Variable Basis Mapping for Real-Time Volumetric Visualization

2026-01-14

AI Summary

Real-time, high-quality visualization of large-scale volumetric data is hindered by substantial computational costs. This work proposes a wavelet-domain analysis framework that establishes, for the first time, a mathematically rigorous analytical mapping between wavelet atoms and 3D Gaussian splats. By leveraging a precomputed basis transformation library, analytically derived Gaussian parameters, and image-space refinement, the method significantly accelerates convergence while enhancing rendering fidelity. Extensive experiments across diverse volumetric datasets demonstrate that the approach achieves efficient, real-time, and high-quality volume visualization.

Technology Category

• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Learning with Manifolds

Application Category

• Web Mining and Content Analysis: Web data visualization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

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.

Problem

• real-time visualization
• volumetric data
• computational cost
• direct volume rendering
• voxel-based methods

Innovation

• Variable Basis Mapping
• 3D Gaussian Splatting
• Wavelet-domain analysis
• Real-time volumetric visualization
• Analytical Gaussian construction