Skip to main content
SpringerLink
Log in

Adaptive rendering based on robust principal component analysis

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

We propose an adaptive sampling and reconstruction method based on the robust principal component analysis (PCA) to denoise Monte Carlo renderings. Addressing spike noise is a challenging problem in adaptive rendering methods. We adopt the robust PCA as a pre-processing step to efficiently decompose spike noise from rendered image after the image space is sampled. Then we leverage patch-based propagation filter for feature prefiltering and apply the robust PCA to reduce dimensionality in high-dimensional feature space. After that, we estimate a per-pixel pilot bandwidth derived from kernel density estimation and construct the multivariate local linear estimator in the reduced feature space to estimate the value of each pixel. Finally, we distribute additional ray samples in the regions with higher estimated mean squared error if sampling budget remains. We demonstrate that our method makes significant improvement in terms of both numerical error and visual quality compared to the state-of-the-art.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Belcour, L., Soler, C., Subr, K., Holzschuch, N., Durand, F.: 5D covariance tracing for efficient defocus and motion blur. ACM Trans. Gr. 32(3), 31:1–31:18 (2013)

    Article  MATH  Google Scholar 

  2. Bitterli, B., Rousselle, F., Moon, B., Guitián, J.A.I., Adler, D., Mitchell, K., Jarosz, W., Novák, J.: Nonlinearly weighted first-order regression for denoising monte carlo renderings. Comput. Graph. Forum 35(4), 107–117 (2016)

    Article  Google Scholar 

  3. Chang, J.H.R., Wang, Y.C.F.: Propagated image filtering. In: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10–18 (2015)

  4. Cheng, M.Y., Peng, L.: Simple and efficient improvements of multivariate local linear regression. J. Multivar. Anal. 97(7), 1501–1524 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dabov, K., Foi, A., Egiazarian, K.: Video denoising by sparse 3D transform-domain collaborative filtering. In: Signal Processing Conference, 2007 15th European, pp. 145–149 (2007)

  6. DeCoro, C., Weyrich, T., Rusinkiewicz, S.: Density-based outlier rejection in Monte Carlo rendering. Comput. Gr. Forum 29(7), 2119–2125 (2010)

    Article  Google Scholar 

  7. Delbracio, M., Musé, P., Buades, A., Chauvier, J., Phelps, N., Morel, J.M.: Boosting Monte Carlo rendering by ray histogram fusion. ACM Trans. Gr. 33(1), 8:1–8:15 (2014)

    Article  MATH  Google Scholar 

  8. Donoho, D.L., Johnstone, I.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3), 425–455 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. Farrugia, J.P., Peroche, B.: A progressive rendering algorithm using an adaptive perceptually based image metric. Comput. Gr. Forum 23(3), 605–614 (2004)

    Article  Google Scholar 

  10. Hachisuka, T., Jarosz, W., Weistroffer, R.P., Dale, K., Humphreys, G., Zwicker, M., Jensen, H.W.: Multidimensional adaptive sampling and reconstruction for ray tracing. In: ACM SIGGRAPH 2008 Papers, SIGGRAPH ’08, pp. 33:1–33:10. ACM, New York (2008)

  11. Kajiya, J.T.: The rendering equation. In: Proceedings of the 13th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’86, pp. 143–150. ACM, New York (1986)

  12. Kalantari, N.K., Bako, S., Sen, P.: A machine learning approach for filtering Monte Carlo noise. ACM Trans. Gr. 34(4), 122:1–122:12 (2015)

    Article  Google Scholar 

  13. Kalantari, N.K., Sen, P.: Removing the noise in Monte Carlo rendering with general image denoising algorithms. Comput. Gr. Forum (Proc. Eurogr. 2013) 32(2), 93–102 (2013)

    Article  Google Scholar 

  14. Kristan, M., Leonardis, A., Skočaj, D.: Multivariate online kernel density estimation with Gaussian kernels. Pattern Recogn. 44(10–11), 2630–2642 (2011)

    Article  MATH  Google Scholar 

  15. Li, T.M., Wu, Y.T., Chuang, Y.Y.: SURE-based optimization for adaptive sampling and reconstruction. ACM Trans. Gr. 31(6), 194:1–194:9 (2012)

    Google Scholar 

  16. Lin, Z., Chen, M., Ma, Y.: The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. ArXiv e-prints (2010)

  17. Liu, X., Zheng, C.: Parallel adaptive sampling and reconstruction using multi-scale and directional analysis. Vis. Comput. 29(6–8), 501–511 (2013)

