Parametrization of Gaussians for Enhanced Image Representation in Gaussian Splatting

We propose a novel parametrization framework for Gaussian primitives that enhances image representation in Gaussian Splatting. Our method introduces a learnable parameter c ∈ ⟨0, 1⟩ that enables smooth interpolation between standard Gaussians (c = 0) and Difference of Gaussians (DoGs, c = 1), allowing the optimization process to adaptively select the most suitable functional form for each primitive. In addition to this hybrid formulation, we extend the representation with frequency-modulated Gaussians using cosine basis functions to better capture high-frequency and periodic image features. Experimental results on image reconstruction tasks demonstrate that our approach consistently improves approximation accuracy over baseline Gaussian Splatting, both in terms of mean squared error and structural similarity. We further analyze the distribution of the learned parameter and its impact on reconstruction quality, revealing a complementary use of Gaussians and DoGs. These findings suggest that flexible functional representations offer a promising direction for advancing neural image rendering methods.