(a.k.a. path guiding) Jaroslav Kivnek Charles University, Prague - - PowerPoint PPT Presentation

▶
a k a path guiding
SMART_READER_LITE
LIVE PREVIEW

(a.k.a. path guiding) Jaroslav Kivnek Charles University, Prague - - PowerPoint PPT Presentation

Nov 08, 2022 396 likes •925 views

Zero variance-based sampling schemes (a.k.a. path guiding) Jaroslav Kivnek Charles University, Prague Render Legion/Chaos Group Path guiding The idea MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT ZERO VARIANCE-BASED SAMPLING SCHEKEMS

slide-1
SLIDE 1

Zero variance-based sampling schemes (a.k.a. path guiding)

Jaroslav Křivánek Charles University, Prague – Render Legion/Chaos Group

slide-2
SLIDE 2

Path guiding – The idea

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-3
SLIDE 3

Zero-variance path sampling in volumes

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • A theoretical framework for path guiding
  • Set of local sampling rules yielding globally optimal path sampling
slide-4
SLIDE 4

Zero-variance path sampling in volumes

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Theoretical construct – ZV cannot be achieved in practice
  • Requires knowing the radiance solution everywhere
  • But it provides a guideline for variance reduction
  • Even approximate radiance solution yields low variance
  • Obtaining the approximate solution
  • MC samples – Machine/statistical learning
  • [Vorba et al. 2014, 2016] – direction sampling, path termination and splitting (surfaces)
  • [Herholz et al., conditional accept] – all decisions (volumes)
  • Analytic solution
  • [Křivánek and d’Eon 2014] – subsurface scattering
slide-5
SLIDE 5

VOLUME PATH GUIDING

slide-6
SLIDE 6

Surfac face e path h guidin ding g – Online learning of parametric mixture models

[Vorba et al. 2014]

slide-7
SLIDE 7

Volume path guiding

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • All events importance sampled
  • Product sampling for collision distance
slide-8
SLIDE 8

Reference​

slide-9
SLIDE 9

Standard sampling 30 min in

slide-10
SLIDE 10

New volu lume path gu guiding 30 min in

slide-11
SLIDE 11

Dis

  • ist. + dir
  • ir. gu

guiding Standard sampling RR + split litting SPP: : 15 1580 relM lMSE: 6.4 .458 SPP: : 1 1288 relM lMSE: 1 1.354 SPP: : 1 1660 relM lMSE: 0 0.401

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-12
SLIDE 12

Reference

slide-13
SLIDE 13

Standard sampling 45 min in

slide-14
SLIDE 14

New volu lumetric path gu guiding 45 min in

slide-15
SLIDE 15

Dis

  • ist. + dir
  • ir. gu

guiding Standard sampling RR + split litting SPP: : 79 796 relM lMSE: 1.7 .725 SPP: : 3 392 relM lMSE: 0.7 .747 SPP: : 1 1068 relM lMSE: 0.1 .123

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-16
SLIDE 16

ZV-BASED SUBSURFACE SCATTERING

with Eugene d’Eon

slide-17
SLIDE 17

image courtesy Eugene d’Eon

slide-18
SLIDE 18
slide-19
SLIDE 19

Classical random walk

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Tends to get lost in the medium
slide-20
SLIDE 20

Goal

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Guide paths toward the boundary
slide-21
SLIDE 21

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-22
SLIDE 22

Previous work in neutron transport

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Reactor shield design
  • One in a billion particles makes it through

concrete slab (reactor shield) incident radiation transmitted radiation

slide-23
SLIDE 23

Previous work in neutron transport

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Path stretching [Clark ’66, Ponti ‘71, Spanier ‘71]

incident radiation transmitted radiation

slide-24
SLIDE 24

Zero-variance random walk theory

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • [Dwivedi ‘81]
  • Optimal path stretching
  • Idea: If you approximate the solution, you can use this to guide sampling
  • Specific application of the zero variance-based sampling
slide-25
SLIDE 25

Setup

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • (Unidirectional) path tracing
slide-26
SLIDE 26

Assumptions

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Flat, semi-infinite medium
  • Uniform, white-sky illumination

x 

slide-27
SLIDE 27

Analytical radiance solution

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Case’s singular eigenfunctions

