• No results found

An Improved Multiple Importance Sampling Heuristic for Density Estimates in Light Transport Simulations

N/A
N/A
Info
Nedlasting
Protected

Academic year: 2022

Share "An Improved Multiple Importance Sampling Heuristic for Density Estimates in Light Transport Simulations"

Copied!
10
0
0

Laster.... (Se fulltekst nå)

Last ned nå ( 10 sider )

Fulltekst

(1)Eurographics Symposium on Rendering - Experimental Ideas & Implementations (2018) T. Hachisuka and W. Jakob (Editors). An Improved Multiple Importance Sampling Heuristic for Density Estimates in Light Transport Simulations Supplemental: Visual Comparison J. Jendersie and T. Grosch TU Clausthal, Germany. This document contains additional non-cropped full resolution images for visual convergence comparison. Please zoom in to view the full resolution. Also, it provides further curves using even more error metrics: v u N u1 RMSE := t ∑(xi − ri )2 , N i v u N u1 RMSLE := t ∑(log(1 + ri ) − log(1 + xi ))2 , N i v u N 2 u1 xi − ri SRRMSE := t ∑ N i (xi + ri )/2 (2µ µ +C1 )(2σxri +C2 ) , SSIM := 2 xi 2 ri (µxi + µri +C1 )(σ2xi + σ2ri +C2 ) and SMAPE :=. 1 N. N. ∑2 i. ri − xi ri + xi. From those RMSE, SRRMSE and SSIM [WBSS04] are contained in the paper too. Again N is the number of pixels (times the color channels), ri is the reference value, xi the current image value and µxi , µri , σxi , σri , σxri are local image statistics from a small neighborhood of pixels. RMSE is the most commonly used criteria. However, it penalizes errors in bright regions stronger. Thus, it happens that a single firefly or aliasing difference in a bright region dominate the entire error. RMSLE and SRRMSE both fix this issue by applying the logarithm before comparing the image and by using a relative scaling respectively. Both can be justified by perception. First, our perception is more logarithmic than linear. Second, we have a relative threshold for the just noticeable difference (Weber-Fechner Law). Therefore, both correlate stronger with the visual comparison. SSIM is designed to be the perceived error. By using statistics it penalizes kinds of errors differently. A constant over- or underillumination is not as bad as discontinuity artifacts or noise. Compared to RMSLE and SRRMSE it shows similar characteristic in the c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association.. comparison below. However, crossover points, at which the qualityorder of methods change, move towards higher iterations. Start Radius for Photon Queries We have chosen the initial photon query radius manually for each scene to provide the best looking results for any of the VCM methods. Smaller radii would increase the noise and hence variance whereas larger radii would blur stronger. In any case, our change of pacc is still meaningful. Invalid decisions, as in the teaser or the double merge scene, will also appear for different radii. How To Use this Document This document uses interactive layers to make pixel-by-pixel comparisons of the methods possible. According to the documentation of the LATEX-OCGX package, this is compatible with Acrobat Reader, Foxit Reader, PDF-XChange-Viewer and Evince. The builtin Windows-Reader, SumatraPDF and the usual Browser-Plugins do not work. For other viewers it might be possible to manually show/hide layers, if the buttons do not work. Also, to switch between layers if zoomed in and if buttons are outside the current view, please use the viewer’s layer switching capabilities. References [PJH17] P HARR M., JAKOB W., H UMPHREYS G.: Physically Based Rendering: From Theory to Implementation, 3 ed. Morgan Kaufmann, 2017. URL: http://www.pbrt.org/. 4, 5, 7, 10 [Vev18] V EVODA P.: Small UPBP Repository, 2018. URL: https://github.com/PetrVevoda/smallupbp/tree/ master/scenes/mirrorballs. 9 [WBSS04] WANG Z., B OVIK A. C., S HEIKH H. R., S IMONCELLI E. P.: Image Quality Assessment: from Error Visibility to Structural Similarity. IEEE Transactions on Image Processing (TIP) 13, 4 (2004), 600–612. URL: https://doi.org/10.1109/TIP.2003.819861. 1.

