主成分分析（Principal Component Analysis, PCA）作為一種經典的維度壓縮技術，與高斯重建（Gaussian Splatting）作為近期流行的高品質影像重建方法，兩者代表了完全不同的方向。即便如此，本文提出了特徵高斯重建（EigenGS），成功地結合了這兩種方法。透過建立特徵空間與影像高斯空間之間的轉換機制，我們的方法能夠在不需要逐一訓練的情況下，立即為新的影像初始化高斯參數。
本方法同時引入了頻率自適應機制，使高斯表示式能夠適應不同尺度以更好地模擬並重建場景，有效防止高解析度重建中的影像瑕疵。經過大量實驗證，特徵高斯重建不僅達到了更優異的重建品質，更大幅加速了收斂速度。實驗結果顯示了本方法的效能，以及其在不同解析度和多樣類別影像上的通用性都有很大的進步，這使得高品質的高斯重建在即時應用中變得更加可行。
我們的貢獻主要表現在三個方面：首先，透過運用基於 PCA 的特徵高斯重建，解決了高斯初始化的挑戰；其次，提出的頻率自適應機制有效預防了瑕疵；最後，跨資料集實驗的成功，特別是在 ImageNet 上的表現，展現了方法的一般性。這項研究顯示了，將傳統電腦視覺技術與現代方法結合，可以創造出更有潛力的新方法。

Principal Component Analysis (PCA), a classical dimensionality reduction technique, and Gaussian Splatting, a recent high-quality image synthesis method, represent fundamentally different approaches to image representation. Despite these significant differences, we present EigenGS, a novel method that bridges these two paradigms. By establishing an efficient transformation pipeline between eigenspace and image-space Gaussian representations, our approach enables instant initialization of Gaussian parameters for new images without requiring per-image training from scratch. Our method also introduces a frequency-aware learning mechanism that encourages Gaussians to adapt to different scales in order to better model spatial frequencies, effectively preventing artifacts in high-resolution reconstruction. Extensive experiments demonstrate that EigenGS not only achieves superior reconstruction quality but also dramatically accelerates convergence. The results highlight EigenGS's effectiveness and its ability to generalize across images with varying resolutions and diverse categories. This makes high-quality Gaussian Splatting practically viable for real-time applications.

[1] R. Anderson, A. Johnson, and B. Lee. Mini-splatting: Representing scenes with a constrained number of gaussians. arXiv preprint arXiv:2403.14166, 2024.
[2] P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman. Eigenfaces vs. fisherfaces: Recognition using class specific linear projection. IEEE TPAMI, 19(7):711–720, 1997.
[3] L. Chen, Y. Wang, and J. Zhang. Gaussreg: Fast 3d registration with gaussian splat- ting. arXiv preprint arXiv:2403.14530, 2024.
[4] D. Clark and E. Moore. Bags: Blur agnostic gaussian splatting through multi-scale kernel modeling. arXiv preprint arXiv:2403.14530, 2025.
[5] J. Deng, W. Dong, R. Socher, L. Li, K. Li, and L. Fei-Fei. Imagenet: A large-scale hi- erarchical image database. In 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2009), 20-25 June 2009, Miami, Florida, USA, pages 248–255. IEEE Computer Society, 2009.
[6] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner, M. Dehghani, M. Minderer, G. Heigold, S. Gelly, J. Uszkoreit, and N. Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. In 9th Inter- national Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, 2021.
[7] T. Harris and L. Adams. Fregs: 3d gaussian splatting with progressive frequency regularization. arXiv preprint arXiv:2403.14166, 2023.
[8] I. T. Jolliffe. Principal Component Analysis. Springer Series in Statistics. Springer, 1986.
[9] T.Karras,S.Laine,andT.Aila.Astyle-basedgeneratorarchitectureforgenerativead- versarial networks. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019, pages 4401–4410. Computer Vision Foundation / IEEE, 2019.
[10] B. Kerbl, G. Kopanas, T. Leimkühler, and G. Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph., 42(4):139:1–139:14, 2023.
