Object-Space Analysis of Local Contrast Sensitivity for Hierarchical Representations of 3D Gaussians

3D Gaussian Splatting (3DGS) has recently attracted considerable attention as an efficient representation for high-quality novel-view synthesis. However, 3DGS typically relies on a large number of Gaussian primitives, making perceptually informed level-of-detail control essential for balancing visual quality and rendering efficiency. In this paper, we present an object-space analysis framework of contrast sensitivity for 3D Gaussian representations. By exploiting the analytical Fourier transform of Gaussian primitives and the projection–slice theorem, we estimate the spatial frequency response of projected Gaussians without explicit rasterization. This enables direct perceptual assessment of Gaussian primitives in object space under given viewing conditions. As an application of this analysis, we integrate the proposed perceptual assessment into a hierarchical 3DGS representation and realize a foveated rendering scheme that selects appropriate Gaussian levels at runtime using simple comparisons. Experimental results on real-world scenes demonstrate that the proposed method preserves visual quality while reducing rendering cost compared to full-quality rendering.