QIRF Quantum-Inspired Non-Orthogonal Function-Space Compression for 3D Gaussian Splatting

2026-07-20

AI Summary

This work addresses the high storage and rendering costs of 3D Gaussian Splatting in complex scenes, where millions of Gaussians induce significant overhead and existing compression methods struggle with functional redundancy among non-orthogonal Gaussian basis functions. The paper introduces, for the first time, a quantum-inspired perspective that treats neighboring Gaussians as local bases within a non-orthogonal function space. By constructing a Gaussian overlap matrix and a radiance response density matrix, the compression problem is reformulated as a subspace-aware selection task. The authors employ generalized eigen-decomposition to identify representative primitives and integrate a detail-preserving protection mechanism to retain visual fidelity. Evaluated on 13 standard scenes, the method reduces Gaussian counts by 71.7% on average (yielding a 3.54× reduction in PLY file size), improves PSNR by 0.10 dB, and accelerates rendering by 34.3%.

Abstract

3D Gaussian Splatting (3DGS) achieves high-quality real-time rendering by representing a scene with a large collection of anisotropic Gaussian primitives. However, complex scenes often require millions of Gaussians, resulting in substantial storage and rendering costs. Existing compression methods mainly reduce redundancy through primitive-wise pruning, attribute quantization, clustering, or neural coding, while redundancy caused by strongly overlapping and non-orthogonal Gaussian basis functions remains largely unexplored. We present QIRF, a quantum-inspired non-orthogonal function-space compression method for 3D Gaussian Splatting. QIRF models neighboring Gaussian primitives as a local non-orthogonal basis and formulates primitive reduction as a subspace-aware selection problem. Specifically, an analytic Gaussian overlap matrix and a radiance-response density matrix are constructed to characterize functional redundancy and rendering relevance. Generalized eigendecomposition is then used to identify the dominant local subspace and select representative Gaussian primitives. An RRDM-based response model and detail-aware safeguarding further preserve visually important high-frequency structures under aggressive pruning. Experiments on 13 scenes from Mip-NeRF 360, Tanks and Temples, and Deep Blending show that QIRF reduces the Gaussian count and raw PLY storage by 71.7 percent on average, corresponding to approximately 3.54 times compression, while maintaining reconstruction quality comparable to 3DGS and achieving a marginal average PSNR improvement of 0.10 dB. QIRF also improves the average rendering speed over 3DGS by 34.3 percent. These results suggest that non-orthogonal function-space redundancy is an important yet underexplored source of representational redundancy in explicit Gaussian radiance fields.

Problem

• 3D Gaussian Splatting
• function-space redundancy
• non-orthogonal basis
• compression
• representational redundancy

Innovation

• non-orthogonal function-space compression
• 3D Gaussian Splatting
• quantum-inspired subspace selection
• Gaussian overlap matrix
• radiance-response density matrix