“Spin-weighted Spherical Harmonics for Polarized Light Transport”
Conference:
Type(s):
Title:
- Spin-weighted Spherical Harmonics for Polarized Light Transport
Presenter(s)/Author(s):
Abstract:
We introduce polarized spherical harmonics (PSH), based on spin-weighted spherical harmonics theory, offering a rotation-invariant representation of Stokes vector fields. Our approach includes frequency domain formulations of polarized rendering and spherical convolution with PSH, making it the first real-time polarization rendering with polarized environment lighting through precomputed polarized radiance transfer.
References:
[1]
Yunhao Ba, Alex Gilbert, Franklin Wang, Jinfa Yang, Rui Chen, Yiqin Wang, Lei Yan, Boxin Shi, and Achuta Kadambi. 2020. Deep shape from polarization. In Proc. the European Conference on Computer Vision (ECCV). Springer, 554–571.
[2]
Seung-Hwan Baek, Daniel S Jeon, Xin Tong, and Min H Kim. 2018. Simultaneous acquisition of polarimetric SVBRDF and normals. ACM Transactions on Graphics (TOG) 37, 6 (2018), 268–1.
[3]
Seung-Hwan Baek, Ramesh Raskar, Jinwei Ye, Akshat Dave, Achuta Kadambi, and Huaijin Chen. 2023. Polarization-based visual computing. In ACM SIGGRAPH 2023 Courses. 1–1.
[4]
Seung-Hwan Baek, Tizian Zeltner, Hyunjin Ku, Inseung Hwang, Xin Tong, Wenzel Jakob, and Min H Kim. 2020. Image-based acquisition and modeling of polarimetric reflectance. ACM Transactions on Graphics (TOG) 39, 4 (2020), 139.
[5]
Laurent Belcour, Guofu Xie, Christophe Hery, Mark Meyer, Wojciech Jarosz, and Derek Nowrouzezahrai. 2018. Integrating clipped spherical harmonics expansions. ACM Transactions on Graphics (TOG) 37, 2 (2018), 1–12.
[6]
Martin Berger. 2011. Approximate importance sampling of functions reconstructed from spherical harmonics. (2011).
[7]
John P Boyd. 2001. Chebyshev and Fourier spectral methods. Courier Corporation.
[8]
Michael Boyle. 2013. Angular velocity of gravitational radiation from precessing binaries and the corotating frame. Physical Review D 87, 10 (2013), 104006.
[9]
Edward Collett. 2005. Field guide to polarization. Spie Bellingham, WA.
[10]
Akshat Dave, Yongyi Zhao, and Ashok Veeraraghavan. 2022. Pandora: Polarization-aided neural decomposition of radiance. In European Conference on Computer Vision. Springer, 538–556.
[11]
Yuqi Ding, Yu Ji, Mingyuan Zhou, Sing Bing Kang, and Jinwei Ye. 2021. Polarimetric helmholtz stereopsis. In Proceedings of the IEEE/CVF International Conference on Computer Vision. 5037–5046.
[12]
RDM Garcia and CE Siewert. 1986. A generalized spherical harmonics solution for radiative transfer models that include polarization effects. Journal of Quantitative Spectroscopy and Radiative Transfer 36, 5 (1986), 401–423.
[13]
Abhijeet Ghosh, Shruthi Achutha, Wolfgang Heidrich, and Matthew O’Toole. 2007. BRDF acquisition with basis illumination. In 2007 IEEE 11th International Conference on Computer Vision. IEEE, 1–8.
[14]
Abhijeet Ghosh, Tongbo Chen, Pieter Peers, Cyrus A Wilson, and Paul Debevec. 2009. Estimating specular roughness and anisotropy from second order spherical gradient illumination. Computer Graphics Forum 28, 4, 1161–1170.
[15]
Abhijeet Ghosh, Graham Fyffe, Borom Tunwattanapong, Jay Busch, Xueming Yu, and Paul Debevec. 2011. Multiview face capture using polarized spherical gradient illumination. Transactions on Graphics (TOG) 30, 6 (2011), 1–10.
[16]
Joshua N Goldberg, Alan J MacFarlane, Ezra T Newman, Fritz Rohrlich, and EC George Sudarshan. 1967. Spin-s Spherical Harmonics and ?. J. Math. Phys. 8, 11 (1967), 2155–2161.
[17]
Inseung Hwang, Daniel S Jeon, Adolfo Mu?oz, Diego Gutierrez, Xin Tong, and Min H Kim. 2022. Sparse ellipsometry: portable acquisition of polarimetric SVBRDF and shape with unstructured flash photography. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1–14.
[18]
Wenzel Jakob, S?bastien Speierer, Nicolas Roussel, Merlin Nimier-David, Delio Vicini, Tizian Zeltner, Baptiste Nicolet, Miguel Crespo, Vincent Leroy, and Ziyi Zhang. 2022. Mitsuba 3 renderer. https://mitsuba-renderer.org.
