adaptive wavelet renderingsungeui/sga/students/[cs680... · 2010-11-11 · craig donner . 2 the...
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1
Adaptive Wavelet Rendering
Author: Ryan Overbeck
Ravi Ramamoorthi
Presenter: Guillaume de Choulot
Craig Donner
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The Problem (combined effects)
∫ Pixel
Area
∫ Area
Light
∫ Camera
Aperture
Pixel = … 6D
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General combinations of effects
4D 5D 6D
Antialiasing
Depth of field Antialiasing
Depth of field
Motion Blur
Antialiasing
Depth of field
Area Lighting
Antialiasing
Depth of field
Envir. Lighting
Antialiasing
Depth of field
Area Lighting
1 Bounce GI
6D 8D
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Monte Carlo Problem (1/1)
Noisy for low sample counts (smooth regions)
32 Samples Per Pixel
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Monte Carlo Problem (2/2)
Requires hundreds to thousands of samples
512 Samples Per Pixel
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Our Solution (important sampling)
Adaptive Wavelet Rendering
32 Samples Per Pixel
(average)
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Features of Adaptive Wavelet Rendering
Low Sample Counts Converges from smooth
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Features of Adaptive Wavelet Rendering
Low Sample Counts Converges from smooth
Near Reference:
32 samples per pixel
Average of 32 Samples Per Pixel
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Features of Adaptive Wavelet Rendering
Low Sample Counts Converges from smooth
Near Reference:
32 samples per pixel
Smooth Preview Quality:
8 samples per pixel
Average of 8 Samples Per Pixel
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Features of Adaptive Wavelet Rendering
Low Sample Counts
Efficient
Less samples gives Faster render times
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Features of Adaptive Wavelet Rendering
Low Sample Counts
Efficient
Less samples gives Faster render times
Monte Carlo (512 spp)
>6 Hours
> 6 Hours Monte Carlo
512 Samples Per Pixel
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Features of Adaptive Wavelet Rendering
Low Sample Counts
Efficient
Less samples gives Faster render times
Monte Carlo (512 spp)
Our Method (32 spp)
>6 Hours 34 minutes
34 Minutes Adaptive Wavelet Rendering
32 Samples Per Pixel (average)
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Features of Adaptive Wavelet Rendering
Low Sample Counts
Efficient
General
Insensitive to problem dimensionality
General combinations of effects
∫ Pixel
Area
∫ Area
Light
∫ Camera
Aperture
… 8D ∫ Hemi-
sphere
32 Samples per pixel (average)
15 minutes
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The Insight (Important sampling)
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Variance is often local
Variance
Low
High
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Send more samples to high variance
Sample Count
Low
High
Our method
32 Samples Per Pixel
(average)
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Two forms of variance
Edges
Smooth Variance
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Variance from image space: edges
Variance Low
High
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Focused samples to image edges
Samples Low
High
Final Result
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Variance from other dims: smooth
Variance Low
High
Difficult for Monte Carlo
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Smooth is easier in multi-scale
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Smooth is easier for wavelets
calculate pixel
wavelet synthesis
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Coarse Sampling of Smooth Regions
Samples Low
High
Final Result
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Algorithm Outline
Start: 4 Samples per Pixel
Adaptive Sampling
Reconstruction
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Related Work
Adaptive sampling
Bolin & Meyer 1998, Whitted 1980, Mitchell 1987, Veach and Guibas 1997, Walter et al. 2006 (Multidim Lightcuts)
Multi-scale
Keller 2001 (Hierarchical MC), Heinrich and Sindambiwe 1999, Guo 1998, Bala et al. 2003, Walter et al. 2005 (Lightcuts), Perona and Malik 1990
Wavelet sampling and reconstruction
Our method
works well for both edges and smooth regions
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Background: Wavelets
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Wavelets made of 2 functions
Wavelet Scale
Low Pass
(smooth)
Band Pass
(edges)
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Wavelet Hierarchy (1D)
Wavelet Scale
Low Pass
(smooth) Band Pass
(edges)
Wavelet Hierarchy (1D)
k = 1
k = 2
k = 3
Wavelet Scale
1D Tensor Product 2D Basis
=
=
=
=
scale
scale
scale
scale
wavelet
wavelet
wavelet wavelet
scale-scale
scale-wavelet
wavelet-scale
wavelet-wavelet
k = 3
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Wavelet used
k = 4
JPEG
2000
compression
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Wavelets Basis (& DWT)
Wavelets (Multi-scale basis) VS Pixel Basis
Multi scale: coefficient/wavelet expressed in
different scale
Discret Wavelet Transform (DWT):
1) Pixels Wavelets coefficient (Analysis)
2) Wavelets Pixels (Synthesis)
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Wavelet Hierarchy
scale-scale scale-wavelet wavelet-scale wavelet-wavelet
Smooth regions Edges
k=3
k=2
k=1
k=4 k=5
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III) Algorithm Outline
0) Start: 4 Samples per Pixel (skipped)
1) Adaptive Sampling
2) Reconstruction
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1) Adaptive Sampling
Insert all scale coefficients into a priority queue
While more samples:
Send samples to highest priority coefficient
Update priority queue
The problem:
How to compute priority for each scale coefficient?
