1. Primary Sample Space Path Guiding
Jerry Jinfeng Guo1, Pablo Bauszat1, Jacco Bikker2 and Elmar Eisemann1
3-July-2018
1: Delft University of Technology, the Netherlands
2: Utrecht University, the Netherlands

2. Background Realistic rendering via light transport simulation
Path tracing and bi-directional path tracing
Monte Carlo integration to solve the equation
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3. Path Construction 101
Motivation in 2D
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4. Related Work – Path Guiding
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5. Related Work – Path Guiding
Reduce Zero Radiance Paths
Guide rays towards more promising region
Essentially importance sampling
PG with pre-computed caches [1][2]
On-line PG [3][4]
PG with reinforced approach [5]
[1] Jensen et al. "Photon maps in bidirectional Monte Carlo ray tracing of complex objects.“, 1995 
[2] Hey et al. "Importance sampling with hemispherical particle footprints.", 2002
[3] Vorba et al. "On-line learning of parametric mixture models for light transport simulation.", 2014 
[4] Müller et al. "Practical Path Guiding for Efficient Light‐Transport Simulation.", 2017
[5] Dahm, Ken, and Alexander Keller. "Learning light transport the reinforced way.", 2017
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6. Related Work – Primary Sample Space
Metropolis light transport [7]
Path configurations as samples
Correlate samples as Markov states
Mutation done by tweaking path configuration
Primary sample space MLT [8]
Tweaking random numbers
Ease of implementation
Primary samples: vectors of random numbers
[ …, , , ,
… ]
[ …, , , ,
… ]
[7] Veach et al. "Metropolis light transport.“, 1997 
[8] Kelemen et al. "A simple and robust mutation strategy for the metropolis light transport algorithm.", 2002.
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7. Our Objective To build a structure that affects sample generation
Takes as input samples from standard RNG
Output are samples more concentrated in valuable regions
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8. Distinction
All methods build spatial-directional structures in scene space
Spatially distributed (3D)
Hemispherical or spherical representation (2D)
We work solely in primary sample space
Out-of-kernel feature
No need to explicitly build structures in scene space
Clarification
This project is about unidirectional path guiding
No Metropolis sampling involved
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9. Overview A standard path tracing solution: {u0, u1, u2, u3, …}
Luminance
Sampler
Path Tracer
Final Image
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10. Overview Our primary sample space guided path tracing:
{u0, u1, u2, u3, …}
{u’0, u’1, u’2, u’3, …}
Sampler
K-d
Tree
Path Tracer
Luminance
{u’0, u’1, u’2, u’3, …}, L
Final Image
Last
Iteration?
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11. Method – Our Structure
We use a K dimensional binary tree as our structure
K = MxN:
M: bounces
N: fixed random numbers each bounce consumes
Each node encodes:
Leaf flag
Counter or right child index
Luminance value
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12. Tree construction (refinement)
Method – Outline
Sample collection
Tree construction (refinement)
Tree sampling
Rendering
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13. Method – Sample Collection
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14. Method – Sample Collection
We use a two-tree design: one for sampling, one for collection
Tree traversal, with samples & luminance ({u’0, u’1, u’2, u’3, …}, L)
{u’0, u’1, u’2, u’3}, L
Node
Range for u0
Add luminance value
Is Leaf?
Get axis ui
Get split via range[] ui
Go left?
Update
Range for u1
Range for u2
Range for u3 …
depth
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15. Method – Tree Construction
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16. Method – Tree Construction
Start with an empty tree
Refine the tree after each iteration
Refine the collection tree
Copy it to the sample tree
Node division criteria: leaf node counter
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17. Method – Tree Sampling
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18. Method – Tree Sampling
Tree traversal, with primary sample {u0, u1, u2, u3, …},
{u0, u1, u2, u3}
Range for u0
Range for u1
Range for u2
Range for u3
Node
Is Leaf?
Go left? Comp. value
Get axis ui
Split range[] ui
Update …
pdf
depth
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19. Method – Tree Sampling
With ranges available, we get the transformed sample by warping the input sample into these ranges
We use a parameter to balance tree sampling and uniform random numbers
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20. Method – Rendering

21. Method – Rendering Feed the path tracer with transformed sample
Simply fetch random number from a proper RNG after the end
The final path length is not limited by k-d tree dimension
Combine guided with uniform using multiple importance sampling
Correctly reweight results using the pdf that comes along:
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22. Implementation Detailsu0 u1 u2 u3
Max depth = 20 …
Implemented in PBRT v3
K-d tree:
K=4, M=2, N=2
K-d tree node division criteria 4 or 8
Max depth 20
8 bytes node layout
K-d tree per image tile (16x16)
Probability of sampling K-d tree 0.5
1/8 total sample budget for collection …
8 bytes
1 bit leaf flag
31 bits counter/index
32 bits node value
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23. Results – Ajar scene 256 collection spl. 2048 rendering spl.
800x450
n/a L: C: R:
2048 rendering spl.
256 collection spl.
1792 rendering spl.
4096 rendering spl.
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24. Results - Dinning room scene
800x450
2k PT: s
2k ours: s
512 ours: 542.5s
256 collection spl.
1792 rendering spl.
64 collection spl.
448 rendering spl.
2048 rendering spl.
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25. Results – Staircase scene
450x800
Ours 256: 238.1s
PT 512: n/a
Ours 512: n/a
512
64 collection spl.
448 rendering spl.
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26. Results – Kitchen scene
800x450
Ours 1K: 812.1s
PT 4K: s
Ours 4K: s
128 collection spl.
869 rendering spl.
512 collection spl.
3584 rendering spl.
4096 rendering spl.
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27. Results – Observations
MSEs
In all scenes, our method brings down MSE
Works in regions from where light can be reached with one or two bounces
Zero radiance path ratios
In all scenes, our method brings down zero radiance paths, best case by 39.5%
Zero radiance path ratio goes down as more samples/iterations are invested
Best case Kitchen scene
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28. Future work Acknowledgement Make the per tile structure adaptive
Higher dimensions
Apply to Bi-directional path tracing
Acknowledgement
PBRT authors for the book and pbrt
Benedikt Bitterli [1] for the awesome 3D scenes freely available online
Reviewers for the insightful feedback
[1]
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29. Conclusion We presented an unbiased path guiding scheme
Path guiding in primary sample space is practical
Easy to implement
Out-of-kernel feature
Efficient
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30. Thank you!
Questions are welcome!
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