[19]
Adrian Jarabo and Victor Arellano. 2018. Bidirectional rendering of vector light transport. Computer Graphics Forum 37, 6, 96–105.
[20]
Henrik Wann Jensen, Stephen R Marschner, Marc Levoy, and Pat Hanrahan. 2001. A practical model for subsurface light transport. In Proc. ACM SIGGRAPH 2001. 511–518.
[21]
Achuta Kadambi, Vage Taamazyan, Boxin Shi, and Ramesh Raskar. 2015. Polarized 3d: High-quality depth sensing with polarization cues. In Proceedings of the IEEE International Conference on Computer Vision. 3370–3378.
[22]
Jan Kautz, Peter-Pike Sloan, and Jaakko Lehtinen. 2005. Precomputed radiance transfer: theory and practice. In ACM SIGGRAPH 2005 Courses. 1–es.
[23]
Phil B Keegstra, GF Smoot, KM Gorski, G Hinshaw, and L Tenorio. 1997. Generalized spherical harmonics for all-sky polarization studies. In Astronomical Data Analysis Software and Systems VI, Vol. 125. 198.
[24]
Youngchan Kim, Wonjoon Jin, Sunghyun Cho, and Seung-Hwan Baek. 2023. Neural Spectro-Polarimetric Fields. In SIGGRAPH Asia 2023 Conference Papers.
[25]
Ivan Ku??er and Marijan Ribari?. 1959. Matrix formalism in the theory of diffusion of light. Optica Acta: International Journal of Optics 6, 1 (1959), 42–51.
[26]
Christian Lessig and Eugene Fiume. 2008. SOHO: Orthogonal and symmetric Haar wavelets on the sphere. ACM Transactions on Graphics (TOG) 27, 1 (2008), 1–11.
[27]
Wan-Chun Ma, Tim Hawkins, Pieter Peers, Charles-Felix Chabert, Malte Weiss, Paul E Debevec, et al. 2007. Rapid Acquisition of Specular and Diffuse Normal Maps from Polarized Spherical Gradient Illumination. Rendering Techniques 9, 10 (2007), 2.
[28]
Ryan G McClarren, Cory D Hauck, and Robert B Lowrie. 2008. Filtered spherical harmonics methods for transport problems. In Proceedings of the 2009 international conference on mathematics and computational methods and reactor physics.
[29]
Michal Mojz?k, Tom?? Sk?ivan, Alexander Wilkie, and Jaroslav K?iv?nek. 2016. Bidirectional polarised light transport. In Proceedings of the Eurographics Symposium on Rendering: Experimental Ideas & Implementations. 97–108.
[30]
Charles Nash and Siddhartha Sen. 1983. Topology and Geometry for Physicists. Academic Press.
[31]
Ezra T Newman and Roger Penrose. 1966. Note on the bondi-metzner-sachs group. J. Math. Phys. 7, 5 (1966), 863–870.
[32]
Kin-Wang Ng and Guo-Chin Liu. 1999. Correlation functions of CMB anisotropy and polarization. International Journal of Modern Physics D 8, 01 (1999), 61–83.
[33]
Ren Ng, Ravi Ramamoorthi, and Pat Hanrahan. 2003. All-frequency shadows using non-linear wavelet lighting approximation. In ACM SIGGRAPH 2003 Papers. 376–381.
[34]
Ren Ng, Ravi Ramamoorthi, and Pat Hanrahan. 2004. Triple product wavelet integrals for all-frequency relighting. In ACM SIGGRAPH 2004 Papers. 477–487.
[35]
Robert A Phinney and Robert Burridge. 1973. Representation of the elastic-gravitational excitation of a spherical Earth model by generalized spherical harmonics. Geophysical Journal International 34, 4 (1973), 451–487.
[36]
Ravi Ramamoorthi et al. 2009. Precomputation-based rendering. Foundations and Trends? in Computer Graphics and Vision 3, 4 (2009), 281–369.
[37]
Ravi Ramamoorthi and Pat Hanrahan. 2001a. An efficient representation for irradiance environment maps. In Proc. ACM SIGGRAPH 2001. 497–500.
[38]
Ravi Ramamoorthi and Pat Hanrahan. 2001b. A signal-processing framework for inverse rendering. In Proc. ACM SIGGRAPH 2001. 117–128.
[39]
Ravi Ramamoorthi and Pat Hanrahan. 2002. Frequency space environment map rendering. In Proc. ACM SIGGRAPH 2002. 517–526.
[40]
Tobias Ritschel, Carsten Dachsbacher, Thorsten Grosch, and Jan Kautz. 2012. The state of the art in interactive global illumination. Computer graphics forum 31, 1, 160–188.
[41]
J?r?my Riviere, Ilya Reshetouski, Luka Filipi, and Abhijeet Ghosh. 2017. Polarization imaging reflectometry in the wild. ACM Transactions on Graphics (TOG) 36, 6 (2017), 1–14.
