Energy Preserving Non-linear Filters

1. Energy Preserving Non-linear Filters Presented by Wei-Yin Chen (R94943040)

2. Outline • Introduction • Problem and Goal • Source of Noise • Filter Model • Algorithm and Application • Monte Carlo • RADIANCE • Result and Conclusion

3. Introduction • Problem • Noise caused by inadequate sampling • Goal • Enhance image quality without more samples • Additional Properties • Preserve energy • Doesn’t blur details • Usage • Filter before tone mapping

4. Source of Noise • “Small probability” area in Monte-Carlo method • Not noise actually • This happens at a region, not at a pixel • Average the “noise” in a larger region

5. Required sample • Define noise • Pixels not converging within range D (typically 13) after tone map • Huge samples are required in the worst case • >1e4 samples for 1e-4 accuracy • Most regions are smooth • Good average case • Target on the noisy regions

6. Filter Model • Constant-width filter • Inherently preserve energy • Variable-width filter • Not energy preserving on the boundary • Region of support • Variable-width filter with energy preserving • Source oriented perspective • Region of influence

7. Algorithm for Monte Carlo rendering • Pre-render a small image (100x100x16) • Find a visual threshold Ltvis = Laverage/128 (1 after tone map) • Find a threshold of sample density that most pixels converge within D • Render with the sampling density at full resolution • For unconverged pixels • Distribute Lexcess=Lu-Ln (average of converged neighbors) to a region, region area = Lexcess/Ltvis • Affected radiance <= 1

8. Co-operation with RADIANCE • RADIANCE • A rendering system • Super-sampled • StDev unknown for the filter • Work-around • Regard extreme values as unconverged pixels

9. Result

11. Conclusion and Comments • Effective in removing noise • Still blur the caustic area • Increasing samples in the noisy region might be better • What if the RADIANCE is not super-sampled?