Variable Basis Mapping for Real-Time Volumetric Visualization

Abstract: Real-time visualization of large-scale volumetric data remains challenging, as direct volume rendering and voxel-based methods suffer from prohibitively high computational cost. We propose Variable Basis Mapping (VBM), a framework that transforms volumetric fields into 3D Gaussian Splatting (3DGS) representations through wavelet-domain analysis. First, we precompute a compact Wavelet-to-Gaussian Transition Bank that provides optimal Gaussian surrogates for canonical wavelet atoms across multiple scales. Second, we perform analytical Gaussian construction that maps discrete wavelet coefficients directly to 3DGS parameters using a closed-form, mathematically principled rule. Finally, a lightweight image-space fine-tuning stage further refines the representation to improve rendering fidelity. Experiments on diverse datasets demonstrate that VBM significantly accelerates convergence and enhances rendering quality, enabling real-time volumetric visualization.