Quantifying the Error of Light Transport Algorithms Adam Celarek, - - PowerPoint PPT Presentation

▶
quantifying the error of light transport algorithms
SMART_READER_LITE
LIVE PREVIEW

Quantifying the Error of Light Transport Algorithms Adam Celarek, - - PowerPoint PPT Presentation

Sep 22, 2023 316 likes •719 views

Quantifying the Error of Light Transport Algorithms Adam Celarek, Wenzel Jakob Michael Wimmer, Jaakko Lehtinen TU Wien, Aalto University (Helsinki), ETH Zrich EGSR 2019 EUROGRAPHICS SYMPOSIUM ON RENDERING ///// Motivation

slide-1
SLIDE 1

Quantifying the Error of Light Transport Algorithms

Adam Celarek¹², Wenzel Jakob³ Michael Wimmer¹, Jaakko Lehtinen²

¹TU Wien, ²Aalto University (Helsinki), ³ETH Zürich

EGSR

2019

EUROGRAPHICS SYMPOSIUM ON RENDERING /////

slide-2
SLIDE 2

2/32

Motivation

MLT PT

slide-3
SLIDE 3

3/32

Motivation

MLT PT

slide-4
SLIDE 4

4/32

Motivation

MLT PT

slide-5
SLIDE 5

5/32

Motivation

MLT PT

slide-6
SLIDE 6

6/32

Motivation / State of the Art

  • Renderings and details

A B C PT MLT

A C B

slide-7
SLIDE 7

7/32

Motivation / State of the Art

  • Renderings and details
  • Error, for instance

abs (R – I)

1.5 3

MLT PT

slide-8
SLIDE 8

8/32

Motivation / State of the Art

  • Renderings and details
  • Error, for instance

abs (R – I)

  • Simple error metrics like

MSE or friends Torus 5 min. PT MLT MSE

0.00213 0.00278

RMSE

0.00462 0.00528

Relative

MSE

0.1077 0.1446

Relative

RMSE

0.3282 0.3802

PSNR

74.83 73.68

slide-9
SLIDE 9

9/32

Motivation / Closer Look at MSE

  • Render for some time, e.g., 1 hour
  • Compute MSE using a high quality reference
slide-10
SLIDE 10

10/32

Motivation / Closer Look at MSE

  • Render for some time,

e.g., 5 minutes

  • Compute MSE using a

high quality reference

  • MSE depends on N, but

does not converge

100 102 104 106

N MSE

closed form E(MSE) MSE

slide-11
SLIDE 11

11/32

Motivation / Closer Look at MSE

  • Render for some time,

e.g., 5 minutes

  • Compute MSE using a

high quality reference

  • MSE depends on N, but

does not converge

cpu time (t) MSE

102 104 106 10-4 10-2 100 102

MLT BDPT

slide-12
SLIDE 12

12/32

Motivation / Goals

  • Convergence with N
  • Notion of how reliable for a given instance
  • Behaviour: frequency content and outliers
slide-13
SLIDE 13

13/32

Proxy Algorithm

  • riginal

vs.

proxy short renders

1 . . . N

slide-14
SLIDE 14

14/32

Proxy Algorithm

  • Estimate E(MSE)

– old – new

100 102 104 106

N MSE

closed form E(MSE)

  • ld method

new method

slide-15
SLIDE 15

15/32

Proxy Algorithm

  • Estimate E(MSE)
  • Estimate per-pixel

standard deviation

slide-16
SLIDE 16

16/32

Proxy Algorithm

  • Estimate E(MSE)
  • Estimate per-pixel standard

deviation

  • Behaviour / frequency

content of error and outliers via short renderings

slide-17
SLIDE 17

17/32

Error Spectrum Ensemble (ESE)

1 . . . N 1 . . . N

Example algorithm (MLT) (RMSE:6.86, s:5.7, t:10x1.9s) mean 00-100 mean 90-100 mean 80-90 mean 50-80 mean 20-50 mean 10-20 mean 00-10

50 100 150 200 250 frequency

tails body head ensemble mean

N=400 50 100 150 200 250 frequency

a) Error images b) error power spectra c) radial averages and percentile means d) Error Spectrum Ensemble

slide-18
SLIDE 18

Error Spectrum Ensemble (ESE)

