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

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

3. Introduction Problem Goal Additional Properties Usage
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 Variable-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
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?