-based importance sampling

  4. Importance Metric • Illumination-based importance sampling • ( a=1 b=0 ) • Area based stratified sampling • ( a=0 b=1 )

  5. Variance Analysis for Visibility • (variance) (empirical)

  6. Variance Analysis for Visibility • Correlation model for visibility

  7. Variance Analysis for Visibility • Mean visibility = ½ (assuming) P(S=0) = P(S=1) = ½ θ-> 0 , α(θ) = 1 θbecomes large α(θ) = ½ (T is the correlation angle)

  8. Variance Analysis for Visibility

  9. Variance Analysis for Visibility

  10. Variance Analysis for Visibility

  11. The Number of Samples The number of samples is proportional to Uniform lighting

  12. Hierarchical Environment Map Stratification • Hierarchical Thresholding • Hierarchical Stratification

  13. Hierarchical Thresholding • σ:Standard deviation of the illumnation in the map

  14. Hierarchical Thresholding

  15. Hierarchical Thresholding N1 N2 N3 N4

  16. Hierarchical Stratification • Hochbaum-Shmoys Algorithm • (K-center problem)

  17. Hochbaum-Shmoys Algorithm

  18. Hochbaum-Shmoys Algorithm

  19. Hochbaum-Shmoys Algorithm

  20. Hochbaum-Shmoys Algorithm

  21. Rendering Optimizations • Pre-integrating the illumination • Jittering • Sorting

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