1. H M V Amortized Supersampling Dec. 18, 2009, Pacifico Yokohama, Japan L EI Y ANG H, D IEGO N EHAB M, P EDRO V. S ANDER H, P ITCHAYA S ITTHI - AMORN V, J ASON L AWRENCE V, H UGUES H OPPE M L EI Y ANG H, D IEGO N EHAB M, P EDRO V. S ANDER H, P ITCHAYA S ITTHI - AMORN V, J ASON L AWRENCE V, H UGUES H OPPE M

2. TOG Article 135: Amortized Supersampling Outline  Problem  Amortized supersampling – basic approach  Challenge - the resampling blur  Our algorithm  Results and conclusion  Problem  Amortized supersampling – basic approach  Challenge - the resampling blur  Our algorithm  Results and conclusion 2/27

3. TOG Article 135: Amortized Supersampling Problem  Shading signals not band-limited  Procedural materials  Complex shading functions  Band-limited version (analytically antialiased)  Ad-hoc  Difficult to obtain  Shading signals not band-limited  Procedural materials  Complex shading functions  Band-limited version (analytically antialiased)  Ad-hoc  Difficult to obtain 3/27

4. TOG Article 135: Amortized Supersampling Problem  Supersampling  General antialiasing solution  Compute a Monte-Carlo integral  Can be prohibitively expensive  Supersampling  General antialiasing solution  Compute a Monte-Carlo integral  Can be prohibitively expensive 4/27

5. TOG Article 135: Amortized Supersampling Accelerating Supersampling  Shading functions usually vary slowly over time  Reuse samples from previous frames  Reprojection  Generate only one sample every frame  Shading functions usually vary slowly over time  Reuse samples from previous frames  Reprojection  Generate only one sample every frame Frame 1 Frame 2 Frame 3 Frame t …… 5/27

6. TOG Article 135: Amortized Supersampling Amortized Supersampling  Cannot afford to store all the samples from history  Keep only a running accumulated result  Update it every frame using exponential smoothing  Cannot afford to store all the samples from history  Keep only a running accumulated result  Update it every frame using exponential smoothing = Frame 1 ~ t-1 Frame t-1 Frame t 6/27

7. TOG Article 135: Amortized Supersampling Reverse Reprojection [Nehab07, Scherzer07]  Compute previous location π t-1 (p) of point p  A bilinear texture fetch for the previous value  Check depth for occlusion changes  Compute previous location π t-1 (p) of point p  A bilinear texture fetch for the previous value  Check depth for occlusion changes p π t-1 (p) 7/27

8. TOG Article 135: Amortized Supersampling Effect of the smoothing factor α  Larger α: less history, more aliasing/noise  Smaller α: less fresh value, more smoothing  Equal weight of samples:  Larger α: less history, more aliasing/noise  Smaller α: less fresh value, more smoothing  Equal weight of samples: Frame t-1 Frame t (1 – α) ·(α) · +→ 8/27

9. TOG Article 135: Amortized Supersampling An artifact of recursive reprojection  Severe blur due to repeated bilinear interpolation Recursive reprojection Ground truth 9/27

10. TOG Article 135: Amortized Supersampling Factors of the blur  Fractional pixel velocity v = (v x, v y )  Exponential smoothing factor α  Fractional pixel velocity v = (v x, v y )  Exponential smoothing factor α …… Frame t-1Frame t-2Frame t-3Frame t v =(0.5, 0.5) …… Frame t-1Frame t-2Frame t-3Frame t (1- α)(1- α) 2 (1- α) 3 10/27

11. TOG Article 135: Amortized Supersampling The amount of blur  The expected blur variance is (derivation in the appendix)  Approaches for reducing the blur: 1. Increase resolution of the history buffer 2. Avoid bilinear resampling whenever possible 3. Limit α when needed  The expected blur variance is (derivation in the appendix)  Approaches for reducing the blur: 1. Increase resolution of the history buffer 2. Avoid bilinear resampling whenever possible 3. Limit α when needed 11/27

12. TOG Article 135: Amortized Supersampling  Option 1: Keep a history buffer at high resolution (2x2)  Have to update it every frame   Option 2: Keep 4 subpixel buffers at normal resolution  Only update one of them each frame  Option 1: Keep a history buffer at high resolution (2x2)  Have to update it every frame   Option 2: Keep 4 subpixel buffers at normal resolution  Only update one of them each frame (1) Increase resolution 12/27 High-resolution buffer Subpixel buffers

13. TOG Article 135: Amortized Supersampling Subpixel buffers 13/27

14. TOG Article 135: Amortized Supersampling (2) Avoid bilinear sampling  Reconstructing from subpixel buffers  Forward reproject the samples from 4 subpixel buffers to the current subpixel quadrant  Weight them using a tent function  GPU approximation/acceleration  Reconstructing from subpixel buffers  Forward reproject the samples from 4 subpixel buffers to the current subpixel quadrant  Weight them using a tent function  GPU approximation/acceleration 14/27

15. TOG Article 135: Amortized Supersampling Reconstruction scheme 15/27

16. TOG Article 135: Amortized Supersampling (3) Limiting blur via bounding α  Derive a relationship between  Blur variance σ 2  Motion velocity v and α  Analytic relationship is not attainable  Numerical simulation and tabulate  Bound α for limiting σ 2 no larger than τ b  Derive a relationship between  Blur variance σ 2  Motion velocity v and α  Analytic relationship is not attainable  Numerical simulation and tabulate  Bound α for limiting σ 2 no larger than τ b 16/27

17. TOG Article 135: Amortized Supersampling Tradeoff of blur and aliasing 17/27

18. TOG Article 135: Amortized Supersampling Adaptive evaluation 18/27  Newly disoccluded pixels are prone to aliasing  Additional shading for subpixels that fail in reconstruction  Newly disoccluded pixels are prone to aliasing  Additional shading for subpixels that fail in reconstruction

19. TOG Article 135: Amortized Supersampling Accounting for signal changes  Detect fast signal change  React by more aggressive update  Estimate residual ε between:  Current sample s t (aliased/noisy)  History estimate f t  Blur the residual estimate to remove aliasing/noise  Bound α for limiting ε no larger than τ ε  Detect fast signal change  React by more aggressive update  Estimate residual ε between:  Current sample s t (aliased/noisy)  History estimate f t  Blur the residual estimate to remove aliasing/noise  Bound α for limiting ε no larger than τ ε 19/27

20. TOG Article 135: Amortized Supersampling Tradeoff of signal lag and aliasing 20/27

21. TOG Article 135: Amortized Supersampling Results 21/27

22. TOG Article 135: Amortized Supersampling Results 22/27

23. TOG Article 135: Amortized Supersampling Results 23/27

24. TOG Article 135: Amortized Supersampling Results 24/27

25. TOG Article 135: Amortized Supersampling Results 25/27

26. TOG Article 135: Amortized Supersampling Conclusion  A real-time scheme for amortizing supersampling costs  Quality comparable to 4x4 stratified supersampling  Speed is 5x-10x of 4x4 supersampling  A single rendering pass  A real-time scheme for amortizing supersampling costs  Quality comparable to 4x4 stratified supersampling  Speed is 5x-10x of 4x4 supersampling  A single rendering pass 26/27

27. Questions?