[42]
Vincent Rossetto. 2009. General framework for multiple scattering of polarized waves including anisotropies and Berry phase. Physical Review E 80, 5 (2009), 056605.
[43]
Sara Fridovich-Keil and Alex Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. 2022. Plenoxels: Radiance Fields without Neural Networks. In CVPR.
[44]
Joseph JG Scanio. 1977. Spin-weighted spherical harmonics and electromagnetic multi-pole expansions. American Journal of Physics 45, 2 (1977), 173–178.
[45]
Zden?k Sekera. 1966. Scattering matrices and reciprocity relationships for various representations of the state of polarization. JOSA 56, 12 (1966), 1732–1740.
[46]
Peter-Pike Sloan. 2008. Stupid spherical harmonics (sh) tricks. In Game developers conference, Vol. 9. 42.
[47]
Peter-Pike Sloan. 2017. Deringing spherical harmonics. In SIGGRAPH Asia 2017 Technical Briefs. 1–4.
[48]
Peter-Pike Sloan, Jan Kautz, and John Snyder. 2002. Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments. In Proc. ACM SIGGRAPH 2002. 527–536.
[49]
Peter-Pike Sloan, Ben Luna, and John Snyder. 2005. Local, deformable precomputed radiance transfer. ACM Transactions on Graphics (TOG) 24, 3 (2005), 1216–1224.
[50]
Shlomi Steinberg, Pradeep Sen, and Ling-Qi Yan. 2022. Towards practical physical-optics rendering. ACM Transactions on Graphics 41, 4 (2022), 1–13.
[51]
Shlomi Steinberg and Ling-Qi Yan. 2021a. A generic framework for physical light transport. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1–20.
[52]
Shlomi Steinberg and Ling-Qi Yan. 2021b. Physical light-matter interaction in hermitegauss space. ACM Transactions on Graphics (TOG) 40, 6 (2021), 1–17.
[53]
Romuald Tapimo, Herv? Thierry Tagne Kamdem, and David Yemele. 2018. A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere. Astrophysics and Space Science 363, 3 (2018), 52.
[54]
Borom Tunwattanapong, Graham Fyffe, Paul Graham, Jay Busch, Xueming Yu, Abhijeet Ghosh, and Paul Debevec. 2013. Acquiring reflectance and shape from continuous spherical harmonic illumination. Transactions on graphics (TOG) 32, 4 (2013), 1–12.
[55]
Dor Verbin, Peter Hedman, Ben Mildenhall, Todd Zickler, Jonathan T Barron, and Pratul P Srinivasan. 2022. Ref-nerf: Structured view-dependent appearance for neural radiance fields. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 5481–5490.
[56]
Jingwen Wang and Ravi Ramamoorthi. 2018. Analytic spherical harmonic coefficients for polygonal area lights. ACM Transactions on Graphics (TOG) 37, 4 (2018), 1–11.
[57]
Alexander Wilkie, Claudia Ulbricht, Robert F Tobler, Georg Zotti, and Werner Purgathofer. 2004. An analytical model for skylight polarisation. In Rendering Techniques. 387–398.
[58]
Alexander Wilkie, Petr Vevoda, Thomas Bashford-Rogers, Luk?? Ho?ek, Tom?? Iser, Monika Kol??ov?, Tobias Rittig, and Jaroslav K?iv?nek. 2021. A fitted radiance and attenuation model for realistic atmospheres. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1–14.
[59]
Alexander Wilkie and Andrea Weidlich. 2012. Polarised light in computer graphics. In SIGGRAPH Asia 2012 Courses. 1–87.
[60]
Lifan Wu, Guangyan Cai, Shuang Zhao, and Ravi Ramamoorthi. 2020. Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights. ACM Transactions on Graphics (TOG) 39, 4 (2020), 134–1.
[61]
Hanggao Xin, Zhiqian Zhou, Di An, Ling-Qi Yan, Kun Xu, Shi-Min Hu, and Shing-Tung Yau. 2021. Fast and accurate spherical harmonics products. ACM Transactions on Graphics (TOG) 40, 6 (2021), 1–14.
[62]
Zilin Xu, Zheng Zeng, Lifan Wu, Lu Wang, and Ling-Qi Yan. 2022. Lightweight Neural Basis Functions for All-Frequency Shading. In Proc. ACM SIGGRAPH Asia 2022. 1–9.
[63]
Matias Zaldarriaga and Uro? Seljak. 1997. All-sky analysis of polarization in the microwave background. Physical Review D 55, 4 (1997), 1830.
[64]
Shuang Zhao, Ravi Ramamoorthi, and Kavita Bala. 2014. High-order similarity relations in radiative transfer. ACM Transactions on Graphics (TOG) 33, 4 (2014), 1–12.
[65]
Kun Zhou, Yaohua Hu, Stephen Lin, Baining Guo, and Heung-Yeung Shum. 2005. Precomputed shadow fields for dynamic scenes. In ACM SIGGRAPH 2005 Papers. 1196–1201.


