用于3D高斯点云的量子启发式非正交函数空间压缩
QIRF Quantum-Inspired Non-Orthogonal Function-Space Compression for 3D Gaussian Splatting
AI总结：
研究针对3D高斯点云存储和渲染成本高的问题，提出量子启发式非正交函数空间压缩方法QIRF，通过构建矩阵、广义特征分解等操作减少高斯数量和存储，提升渲染速度，且保持重建质量，揭示了非正交函数空间冗余的重要性。
AI中文摘要：
3D高斯点云（3DGS）通过大量各向异性高斯基元表示场景来实现高质量实时渲染。然而，复杂场景通常需要数百万个高斯基元，导致存储和渲染成本高昂。现有压缩方法主要通过基元修剪、属性量化、聚类或神经编码来减少冗余，而强重叠和非正交高斯基函数引起的冗余在很大程度上未被探索。我们提出了QIRF，一种用于3D高斯点云的量子启发式非正交函数空间压缩方法。QIRF将相邻高斯基元建模为局部非正交基，并将基元减少公式化为子空间感知选择问题。具体而言，构建解析高斯重叠矩阵和辐射响应密度矩阵来表征功能冗余和渲染相关性。然后使用广义特征分解来识别主导局部子空间并选择代表性高斯基元。基于RRDM的响应模型和细节感知保护进一步在激进修剪下保留视觉上重要的高频结构。在来自Mip-NeRF 360、Tanks and Temples和Deep Blending的13个场景上的实验表明，QIRF平均将高斯数量和原始PLY存储减少了71.7%，相当于约3.54倍的压缩，同时保持与3DGS相当的重建质量，并实现了0.10 dB的边际平均PSNR改进。QIRF还将平均渲染速度比3DGS提高了34.3%。这些结果表明，非正交函数空间冗余是显式高斯辐射场中一个重要但未被充分探索的表示冗余来源。
英文摘要：
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.
