Ranveer Aggarwal
Software Engineer
Bidirectional Lightcuts
Bruce Walter, Pramook Khungurn, Kavita Bala
A presentation by:
Ranveer Aggarwal &
Abhinav Gupta
Guide: Prof. Parag Chaudhuri
Introduction
- We all love a fast noise-free rendering algorithm which handles all materials and phenomena.
- General unbiased algorithms: Noise! Eg. Path tracing
- Specialized noise-free algorithms: Bias! Eg. Instant Radiosity
Preliminaries
Bidirectional Path Tracing
- Follow paths from both the eye and the light and join them to form a complete path.
- Works better than normal path tracing.
- Induces noise and needs large number of samples to converge.
VPLs
Virtual Point Lights: Recursively trace a direction from light source. Generate VPL at every hit with reducing intensity.
VPSs
Virtual Sensor Points: Similar to VPL. Start from the eye and generate VPS at every hit.
Terminlogy
- : Direction of VPL from VPS
- : Direction of VPS from VPL
- : Proportion of light reflected along
- : Proportion of light reflected along
- : Transit term
- : Strength of material after path tracing
- : Intensity of light after path tracing
\psi
ψ
\omega
ω
M(\psi)
M(ψ)
D(\omega)
D(ω)
T_{i, i+1}
Ti,i+1
S
S
I
I
(visibility + attenuation)/||v_i-v_{i+1}||^2
(visibility+attenuation)/∣∣vi−vi+1∣∣2
\psi
ψ
\omega
ω
Weights
- Assuming equal contribution of VPS-VPL pairs generates noise. Use weights.
- Weight for a pair such that the VPS is the vertex in the path. Assume all adjacent vertices are VPS-VPL pairs.
- Calculate . Use them for .
- Evaluate four weight constraints.
w_j
wj
j^{th}
jth
w_1, w_2, ... w_{j-1}
w1,w2,...wj−1
w_j
wj
w_j = max(0, min(w_j^E, w_j^C, w_j^D, w_j^V))
wj=max(0,min(wjE,wjC,wjD,wjV))
1. Energy Conservation and Favoring Shorter Eye Paths
- Sum of connection weights never exceeds 1.
- VPLs useful for all pixels, VPS just one.
- Prefer shorter eye paths and avoid computation!
w_j^E = 1 - \sum_{i=1}^{j-1} w_i.
wjE=1−∑i=1j−1wi.
2. Clamping
- Standard clamping in VPL based methods.
- Avoid visible effect of any one VPL.
- Weigh down if VPS and VPL are close.
- Weigh down if they the VPS material is glossy and oriented in the VPL direction.
- Similarly for the VPL.
w_j^C = min(1, C_{clamp}/(M_jT_{j,j+1}D_{j+1}))
wjC=min(1,Cclamp/(MjTj,j+1Dj+1))
3. Diffuse VPLs
- Limit the illumination from a VPL to only include diffuse components.
- Not strictly necessary but highly directional VPLs are a computational waste.
- Also, a big D will get clamped anyway.
w_j^D = min(1, C_D/D_{j+1})
wjD=min(1,CD/Dj+1)
4. Exclusion of High-Variance Eye Subpaths
- Eliminate high noise estimators. The ones with spread out eye paths.
- Directional Spread
w_j^V = \mu_j - \sum_{i=1}^{j-1}w_i
wjV=μj−∑i=1j−1wi
\Theta_j = \sum_{i=1}^{j-1}(\pi M_i)^{-1/2}
Θj=∑i=1j−1(πMi)−1/2
Lightcuts
-
Computing illumination from tens of thousands of lights is expensive.
-
Solution: Clustering!
-
Cluster similar lights together and treat them as a single light.
-
Give theoretical upper bound on error.
-
Choose cut with error less than a perceptibility threshold (Weber’s Law).
Cut of a Tree
A set of nodes such that exactly one node from the set is present in any path from the root to a leaf.
Light Tree
Bounding Function
- This gives the maximum error bound because of clustering.
- Actual value =
- Approximate value = where j is the representative light.
- Error <= product of maximum error in M, G & V and sum of intensities.
- For V, it’s 1. For M & G compute using cluster bounding box.
\sum M_iG_iV_iI_i
∑MiGiViIi
M_jG_jV_j\sum I_i
MjGjVj∑Ii
Cut Selection
-
Set the lightcut to { root }.
-
Computer the error bound for the light cut. If this is less that the threshold we are done.
-
Pick the node with the maximum error and refine it by replacing it with it’s children in the lightcut.
-
Go to Step 2
Building the Light Tree
-
Use a bottom-up greedy strategy.
-
Pair lights/clusters with the highest similarity.
-
Similarity Metric is based on the diagonal length of the bounding box and the cone-angle of the direction (in case of oriented lights)
-
Representative light is randomly chosen with probabilities in proportion to intensities.
Multidimensional Lightcuts
-
Have to evaluate Lots of VPLs and VPSs. Building a light graph for is expensive.
-
Build an implicit graph from individual light trees.
-
Traverse the light graph by refining a node in one of the trees.
|n_{VPLs}n_{VPSs}|
∣nVPLsnVPSs∣
Some Pretty Pictures
* The above result has been taken from the original paper and not rendered by us.
Some More Pretty (or not) Pictures
* The above result has been taken from the original paper and not rendered by us.
References
-
Bruce Walter, Pramook Khungurn, and Kavita Bala. Bidirectional lightcuts. ACM Trans. Graph., 31(4):59:1–59:11, July 2012.
-
Bruce Walter, Adam Arbree, Kavita Bala, and Donald P. Greenberg. Multidimensional lightcuts. ACM Trans. Graph., 25(3):1081–1088, July 2006.
-
Bruce Walter, Sebastian Fernandez, Adam Arbree, Kavita Bala, Michael Donikian, and Donald P. Greenberg. Lightcuts: A scalable approach to illumination. ACM Trans. Graph., 24(3):1098–1107, July 2005.
Thank You!
Questions?
Bidirectional Lightcuts Bruce Walter, Pramook Khungurn, Kavita Bala A presentation by: Ranveer Aggarwal & Abhinav Gupta Guide: Prof. Parag Chaudhuri
Bidirectional Lightcuts
By Ranveer Aggarwal
Bidirectional Lightcuts
- 2,545
