Is Gaussian Enough? On the Local Specialization of Kernels in 3D Splatting

Recent 3D splatting methods have extended Gaussian primitives toward increasingly expressive and adaptive kernel formulations. However, it remains unclear whether greater within-family adaptability makes kernel families effectively interchangeable or whether they retain distinct local representation biases. Existing studies primarily rely on scene-level reconstruction metrics, potentially obscuring heterogeneous behavior within a scene. We systematically characterize local cross-family specialization across Gaussian, generalized exponential, and deformable radial kernels using real-scene analysis, structure-conditioned characterization, controlled synthetic manipulations, and robustness controls. We find substantial local complementarity: different families achieve lower reconstruction error in different regions, with relative performance varying systematically with local scene structure. Controlled structural manipulations produce reproducible changes in cross-family performance, while specialization persists across spatial scales and under a matched primitive budget. These results show that within-family adaptability does not necessarily eliminate cross-family representation differences, motivating representations that account for compatibility between kernel families and local scene structure.