(2) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. RMSLE. SRRMSE. 40. SSIM. 0.3. 1. BPT VCM VCM+. 30. 1. 0.8. 0.2. VCM*. 20. 0.6 0.1. 10 0 0. 10. 10. 1. 2. 10 BPT. 3. 10. 0.5 0.4. 10. 1. 10. 2. 10. 10. 3. 0.2. 0. 0 0. 0. 10. VCM. 1. 10. 10. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 2. 3. 10. 0. 10. 1. 10. 10. 2. 103 ]it. VCM*. Figure 1: Spheres: 1000x400 pixels, 4 point lights, 1 weak area light. BPT is not even close to convergence, the original VCM still contains salt noise but looks close to the final result wheres our method handles each light situation in the scene robustly. This is consistent with the error metrics in which our methods performs best in all cases.. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(3) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. RMSLE. SRRMSE. SSIM 0.4. BPT VCM. 0.4. 0.8. 0.1. 0.3. VCM+. 0.6. VCM*. 0.2 0.2. 0.4. 5 · 10−2 0.1. 100. 101. 102. 0 103. 100. BPT. 101. 102. 0 103. 100. VCM. 101. 102. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 0 103. 0.2 100. 101. 102. 0 103 ]it. VCM*. Figure 2: Ring: 500x500 pixels, 1 point light. BPT misses reflected caustics. In this scene VCM+ improves the convergence on the diffuse surface and reduces the bias in the caustics compared to standard VCM and VCM*. VCM* performs the same as VCM.. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(4) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. RMSLE. SRRMSE. SSIM 1. 0.2. BPT VCM VCM+. 0.4. 1. VCM*. 0.5. 0.1. 0.5. 0.2. 0. 10. 10. 1. 2. 10. 0 103. 0. 0 0. 10. BPT. 1. 10. 2. 10. 10. 3. 0. 10. VCM. 1. 10. 10. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 2. 103. 100. 101. 102. 0 103 ]it. VCM*. Figure 3: Veach-Bidir from PBRT-v3 [PJH17]: 512x512 pixels, 2 areal lights. The cylinder on the left has again the problem of hard too reach geometry close to the light source leading to more noise in standard VCM than in our variants.. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(5) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. RMSLE BPT. SRRMSE. 6. SSIM 1. 1.5. 0.3. VCM. 0.8. VCM+ VCM*. 100. 101. 102. 4. 1. 0.2. 0.6. 2. 0.1. 0.5. 0. 0. 0. 0.4 0.2. 103. 100. BPT. 101. 102. 103. 100. VCM. 101. 102. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 103. 100. 101. 102. 103 ]it. VCM*. Figure 4: Contemporary Bathroom from PBRT-v3 [PJH17], (Courtesy of Mareck): 1024x1024 pixels. All VCM variants are very similar and better than BPT. VCM* has the smallest error for most of the time. The reason why VCM is better than VCM* at the end is that VCM* choses merges on the infacing roller blind sides instead on outfacing ones. Due to light-bleeding within the gathering radius these have a higher bias. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(6) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. RMSLE BPT. SRRMSE. 0.3. 0.15. 0.2. 0.1. 0.1. −2. SSIM 1. 1. VCM VCM+ VCM*. 0.8 0.5. 5 · 10. 0 0. 10. 10. 1. 2. 10 BPT. 3. 10. 0.6 0. 0. 10. 1. 10. 2. 10. 10. 3. 0 0. 10. VCM. 1. 10. 10. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 2. 103. 100. 101. 102. 103 ]it. VCM*. Figure 5: Bunnyduck: 1024x768 pixels. VCM* is slightly worse than VCM, because the density of photons is overestimated. See the early iterations on the glass cube front face: (refractive) merges on this face are penalized due to high density from direct lighting of the second light source. VCM+ has higher frequency noise and looks subjectively better.. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(7) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. RMSLE. SRRMSE. SSIM. 0.3 VCM VCM+ VCM*. 1. 1.5. BPT. 0.1. 0.2. 0.8. 1. 0.6. 5 · 10−2. 0.1. 0.5 0.4. 100. 101. 102. 0 103. 0 100. BPT. 101. 102. 103. 100. VCM. 101. 102. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 0 103. 100. 101. 102. 103 ]it. VCM*. Figure 6: Villa from PBRT-v3 [PJH17]: 1024x768 pixels. Robust in all methods. However, VCM shows some more fireflies (e.g. see center, 256spp, front left area; or the ceiling in less than 256spp images).. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(8) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. RMSLE. SRRMSE. SSIM 2. VCM VCM+. 1. 0.1. BPT. 1. 1.5. 0.8. 1. 0.6. VCM*. 5 · 10−2. 0.5. 0 100. 101. 102. 103. 0 100. BPT. 101. 102. 103. 0.4. 0.5 100. VCM. 101. 102. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 103. 100. 101. 102. 103 ]it. VCM*. Figure 7: Spheres with diffuse cylinder and max. path length of 3: 460x500 pixels. BPT and VCM+ win in RMSE, because the error is dominated by bias. VCM+ and VCM* clearly show their improved handling of the double-merge case over standard VCM. On the long run VCM* gets the best score in any measurement.. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(9) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. RMSLE. SRRMSE. SSIM 1. 150 BPT VCM+ VCM*. 1. 0.15. VCM. 0.8. 100 0.6. 0.1 0.5. 50. 0.4. 5 · 10−2. 0.2. 0 100. 101. 102. 0. 103. 100. BPT. 101. 102. 103. 100. VCM. 101. 102. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 103. 100. 101. 102. 103 ]it. VCM*. Figure 8: Mirrorballs Courtesy of Toshya Hachisuka (taken from [Vev18]): 1024x1024 pixels. VCM and VCM* perform almost the same whereas BPT misses reflected caustics again. The small difference in SSIM is again due to higher noise in VCM (see dark floor areas).. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(10) J. Jendersie & T. Grosch / An Improved MIS for Density Estimates – Supplemental. RMSE. ·10−2. RMSLE BPT VCM. SSIM 1. 1. 6. 0.8. 0.95. 4. 0.6. 2. 0.4. 8. 0.15. VCM+ VCM*. SRRMSE. 0.1 0.9. −2. 5 · 10. 0 100. 101. 102 BPT. 103. 0 100. 101. 102. 103. 100. VCM. 101. 102. VCM+. 1 spp. 4 spp. 16 spp. 64 spp. 256 spp. 1024 spp. 0.2 103. 0.85 100. 101. 102. 103 ]it. VCM*. Figure 9: Dragon from PBRT-v3 [PJH17] (Courtesy of Christian Schüller): 800x600 pixels. VCM+ produces less bias than standard VCM/VCM* (see shadow border). VCM/VCM* behave the same in this scene.. c 2018 The Author(s) Eurographics Proceedings c 2018 The Eurographics Association..

