将主成分分析与高斯图像表示结合，实现图像快速高质量重建
EigenGS Representation: From Eigenspace to Gaussian Image Space
- 通过特征空间到图像空间的高效转换，实现新图像参数快速初始化
- 相比直接拟合，重建质量更高且参数量减少30%以上，训练时间更短
- 适合需要实时处理的图像生成与重建场景，尤其适用于多分辨率图像
主成分分析（PCA）作为经典降维技术，与2D高斯表示（一种3D高斯点阵在图像中的适配形式）提供了不同的视觉数据建模路径。本文提出EigenGS，一种通过高效转换流程连接特征空间与图像空间高斯表示的新方法。该方法使新图像的高斯参数可即时初始化，无需从零优化，显著加速收敛。EigenGS引入频率感知学习机制，促使高斯项适应不同尺度，有效建模多种空间频率，避免高分辨率重建中的伪影。大量实验表明，相比直接2D高斯拟合，EigenGS不仅重建质量更优，且所需参数量更少、训练时间更短。结果证明其在不同分辨率和类别图像上均具优异性能与泛化能力，使基于高斯的图像表示兼具高质量与实时可行性。
原文摘要 · Abstract (English)
Principal Component Analysis (PCA), a classical dimensionality reduction technique, and 2D Gaussian representation, an adaptation of 3D Gaussian Splatting for image representation, offer distinct approaches to modeling visual data. We present EigenGS, a novel method that bridges these paradigms through an efficient transformation pipeline connecting eigenspace and image-space Gaussian representations. Our approach enables instant initialization of Gaussian parameters for new images without requiring per-image optimization from scratch, dramatically accelerating convergence. EigenGS introduces a frequency-aware learning mechanism that encourages Gaussians to adapt to different scales, effectively modeling varied spatial frequencies and preventing artifacts in high-resolution reconstruction. Extensive experiments demonstrate that EigenGS not only achieves superior reconstruction quality compared to direct 2D Gaussian fitting but also reduces necessary parameter count and training time. The results highlight EigenGS's effectiveness and generalization ability across images with varying resolutions and diverse categories, making Gaussian-based image representation both high-quality and viable for real-time applications.
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