1 . . . N

a) Error images

50 10

c) radial percen b) error power spectra

1 . . . N

slide-19
SLIDE 19

Error Spectrum Ensemble (ESE)

mean 00-100 mean 90-100 mean 80-90 mean 50-80 mean 20-50 mean 10-20 mean 00-10

50 100 150 200 250 frequency

c) radial averages and percentile means

Example algorithm (MLT) (RMSE:6.86, s:5.7, t:10x1.9s) tails body head ensemble mean

N=400 50 100 150 200 250 frequency

d) Error Spectrum Ensemble b) error power spectra

1 . . . N

slide-20
SLIDE 20

20/32

Error Spectrum Ensemble (ESE)

mean 00-100 mean 90-100 mean 80-90 mean 50-80 mean 20-50 mean 10-20 mean 00-10

50 100 150 200 250 frequency

c) radial averages and percentile means

Example algorithm (MLT) (RMSE:6.86, s:5.7, t:10x1.9s) tails body head ensemble mean

N=400 50 100 150 200 250 frequency

d) Error Spectrum Ensemble

slide-21
SLIDE 21

21/32

Example / Bathroom

slide-22
SLIDE 22

22/32

Example / Bathroom

MLT PT

slide-23
SLIDE 23

23/32

Example / Bathroom

MLT PT

slide-24
SLIDE 24

24/32

Example / Bathroom

MLT PT

slide-25
SLIDE 25

25/32

Example / Bathroom

MLT PT

slide-26
SLIDE 26

26/32

Example / Bathroom

N=4000

50 100 150 200 250

frequency

108 1010

error

PT (RMSE:11.9) MEMLT (RMSE:7.19)

slide-27
SLIDE 27

27/32

Example / Bottle

N=4000

50 100 150 200 250

frequency

106 107 108 109

error

PT (RMSE:4.7) MEMLT (RMSE:32.4)

slide-28
SLIDE 28

28/32

Example / Bottle

MLT PT

slide-29
SLIDE 29

29/32

Example / Bottle

MLT

slide-30
SLIDE 30

30/32

Conclusion / Summary

slide-31
SLIDE 31

31/32

Conclusion / Limitations und Future Work

Limitations:

  • Proxy algorithm limits convergence rate based on CLT
  • High complexity compared to scalar metrics like MSE
  • Computation cost (short renderings + 10s of minutes)

Future work:

  • Local pixel correlation
  • Convergence of biased but consistent algorithms
slide-32
SLIDE 32

32/32

End / Questions

slide-33
SLIDE 33

33/32

Breaking up of MLT chains (Veach Door)

slide-34
SLIDE 34

34/32

Changing PSSMLT Parameters (Box / large mutations)

slide-35
SLIDE 35

35/32

Changing PSSMLT Parameters (Box / small mutations)

slide-36
SLIDE 36

36/32

Smaller N of short renderings (Torus)

N=40

50 100 150 200 250

frequency

106 108

error

PT (RMSE:1.54, s:0.0486, t:19x0.538s) MEMLT (RMSE:1.24, s:0.738, t:12x0.914s)

N=400

50 100 150 200 250

frequency

106 108

error

PT (RMSE:1.56, s:0.0489, t:19x0.538s) MEMLT (RMSE:2.17, s:1.85, t:12x0.914s)

N=4000

50 100 150 200 250

frequency

106 108

error

PT (RMSE:1.56, s:0.0496, t:19x0.538s) MEMLT (RMSE:2.24, s:1.91, t:12x0.914s)

slide-37
SLIDE 37

37/32

Smaller N of short renderings (Bottle)

N=4000

50 100 150 200 250

frequency

106 107 108 109

error

PT (RMSE:4.7, s:1.89, t:5x2.06s) MEMLT (RMSE:32.4, s:32, t:10x1.11s)

N=40

50 100 150 200 250

frequency

106 108 1010

error

PT (RMSE:4.66, s:1.93, t:5x2.06s) MEMLT (RMSE:51.8, s:49.8, t:10x1.11s)

N=400

50 100 150 200 250

frequency

106 107 108 109

error

PT (RMSE:4.76, s:1.92, t:5x2.06s) MEMLT (RMSE:21.6, s:21.3, t:10x1.11s)

slide-38
SLIDE 38

38/32

Biased but consistent algorithm