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

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 /////

Motivation PT MLT 2/32

Motivation PT MLT 3/32

Motivation PT MLT 4/32

Motivation PT MLT 5/32

Motivation / State of the Art ● Renderings and details PT MLT A A B B C C 6/32

Motivation / State of the Art PT 3 ● Renderings and details ● Error, for instance abs (R – I) MLT 1.5 0 7/32

Motivation / State of the Art ● Renderings and details Torus PT MLT 5 min. ● Error, for instance MSE 0.00213 0.00278 abs (R – I) RMSE 0.00462 0.00528 ● Simple error metrics like Relative MSE or friends 0.1077 0.1446 MSE Relative 0.3282 0.3802 RMSE PSNR 74.83 73.68 8/32

Motivation / Closer Look at MSE ● Render for some time, e.g., 1 hour ● Compute MSE using a high quality reference 9/32

Motivation / Closer Look at MSE ● Render for some time, closed form E(MSE) MSE e.g., 5 minutes ● Compute MSE using a MSE high quality reference ● MSE depends on N, but does not converge 10 0 10 2 10 4 10 6 N 10/32

Motivation / Closer Look at MSE 10 2 ● Render for some time, e.g., 5 minutes 10 0 MSE ● Compute MSE using a 10 -2 high quality reference ● MSE depends on N, but 10 -4 10 2 10 4 10 6 does not converge cpu time (t) MLT BDPT 11/32

Motivation / Goals ● Convergence with N ● Notion of how reliable for a given instance ● Behaviour: frequency content and outliers 12/32

Proxy Algorithm original proxy short renders vs. 1 . . . N 13/32

Proxy Algorithm closed form E(MSE) ● Estimate E(MSE) old method new method – old MSE – new 10 0 10 2 10 4 10 6 N 14/32

Proxy Algorithm ● Estimate E(MSE) ● Estimate per-pixel standard deviation 15/32

Proxy Algorithm ● Estimate E(MSE) ● Estimate per-pixel standard deviation ● Behaviour / frequency content of error and outliers via short renderings 16/32

Error Spectrum Ensemble (ESE) a) Error images mean 00-100 Example algorithm (MLT) mean 90-100 (RMSE:6.86, s:5.7, t:10x1.9s) mean 80-90 1 mean 50-80 . . . tails mean 20-50 mean 10-20 body N mean 00-10 head ensemble mean 1 . . . 0 50 100 150 200 250 0 50 100 150 200 250 N frequency N=400 frequency b) error power c) radial averages and d) Error Spectrum Ensemble spectra percentile means 17/32

Error Spectrum Ensemble (ESE) 1 1 . . . . . . N N b) error power a) Error images spectra 0 50 10 c) radial percen

Error Spectrum Ensemble (ESE) mean 00-100 Example algorithm (MLT) mean 90-100 (RMSE:6.86, s:5.7, t:10x1.9s) mean 80-90 mean 50-80 mean 20-50 tails mean 10-20 body mean 00-10 head 1 . ensemble mean . . N b) error power spectra 0 50 100 150 200 250 0 50 100 150 200 250 frequency frequency N=400 c) radial averages and d) Error Spectrum Ensemble percentile means

Error Spectrum Ensemble (ESE) mean 00-100 Example algorithm (MLT) mean 90-100 (RMSE:6.86, s:5.7, t:10x1.9s) mean 80-90 mean 50-80 mean 20-50 tails mean 10-20 body mean 00-10 head ensemble mean 0 50 100 150 200 250 0 50 100 150 200 250 frequency frequency N=400 c) radial averages and d) Error Spectrum Ensemble 20/32 percentile means

Example / Bathroom 21/32

Example / Bathroom PT MLT 22/32

Example / Bathroom PT MLT 23/32

Example / Bathroom PT MLT 24/32

Example / Bathroom PT MLT 25/32

Example / Bathroom 10 10 error 10 8 0 50 100 150 200 250 N=4000 frequency PT (RMSE:11.9) MEMLT (RMSE:7.19) 26/32

Example / Bottle 10 9 error 10 8 10 7 10 6 0 50 100 150 200 250 N=4000 frequency PT (RMSE:4.7) MEMLT (RMSE:32.4) 27/32

Example / Bottle PT MLT 28/32

Example / Bottle MLT 29/32

Conclusion / Summary 30/32

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 31/32

End / Questions 32/32

Breaking up of MLT chains (Veach Door) 33/32

Changing PSSMLT Parameters (Box / large mutations) 34/32

Changing PSSMLT Parameters (Box / small mutations) 35/32

Smaller N of short renderings (Torus) 10 8 10 8 error error 10 6 10 6 0 50 100 150 200 250 0 50 100 150 200 250 N=40 N=400 frequency frequency PT (RMSE:1.54, s:0.0486, t:19x0.538s) PT (RMSE:1.56, s:0.0489, t:19x0.538s) MEMLT (RMSE:1.24, s:0.738, t:12x0.914s) MEMLT (RMSE:2.17, s:1.85, t:12x0.914s) 10 8 error 10 6 0 50 100 150 200 250 N=4000 frequency 36/32 PT (RMSE:1.56, s:0.0496, t:19x0.538s) MEMLT (RMSE:2.24, s:1.91, t:12x0.914s)

Smaller N of short renderings (Bottle) 10 10 10 9 error error 10 8 10 8 10 7 10 6 10 6 0 50 100 150 200 250 0 50 100 150 200 250 N=40 frequency N=400 frequency PT (RMSE:4.66, s:1.93, t:5x2.06s) PT (RMSE:4.76, s:1.92, t:5x2.06s) MEMLT (RMSE:51.8, s:49.8, t:10x1.11s) MEMLT (RMSE:21.6, s:21.3, t:10x1.11s) 10 9 error 10 8 10 7 10 6 0 50 100 150 200 250 N=4000 frequency 37/32 PT (RMSE:4.7, s:1.89, t:5x2.06s) MEMLT (RMSE:32.4, s:32, t:10x1.11s)

Biased but consistent algorithm 38/32