EigenGS Representation: From Eigenspace to Gaussian Image Space
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.