Frame-Free Representation of Polarized Light for Resolving Stokes Vector Singularities

Stokes parameters are the standard representation of polarized light intensity in Mueller calculus and are widely used in polarization-aware computer graphics. However, their reliance on local frames-aligned with ray propagation directions-introduces a fundamental limitation: numerical discontinuities in Stokes vectors despite physically continuous fields of polarized light. This issue originates from the Hairy Ball Theorem, which guarantees unavoidable singularities in any frame-dependent function defined over spherical directional domains. In this paper, we overcome this long-standing challenge by introducing the first frame-free representation of Stokes vectors. Our key idea is to reinterpret a Stokes vector as a Dirac delta function over the directional domain and project it onto spin-2 spherical harmonics, retaining only the lowest-frequency coefficients. This compact representation supports coordinate-invariant interpolation and distance computation between Stokes vectors across varying ray directions-without relying on local frames. We demonstrate the advantages of our approach in two representative applications: spherical resampling of polarized environment maps (e.g., between cube map and equirectangular formats), and view synthesis from polarized radiance fields. In both cases, conventional frame-dependent methods produce singularity artifacts. In contrast, our frame-free representation eliminates these artifacts, improves numerical robustness, and simplifies implementation by decoupling polarization encoding from local frames.