EigenGS Representation: From Eigenspace to Gaussian Image Space

2025-03-10

AI Summary

This work addresses the slow initialization and difficulty in multi-scale modeling—leading to high-frequency artifacts—in 2D Gaussian splatting reconstruction. We propose a PCA-guided, frequency-aware Gaussian parameterization method. By establishing an end-to-end differentiable mapping from a learned feature subspace to Gaussian ellipsoid parameters (center, covariance, opacity), our approach enables instantaneous initialization of Gaussian parameters for novel views. A frequency-aware learning mechanism further allows ellipsoids to adaptively capture multi-scale spatial structures. To the best of our knowledge, this is the first work to establish a generalizable, differentiable mapping paradigm between feature space and Gaussian image representations. Evaluated on multi-resolution and multi-category datasets, our method achieves superior reconstruction quality over direct 2D Gaussian fitting, reduces parameter count by 37%, accelerates training by 5.2×, and supports real-time, high-fidelity image representation.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Bridges PCA and 2D Gaussian representation for image modeling
• Enables instant Gaussian parameter initialization for new images
• Improves reconstruction quality and reduces training time

Innovation

• EigenGS bridges PCA and Gaussian image representation
• Frequency-aware learning adapts Gaussians to different scales
• EigenGS reduces parameters and accelerates training time