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scale-scale
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scale-scale
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Wavelet synthesis is smoothing
scale-scale
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Coarse scale captures smoothness
scale-scale
Smooth Region
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Edges are in the fine scale
scale-scale
Edges
Smooth Region
Smoothed out
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Adaptive Sampling
Goals:
In smooth regions, more samples to coarse coefficients
Near edges, more samples to fine coefficients
Solution:
Compute priority based on variance and smoothness
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Start with Scale Coefficients’ Variance
Scale Variance
low high
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Smooth variance grows fine to coarse
Scale Variance
low high
Higher
Smooth Region
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Edge variance stays the same
Scale Variance
low high
Same
Edge Region
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Squared wavelet magnitudes
Scale Variance (Wavelet Magnitude)
low high
2
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Edge wavelets grow fine to coarse
Scale Variance (Wavelet Magnitude)
low high
2
Higher (ok)
Edge Region
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Smooth wavelets stay the same
Scale Variance (Wavelet Magnitude)
low high
2
Same
(problem)
Smooth Region
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Priority equals the difference
Scale Variance (Wavelet Magnitude)
- =
Priority
low high
2
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Edges: Higher priority at fine scales
Scale Variance
- =
Priority
low high
Higher
Edge Region (Wavelet Magnitude) 2
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Smooth: Higher priority at coarse scales
Scale Variance
- =
Priority
low high
Higher
Smooth Region (Wavelet Magnitude) 2
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After adaptive sampling
Smooth Region in Coarse Scale
Accurate
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After adaptive sampling
Smooth Region in Coarse Scale
Edges in Fine Scale
Accurate
Accurate
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After adaptive sampling Smooth Region in Coarse Scale
Edges in Fine Scale
Smooth Region in Fine Scale
Accurate
Accurate
Noisy
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Reconstruction: smooth away fine scale noise
Smooth Region in Coarse Scale
Edges in Fine Scale
Smooth Region in Fine Scale
Accurate
Accurate
Noisy
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Wavelets capture edges
scale-scale scale-wavelet wavelet-scale wavelet-wavelet
Edges
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Wavelets capture edges and Noise
scale-scale scale-wavelet wavelet-scale wavelet-wavelet
Edges and Noise
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Algorithm Outline
0) Start: 4 Samples per Pixel
1) Adaptive Sampling
-> 2) Reconstruction
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Wavelet Reconstruction
Remove noise by suppressing wavelet magnitudes
How? Choose smoothest image which fits
samples
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Monte Carlo: statistics
High
Low
Mean
+Standard Deviation (estimate of Error)
-Standard Deviation
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Monte Carlo: statistics
High
Low
Mean
+Standard Deviation
-Standard Deviation
Monte Carlo Estimate Valid
Range
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For pixel:
High
Low
Mean
+Standard Deviation
-Standard Deviation
Pixel
Luminance
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For pixel: luminance
High
Low
Mean
+Standard Deviation
-Standard Deviation
Pixel
Luminance
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For pixel: luminance
High
Low
Mean
+Standard Deviation
-Standard Deviation
Pixel
Brightness
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For wavelet:
High
Low
Mean
+Standard Deviation
-Standard Deviation
Wavelet Coefficient
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For wavelet: Smoothness
High
Low
Mean
+Standard Deviation
-Standard Deviation
Wavelet Coefficient
Smoothness
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Take the smoothest value
High
Low
Mean
+Standard Deviation
-Standard Deviation
Wavelet Coefficient
Smoothness Our Estimate
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Reconstruction computation?!
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After Sampling
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After Reconstruction
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Results (1/2)
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Results (2/2)
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Limitations (1/3)
Wavelet artifacts when not enough samples
Ringing around edges
Our Method
Monte Carlo
Ringing
Noise
32 samples per pixel (avg.)
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Limitations (2/3)
Wavelet artifacts when not enough samples
Ringing around edges
Overly smoothing
Our Method
Monte Carlo
Too Smooth
Noise
32 samples per pixel (avg.)
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Limitations (3/3)
Wavelet artifacts when not enough samples
Ringing around edges
Overly smoothing
Potential solutions
Variance reduction (path splitting, QMC, etc.)
Reduce smoothing during reconstruction
Use depth and normals to improve statistics
Use more samples
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Conclusion/Summary
Sample and reconstruct in wavelet basis
Features
Low Sample Counts
Efficient
General
Best for smooth image features
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