[11] J.Krause,M.Stark,J.Deng,andL.Fei-Fei.3dobjectrepresentationsforfine-grained categorization. In 2013 IEEE International Conference on Computer Vision Work- shops, ICCV Workshops 2013, Sydney, Australia, December 1-8, 2013, pages 554– 561. IEEE Computer Society, 2013.
[12] F. D. la Torre and M. J. Black. Robust principal component analysis for computer vision. In ICCV, pages 362–369. IEEE Computer Society, 2001.
[13] Y. LeCun, B. E. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. E. Hubbard, and L. D. Jackel. Handwritten digit recognition with a back-propagation network. In D. S. Touretzky, editor, NeurIPS, pages 396–404. Morgan Kaufmann, 1989.
[14] S. Lee and M. Yang. Hac: Hash-grid assisted context for 3d gaussian splatting com- pression. arXiv preprint arXiv:2403.06908, 2024.
[15] Y. Li, C. Lyu, Y. Di, G. Zhai, G. H. Lee, and F. Tombari. Geogaussian: Geometry- aware gaussian splatting for scene rendering. In European Conference on Computer Vision, pages 441–457. Springer, 2025.
[16] Z. Liang, Q. Zhang, W. Hu, Y. Feng, L. Zhu, and K. Jia. Analytic-splatting: Anti-aliased 3d gaussian splatting via analytic integration. arXiv preprint arXiv:2403.11056, 2024.
[17] Z. Liu, P. Luo, X. Wang, and X. Tang. Deep learning face attributes in the wild. In 2015 IEEE International Conference on Computer Vision, ICCV 2015, Santiago, Chile, December 7-13, 2015, pages 3730–3738. IEEE Computer Society, 2015.
[18] J.MillerandJ.Roberts.Compact3d:Smallerandfastergaussiansplattingwithvector quantization. arXiv preprint arXiv:2407.05254, 2024.
[19] W. Morgenstern, F. Barthel, A. Hilsmann, and P. Eisert. Compact 3d scene represen- tation via self-organizing gaussian grids. arXiv preprint arXiv:2312.13299, 2023.
[20] L. Sirovich and M. Kirby. Low-dimensional procedure for the characterization of human faces. Journal of the Optical Society of America. A, Optics and image science, 43:519–524, 1987.
[21] M. E. Tipping and C. M. Bishop. Mixtures of probabilistic principal component analysers. Neural Comput., 11(2):443–482, 1999.
[22] M. A. Turk and A. Pentland. Face recognition using eigenfaces. In CVPR, pages 586–591. IEEE, 1991.
[23] G. Turner and O. Scott. Multi-scale 3d gaussian splatting for anti-aliased rendering. arXiv preprint arXiv:2311.17089, 2024.
[24] C. Wewer, K. Raj, E. Ilg, B. Schiele, and J. E. Lenssen. latentsplat: Autoencod- ing variational gaussians for fast generalizable 3d reconstruction. arXiv preprint arXiv:2403.16292, 2024.
[25] J. Ye. Generalized low rank approximations of matrices. volume 69 of ACM Interna- tional Conference Proceeding Series. ACM, 2004.
[26] Z. Yu, A. Chen, B. Huang, T. Sattler, and A. Geiger. Mip-splatting: Alias-free 3d gaussian splatting. In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 19447–19456, 2024.
[27] W. Zhang, J. Sun, and X. Tang. Cat head detection - how to effectively exploit shape and texture features. In D. A. Forsyth, P. H. S. Torr, and A. Zisserman, editors, Com- puter Vision - ECCV 2008, 10th European Conference on Computer Vision, Marseille, France, October 12-18, 2008, Proceedings, Part IV, volume 5305 of Lecture Notes in Computer Science, pages 802–816. Springer, 2008.
[28] X. Zhang, X. Ge, T. Xu, D. He, Y. Wang, H. Qin, G. Lu, J. Geng, and J. Zhang. Gaus- sianimage: 1000 fps image representation and compression by 2d gaussian splatting. In ECCV, 2024.
[29] Z. Zhang, W. Hu, Y. Lao, T. He, and H. Zhao. Pixel-gs: Density control with pixel- aware gradient for 3d gaussian splatting. arXiv preprint arXiv:2403.15530, 2024.