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.

翻译：大规模体数据的实时可视化仍面临挑战，因为直接体绘制与基于体素的方法存在计算成本过高的问题。本文提出可变基映射（VBM）框架，该框架通过小波域分析将体数据场转换为三维高斯泼溅（3DGS）表示。首先，我们预计算一个紧凑的小波-高斯转换库，为跨多尺度的规范小波原子提供最优高斯代理。其次，我们执行解析式高斯构造，利用封闭形式的数学原理规则将离散小波系数直接映射到3DGS参数。最后，通过轻量级的图像空间微调阶段进一步优化表示以提升绘制保真度。在多类数据集上的实验表明，VBM能显著加速收敛并提升绘制质量，从而实现实时体数据可视化。