# EigenGS Representation: From Eigenspace to Gaussian Image Space

arXiv: https://arxiv.org/abs/2503.07446 · HTML: https://mlsanity.com/paper/2503.07446/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [Mini-Splatting: Representing Scenes with a Constrained Number of Gaussians](https://mlsanity.com/paper/2403.14166/) (2024)
- [HAC: Hash-grid Assisted Context for 3D Gaussian Splatting Compression](https://mlsanity.com/paper/2403.14530/) (2024)
- [Compact 3D Scene Representation via Self-Organizing Gaussian Grids](https://mlsanity.com/paper/2312.13299/) (2023)
- [Multi-Scale 3D Gaussian Splatting for Anti-Aliased Rendering](https://mlsanity.com/paper/2311.17089/) (2023)
- [CompGS: Smaller and Faster Gaussian Splatting with Vector Quantization](https://mlsanity.com/paper/2311.18159/) (2023)
- [latentSplat: Autoencoding Variational Gaussians for Fast Generalizable 3D Reconstruction](https://mlsanity.com/paper/2403.16292/) (2024)
- [Pixel-GS: Density Control with Pixel-aware Gradient for 3D Gaussian Splatting](https://mlsanity.com/paper/2403.15530/) (2024)
- [FreGS: 3D Gaussian Splatting with Progressive Frequency Regularization](https://mlsanity.com/paper/2403.06908/) (2024)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [Analytic-Splatting: Anti-Aliased 3D Gaussian Splatting via Analytic Integration](https://mlsanity.com/paper/2403.11056/) (2024)
- [GeoGaussian: Geometry-aware Gaussian Splatting for Scene Rendering](https://mlsanity.com/paper/2403.11324/) (2024)
- [BAGS: Blur Agnostic Gaussian Splatting through Multi-Scale Kernel Modeling](https://mlsanity.com/paper/2403.04926/) (2024)
- [GaussReg: Fast 3D Registration with Gaussian Splatting](https://mlsanity.com/paper/2407.05254/) (2024)

## Built on by (most cited first, 2 of 2)

- [Versatile Video Representation via Feed-Forward 2D Gaussian Splatting Tokenization](https://mlsanity.com/paper/2508.11183/) (2025)
- [Affine-Aligned Atlas for Canonical Gaussian Construction in Video Representation](https://mlsanity.com/paper/2610.01114/) (2026)

## Abstract (arXiv)

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.