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ACM SIGGRAPH 2024 (Transactions on Graphics)

Spin-Weighted Spherical Harmonics for Polarized Light Transport
  Shinyoung Yi   Donggun Kim   Jiwoong Na  
  Xin Tong   Min H. Kim  
  KAIST Microsoft Research Asia  
  Real-time rendering of polarized light has been unavailable due to its higher dimensional space of polarized light.We introduce a new frequency-domain analysis of polarized light transport and propose a new method, called polarized spherical harmonics, based on the spin-weighted spherical harmonics theory in physics. Our method provides a rotation-invariant representation and spherical convolution of Stokes vector fields, enabling efficient simulation and reproduction of polarized light interactions We demonstrate the first real-time polarization rendering under polarized environmental illumination through polarized spherical harmonics. Refer to the supplemental video for real-time video results.  
  Supplemental video results  

The objective of polarization rendering is to simulate the interaction of light with materials exhibiting polarization-dependent behavior. However, integrating polarization into rendering is challenging and increases computational costs significantly. The primary difficulty lies in efficiently modeling and computing the complex reflection phenomena associated with polarized light. Specifically, frequency-domain analysis, essential for efficient environment lighting and storage of complex light interactions, is lacking. To efficiently simulate and reproduce polarized light interactions using frequency-domain techniques, we address the challenge of maintaining continuity in polarized light transport represented by Stokes vectors within angular domains. The conventional spherical harmonics method cannot effectively handle continuity and rotation invariance for Stokes vectors. To overcome this, we develop a new method called polarized spherical harmonics (PSH) based on the spin-weighted spherical harmonics theory. Our method provides a rotation-invariant representation of Stokes vector fields. Furthermore, we introduce frequency domain formulations of polarized rendering equations and spherical convolution based on PSH.We first define spherical convolution on Stokes vector fields in the angular domain, and it also provides efficient computation of polarized light transport, nearly on an entry-wise product in the frequency domain. Our frequency domain formulation, including spherical convolution, led to the development of the first real-time polarization rendering technique under polarized environmental illumination, named precomputed polarized radiance transfer, using our polarized spherical harmonics. Results demonstrate that our method can effectively and accurately simulate and reproduce polarized light interactions in complex reflection phenomena, including polarized environmental illumination and soft shadows.

  author  = {Shinyoung Yi and Donggun Kim and Jiwoong Na and 
             Xin Tong and Min H. Kim},
  title   = {Spin-Weighted Spherical Harmonics for 
             Polarized Light Transport},
  journal = {ACM Transactions on Graphics (Proc. SIGGRAPH 2024)},
  year    = {2024},
  volume  = {43},
  number  = {4},
Preprint paper:
PDF (14.2MB)
PDF (3.9MB)
SIGGRAPH 2024 slides (TBA)
www GitHub code &
dataset (TBA)
www ACM
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