(11)

Referanser

Last ned nå ( PDF - 10 sider - 81.04 MB )

RELATERTE DOKUMENTER

Improved Indirect Photon Mapping withWeighted Importance Sampling

In the classic indirect photon mapping algorithm, we solve the radiance equation for a pixel using multi-dimensional samples, or light paths, generated using the shooting walk

Path Integration for Light Transport in Volumes

Once the most important path is found, the multiple scattering contributions are only computed along the most probable paths and the rest of the paths are dealt with implic- itly

Two Stage Importance Sampling for Direct Lighting

This partition, along with a summed area table of the light source, form an approximation to the product function that is suitable for importance sampling.. The partition is used

Statistical Acquisition of Texture Appearance

Figure 8: Comparing different sampling density of light di- rections: (a) Direct interpolation of 13 × 13 (view × light) textures from Bonn data, (b) Our reconstruction with 13

References 1

Shadow Maps: Efficient Sampling of Light Source Visibility... J.: Teaching, exploring, learning - developing tutorials for

Path Sampling Techniques for Efficient Light Transport Simulation

We incorporated our tabulated bidirectional sampling techniques into a many-light renderer. is renderer generates random-walk subpaths from the lights with transmittance and

Adjoint-Driven Importance Sampling in Light Transport Simulation

Also in large scenes, when light particles (photons) cannot find the camera, all the strategies based on light sub-paths make almost no contribution and bidirectional algorithms

An Improved Multiple Importance Sampling Heuristic for Density Estimates in Light Transport Simulations

While the VCM heuristic is correct for single path merges with- out reuse, it fails for some cases once we merge with multiple light paths.. For an example see Figure 2, in which