A Spherical Representation of HDR Environment Maps with Adaptive Gaussian Primitives

HDR environment maps are widely used in computer graphics to represent complex illumination and reproduce realistic lighting and reflections in 3D scenes. Representing these signals compactly is challenging because they combine smooth low-frequency illumination, highly localized light sources, and structured regions with sharp transitions. Conventional image-based representations also rely on planar parameterizations of the sphere, introducing distortions and discontinuities that are unrelated to the underlying spherical signal. This thesis presents a compact and continuous representation of HDR environment maps defined directly on the sphere. The proposed model extends Anisotropic Spherical Gaussians (ASGs) with two independent shape parameters controlling radial falloff and contour geometry. These additional degrees of freedom allow each primitive to adapt to local signal structure beyond the Gaussian profile and elliptical contours of standard ASGs. A moment-preserving normalization in the tangent plane keeps the interpretation of kernel scale and coefficient magnitude consistent as the kernel shape changes. Reconstruction is formulated as the optimization of a positive mixture of spherical kernels. The fitting procedure jointly optimizes position, orientation, scale, color, and shape, while adaptive spherical sampling, an HDR-aware objective, and residual-driven densification progressively allocate additional primitives to regions that require greater representational capacity. A compact codec is also introduced to quantize and store the resulting model parameters. The method is evaluated through reconstruction quality, rate-distortion analysis, shape ablations, visual comparisons, and image-based lighting experiments. Comparisons against standard ASGs and Image-GS, an adaptive image-space representation based on 2D Gaussian primitives, are used to assess the effect of shape adaptation and the benefits of operating directly on the sphere. The results show that adapting radial profile and contour geometry increases the expressive capacity of spherical Gaussian kernels while preserving a compact, continuous, and parameterization-independent representation. Radial and contour adaptation play complementary roles, allowing the model to better capture localized emitters, elongated structures, and sharp boundaries that are difficult to represent with fixed Gaussian footprints.