SLIDE 1
2
Class Objectives:
- Extensions to the basic MC path tracer
- Bidirectional path tracer
- Metropolis sampling
- Biased techniques
- Irradiance caching
- Photon mapping
MC Ray Tracing: Part III, Acceleration and Biased Tech. Sung-Eui - - PowerPoint PPT Presentation
MC Ray Tracing: Part III, Acceleration and Biased Tech. Sung-Eui - - PowerPoint PPT Presentation
CS580: MC Ray Tracing: Part III, Acceleration and Biased Tech. Sung-Eui Yoon ( ) Course URL: http://sglab.kaist.ac.kr/~sungeui/GCG Class Objectives: Extensions to the basic MC path tracer Bidirectional path tracer
SLIDE 2
SLIDE 3
3
General GI Algorithm
- Design path generators
- Path generators determine efficiency of GI
algorithm
- Black boxes
- Evaluate BRDF, ray intersection, visibility
evaluations, etc
SLIDE 4
4
Other Rendering Techniques
- Bidirectional path tracing
- Metropolis
- Biased techniques
- Irradiance caching
- Photon mapping
SLIDE 5
5
SLIDE 6
6
SLIDE 7
7
SLIDE 8
8
SLIDE 9
9
SLIDE 10
10
SLIDE 11
11
SLIDE 12
12
Other Rendering Techniques
- Metropolis
- Biased techniques
- Irradiance caching
- Photon mapping
SLIDE 13
13
Metropolis
- Based on Metropolis sampling (1950’s)
- Introduced by Veach and Guibas to CG
- Deals with hard to find light paths
- Robust
- Hairy math, but it works
- Not that easy to implement
SLIDE 14
14
Metropolis
- Generate paths
- Once a valid path is found, mutate it to
generate new valid paths
- Advantages:
- Path re-use
- Local exploration: found hard-to-find light
distribution, mutate to find other such paths
SLIDE 15
15
SLIDE 16
16
SLIDE 17
17
SLIDE 18
18
SLIDE 19
19
Metropolis
- Advantages
- Robust
- Good for hard to find light paths
- Disadvantage
- Slow convergence for many important paths
- Tricky to implement and get right
SLIDE 20
20
Unbiased vs. Consistent
- Unbiased
- No systematic error
- E[Iestimator] = I
- Better results with larger N
- Consistent
- Converges to correct results with more samples
- E[Iestimator] = I + ε, where limn∞ ε = 0
SLIDE 21
21
Biased Methods
- MC methods
- Too noisy and slow
- Nose is objectionable
- Biased methods: store information
(caching)
- Irradiance caching
- Photon mapping
SLIDE 22
22
Irradiance Caching
- Introduced by Greg Ward 1988
- Implemented in RADIANCE
- Public-domain software
- Exploits smoothness of irradiance
- Cache and interpolate irradiance estimates
SLIDE 23
23
Irradiance Caching
- Indirect changes smoothly.
From Wang’s slides
SLIDE 24
24
Irradiance Caching
- Indirect changes smoothly.
- Cache irradiance.
From Wang’s slides
SLIDE 25
25
Irradiance Caching
- Indirect changes smoothly.
- Cache irradiance.
From Wang’s slides
SLIDE 26
26
Irradiance Caching
- Indirect changes smoothly.
- Cache irradiance.
- Interpolate them.
From Wang’s slides
SLIDE 27
27
Irradiance Caching Approach
- Irradiance E(x) estimated using MC
- Cache irradiance when possible
- Store in octree for fast access
- When do we use this cache of irradiance
values?
SLIDE 28
28
SLIDE 29
29
Direct Indirect Indirect
From thesis of Jarosz
SLIDE 30
30
Photon Mapping
- 2 passes:
- Shoot “photons” (light-rays) and record any
hit-points
- Shoot viewing rays and collect information
from stored photons
SLIDE 31
31
SLIDE 32
32
Flux for each photon
SLIDE 33
33
for diffuse materials
SLIDE 34
34
Stored Photons
Generate a few hundreds of thousands of photons
SLIDE 35
35
SLIDE 36
36
Radiance Estimation
- Compute N nearest photons
- Consider a few hundreds of photons
- Compute the radiance for each photon to
- utgoing direction
- Consider BRDF and
- Divided by area
SLIDE 37
37
Efficiency
- Want k nearest photons
- Use kd-tree
- Using photon maps as it create noisy
images
- Need extremely large amount of photons
SLIDE 38
38
Perform direct illumination for visible surface using regular MC sampling
SLIDE 39
39
Specular reflection and transmission are ray traced
SLIDE 40
40
SLIDE 41
41
SLIDE 42
42
Result
350K photons for the caustic map
SLIDE 43
43
- Photon mapping
- A consistent algorithm and good at caustics
and SDS paths
- Requires huge # of photons to avoid noises
Img.blog.yahoo.co.kr/ybi
Progressive Photon Mapping [Hachisuka et al., SIG. A. 08]
SLIDE 44
44
- Photon mapping
- Requires huge # of photons to avoid noises
- Its quality is limited by the available memory
20M photons 165M photons 22 hours
Progressive Photon Mapping [Hachisuka et al., SIG. A. 08]
SLIDE 45
45
- Achieve arbitrary accuracy without requiring
infinite memory
- Uses multiple phases
- Store extra information for all the hit points along
all the ray paths
- E.g., accumulated # of photons, flux, and current radius
Overall Framework
SLIDE 46
46
Key Idea
- We want to increase # of photons and
reduce radius while keeping photon density
- Key assumption:
- Uniform photon density and illumination
within each radius
SLIDE 47
47
Results
213M photons
SLIDE 48
48
Comparison
SLIDE 49
49
Future Work
- Stopping criteria and error estimate
- How many photons do we need?
- Adaptive photon tracing
- We know how many photons are used in each
hit point in the PPM framework
SLIDE 50
50
Class Objectives were:
- Extensions to the basic MC path tracer
- Bidirectional path tracer
- Metropolis sampling
- Biased techniques
- Irradiance caching
- Photon mapping
SLIDE 51
51
Summary
- Two basic building blocks
- Radiometry
- Rendering equation
- MC integration
- MC ray tracing
- Unbiased methods
- Biased methods
SLIDE 52
52