[Case 1960, McCormick and Kuscer 1973]

/ 1 1 /

) , ( ) , ( ) , (

v x v x

e v dv e v x L

  

        x 

transient terms asymptotic term

Singular eigenfunctions

slide-28
SLIDE 28

Approximate solution

  • Drop transient terms

/ 1 1 /

) , ( ) , ( ) , (

v x v x

e v dv e v x L

  

        x 

asymptotic term

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-29
SLIDE 29

Approximate solution

  • Only the asymptotic term

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

albedo = 0.95

solution depth x

albedo = 0.2

depth x

slide-30
SLIDE 30

) / 1 ( ' ) ' exp( ) / exp( ) exp( ) ( v s v x s s p             

Distance sampling

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

x 

transmittance solution

s

path stretching!

slide-31
SLIDE 31

    ) ( v v p

Directional distribution

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-32
SLIDE 32

Directional distribution

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

albedo = 0.95 albedo = 0.2

direction cos (µ) direction cos (µ)

up down up down

    ) ( v v p

slide-33
SLIDE 33

Semi-infinite half-space test

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

albedo 0.4 0.8 0.95 Dwivedi sampling classical sampling

slide-34
SLIDE 34

Semi-infinite half-space test

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

Dwivedi sampling classical sampling albedo 0.4 0.8 0.95

0.132 0.025 (5.3×) variance variance 0.093 0.034 (2.7×) 0.020 0.020 (1×)

slide-35
SLIDE 35

Use in rendering

slide-36
SLIDE 36

Use in rendering – IBL

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

sampling + 25% “analog” equal-time comparison, 100 samples per pixel, MIS 25% classical + 75% Dwivedi Dwivedi sampling classical sampling Dwivedi sampling classical sampling

slide-37
SLIDE 37

Better application to rendering

  • [Meng et al. 2016]

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-38
SLIDE 38
slide-39
SLIDE 39

CAN WE DO BETTER?

slide-40
SLIDE 40

Exponential radiance falloff

  • … does not hold for low scattering

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

albedo=0.95 albedo = 0.2

slide-41
SLIDE 41

Directional distribution

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

Dwivedi boundary-aware

slide-42
SLIDE 42

Radiance distribution

42

albedo=0.95

Dwivedi Reference Difference

dir depth

albedo = 0.2

Dwivedi Reference Difference

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-43
SLIDE 43

Improved sampling

  • Take boundary into account
  • Better radiance approximation
  • Matching 1st and 2nd moments of the true solution

43 MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-44
SLIDE 44

Semi-infinite half-space test

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

Dwivedi sampling classical sampling albedo 0.4 0.8 0.95

0.132 0.025 (5.3×) variance variance 0.093 0.034 (2.7×) 0.020 0.020 (1×)

improved scheme

variance .001 (132×) .0008 (116×) .0002 (100×)

slide-45
SLIDE 45

Future work

  • Boundary (Fresnel, rough)
  • Anisotropic scattering

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-46
SLIDE 46

Conclusion

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Zero variance schemes – solid framework for variance reduction
  • Requires (approximate) solution
  • Learning from MC samples (Machine/statistical learning techniques)
  • Analytical approximation
slide-47
SLIDE 47

Thank you

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

  • Acknowledgments
  • Czech Science Foundation (16-18964S)
  • EU ITN No 642841 – “DISTRO”

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642841.

slide-48
SLIDE 48

BACKUP SLIDES

slide-49
SLIDE 49

Dis istance Dir irection Dir

  • ir. + Dis

ist. +ADRRS

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-50
SLIDE 50

Dis

  • ist. + dir
  • ir. gu

guiding Standard sampling RR + split litting SPP: : 79 796 relM lMSE: 1.7 .725 SPP: : 3 392 relM lMSE: 0.7 .747 SPP: : 1 1068 relM lMSE: 0.1 .123

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)

slide-51
SLIDE 51

Application to rendering

MC METHODS FOR VOLUMETRIC LIGHT TRANSPORT – ZERO VARIANCE-BASED SAMPLING SCHEKEMS (A.K.A. PATH GUIDING)