Variable Basis Mapping for Real-Time Volumetric Visualization

TL;DR

This work tackles the bottleneck of real-time visualization for large volumetric data by introducing Variable Basis Mapping (VBM), a principled framework that converts volumetric fields into 3D Gaussian Splatting (3DGS) representations via wavelet-domain analysis. It first builds a Wavelet-to-Gaussian Transition Bank to obtain optimal Gaussian surrogates for canonical wavelet atoms, then derives an analytical Gaussian construction that maps discrete wavelet coefficients to 3DGS parameters, and finally applies a lightweight image-space fine-tuning stage to refine fidelity. The key contributions are the transition bank with translation-consistent Gaussian replacements, the analytical mapping from multiscale wavelets to Gaussian primitives, and the demonstrated efficiency and quality gains across diverse datasets, achieving real-time interactive rendering. By bridging multiresolution analysis with explicit scene representations, VBM provides a robust foundation for fast, accurate volumetric visualization and may influence future structured neural representations and visualization systems.

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.

Figures (6)

• Figure 1: Left: Our excellent PSNR curve demonstrating the performance of the VBM framework on Supernova data. Right: The VBM-based Gaussian model effectively captures fine details.
• Figure 2: Overview of the VBM framework. A volumetric radiance field is projected onto the wavelet subspace using discrete wavelet transform (DWT), and then mapped to the function subspace spanned by Gaussian primitives. This is followed by efficient image-space fine-tuning to obtain the optimal parameters. The process is supported by the Wavelet-to-Gaussian Transition Bank, built from canonical wavelets and Gaussians, and an analytic Gaussian construction strategy leveraging the linearity and translation consistency of the IDWT.
• Figure 3: Wavelet-to-Gaussian Transition Bank. Illustration of the transition from localized wavelet kernels to Gaussian primitives across multiple scales.
• Figure 4: Qualitative comparison at an early training stage (0.5K). Our VBM-based Gaussians already captures fine structural details, demonstrating strong initialization and efficient convergence.
• Figure 5: Qualitative comparison across training iterations. Our method rapidly refines structural details on both the Supernova simulation (left) and the Colon Prone CT volume (right), demonstrating consistent convergence across scientific and medical data.