    Article  Google Scholar 

  18. Liu, X., Zheng, C.: Adaptive cluster rendering via regression analysis. Vis. Comput. 31(1), 105–114 (2015)

    Article  Google Scholar 

  19. Liu, X.D., Wu, J.Z., Zheng, C.W.: Kd-tree based parallel adaptive rendering. Vis. Comput. 28(6–8), 613–623 (2012)

    Article  Google Scholar 

  20. Mitchell, D.P.: Generating antialiased images at low sampling densities. In: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’87, pp. 65–72. ACM, New York (1987)

  21. Moon, B., Carr, N., Yoon, S.E.: Adaptive rendering based on weighted local regression. ACM Trans. Gr. 33(5), 170:1–170:14 (2014)

    Article  Google Scholar 

  22. Moon, B., Iglesias-Guitian, J.A., Yoon, S.E., Mitchell, K.: Adaptive rendering with linear predictions. ACM Trans. Gr. 34(4), 121:1–121:11 (2015)

    Article  Google Scholar 

  23. Moon, B., McDonagh, S., Mitchell, K., Gross, M.: Adaptive polynomial rendering. ACM Trans. Gr. 35(4), 40:1–40:10 (2016)

    Article  Google Scholar 

  24. Overbeck, R.S., Donner, C., Ramamoorthi, R.: Adaptive wavelet rendering. In: ACM SIGGRAPH Asia 2009 Papers, SIGGRAPH Asia ’09, pp. 140:1–140:12. ACM, New York (2009)

  25. Pharr, M., Humphreys, G.: Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann Publishers Inc., San Francisco (2010)

    Google Scholar 

  26. Rigau, J., Feixas, M., Sbert, M.: Refinement criteria based on f-divergences. In: Proceedings of the 14th Eurographics Workshop on Rendering, EGRW ’03, pp. 260–269. Eurographics Association, Aire-la-Ville (2003)

  27. Rousselle, F., Knaus, C., Zwicker, M.: Adaptive sampling and reconstruction using greedy error minimization. ACM Trans. Gr. 30(6), 159:1–159:12 (2011)

    Article  Google Scholar 

  28. Rousselle, F., Knaus, C., Zwicker, M.: Adaptive rendering with non-local means filtering. ACM Trans. Gr. 31(6), 195:1–195:11 (2012)

    Article  Google Scholar 

  29. Rousselle, F., Manzi, M., Zwicker, M.: Robust denoising using feature and color information. Comput. Gr. Forum 32(7), 121–130 (2013)

    Article  Google Scholar 

  30. Sen, P., Darabi, S.: On filtering the noise from the random parameters in Monte Carlo rendering. ACM Trans. Gr. 31(3), 18:1–18:15 (2012)

    Article  Google Scholar 

  31. Stein, C.M.: Estimation of the mean of a multivariate normal distribution. Ann. Stat. 9(6), 1135–1151 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  32. Wand, M.P., Jones, M.C.: Kernel Smoothing. Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, Boca Raton (1995)

    Book  Google Scholar 

  33. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. Trans. Imaging Proc. 13(4), 600–612 (2004)

    Article  Google Scholar 

  34. Yan, L.Q., Mehta, S.U., Ramamoorthi, R., Durand, F.: Fast 4D sheared filtering for interactive rendering of distribution effects. ACM Trans. Gr. 35(1), 7:1–7:13 (2015)

    Article  Google Scholar 

  35. Zwicker, M., Jarosz, W., Lehtinen, J., Moon, B., Ramamoorthi, R., Rousselle, F., Sen, P., Soler, C., Yoon, S.E.: Recent advances in adaptive sampling and reconstruction for Monte Carlo rendering. Comput. Gr. Forum (Proc. Eurogr.) 34(2), 667–681 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

Funding was provided by The National High Technology Research and Development Program of China (863 Program) (Grant No. 2012AA011206).

Author information

Authors and Affiliations

  1. Science and Technology on Integrated Information System Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Hongliang Yuan & Changwen Zheng

  2. University of Chinese Academy of Sciences, Beijing, China

    Hongliang Yuan

Authors
  1. Hongliang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Changwen Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongliang Yuan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, H., Zheng, C. Adaptive rendering based on robust principal component analysis. Vis Comput 34, 551–562 (2018). https://doi.org/10.1007/s00371-017-1360-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-017-1360-2

Keywords

Search

Navigation