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Shu-Jheng Huang 1 / 25 Structured Importance Sampling of Environment Maps Agarwal, S., R. Ramamoorthi, S. Belongie, and H. W. Jensen.

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Presentation on theme: "Shu-Jheng Huang 1 / 25 Structured Importance Sampling of Environment Maps Agarwal, S., R. Ramamoorthi, S. Belongie, and H. W. Jensen."— Presentation transcript:

1 Shu-Jheng Huang 1 / 25 Structured Importance Sampling of Environment Maps Agarwal, S., R. Ramamoorthi, S. Belongie, and H. W. Jensen

2 Shu-Jheng Huang 2 / 25 Outline Monte Carlo Sampling and Importance metric Variance Analysis for Visibility Hierarchical Environment Map Stratification Rendering Optimizations

3 Shu-Jheng Huang 3 / 25

4 Shu-Jheng Huang 4 / 25 Monte Carlo Sampling and Importance Area based stratified sampling Illumination-based importance sampling

5 Shu-Jheng Huang 5 / 25 Importance Metric Illumination-based importance sampling ( a=1 b=0 ) Area based stratified sampling ( a=0 b=1 )

6 Shu-Jheng Huang 6 / 25 Variance Analysis for Visibility (variance) (empirical)

7 Shu-Jheng Huang 7 / 25 Variance Analysis for Visibility Correlation model for visibility

8 Shu-Jheng Huang 8 / 25 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)

9 Shu-Jheng Huang 9 / 25 Variance Analysis for Visibility

10 Shu-Jheng Huang 10 / 25 Variance Analysis for Visibility

11 Shu-Jheng Huang 11 / 25 Variance Analysis for Visibility

12 Shu-Jheng Huang 12 / 25 The Number of Samples The number of samples is proportional to Uniform lighting

13 Shu-Jheng Huang 13 / 25 Hierarchical Environment Map Stratification Hierarchical Thresholding Hierarchical Stratification

14 Shu-Jheng Huang 14 / 25 Hierarchical Thresholding σ:Standard deviation of the illumnation in the map

15 Shu-Jheng Huang 15 / 25 Hierarchical Thresholding

16 Shu-Jheng Huang 16 / 25 Hierarchical Thresholding N1N1 N2N2 N3N3 N4

17 Shu-Jheng Huang 17 / 25 Hierarchical Stratification Hochbaum-Shmoys Algorithm (K-center problem)

18 Shu-Jheng Huang 18 / 25 Hochbaum-Shmoys Algorithm

19 Shu-Jheng Huang 19 / 25 Hochbaum-Shmoys Algorithm

20 Shu-Jheng Huang 20 / 25 Hochbaum-Shmoys Algorithm

21 Shu-Jheng Huang 21 / 25 Hochbaum-Shmoys Algorithm

22 Shu-Jheng Huang 22 / 25 Rendering Optimizations Pre-integrating the illumination Jittering Sorting

23 Shu-Jheng Huang 23 / 25

24 Shu-Jheng Huang 24 / 25

25 Shu-Jheng Huang 25 / 25

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