Where Should the Gaussians Go? Reusable Label-Aware Allocation for Budget-Constrained Gaussian Splatting of Cinematic CT

3D Gaussian Splatting represents scenes as finite mixtures of anisotropic Gaussians whose number of components $K$ is set by heuristic density control or user caps. Variational Bayes Gaussian Splatting (VBGS) recast splat fitting as conjugate variational inference, but $K$ remains fixed. We replace the finite symmetric Dirichlet over mixture weights with a truncated stick-breaking Dirichlet-process prior -- and, as a theory-backed alternative, a sparse overfitted finite Dirichlet -- so that the number of occupied components adapts to the data while every update remains a closed-form coordinate-ascent step; a natural-gradient stochastic variant makes the per-step cost independent of the number of points. We give an exact monotonicity guarantee, a rigorous truncation-error bound correcting an anti-conservative large-$α$ approximation in common use, and an honest account of what the fitted number of components estimates. Empirically: (i) the effective complexity $\hat{K}$ adapts to scene complexity and recovers the true $K$ within $\pm 1$ on well-separated synthetic data with regime-appropriate concentration; (ii) a deconfounded comparison shows the DP prior's contribution is complexity selection, not per-component efficiency -- converged DP fits exceed single-pass fixed-$K$ VBGS by +2.7 dB at matched budgets yet tie an equally converged fixed-$K$ baseline, and on 3D scenes DP-Splat matches or exceeds VBGS's held-out color prediction with 5.9-7.6x fewer components; (iii) the posterior-predictive color variance is well calibrated on model-matched synthetic data; and (iv) the ordering suggested by exact-posterior asymptotics reverses under mean-field coordinate ascent: the DP prior resists over-splitting while the sparse finite mixture saturates its truncation, a gap between variational practice and posterior asymptotics documented across three orders of magnitude in $N$.

Scalable 3D Gaussian Splatting allows one scene representation to serve different Gaussian-count budgets, yet its quality-budget curve may lag behind models optimized separately for each budget. Reducing the number of Gaussians changes both the selected members and the reconstruction tasks carried by the survivors; parameters inherited from a high-budget model may fit a low-budget representation poorly. We propose ParetoGS, which describes member changes and parameter evolution with a small set of adapted budget anchors and decodes intermediate budgets without separate optimization at every requested count. ParetoGS alternates pruning and fixed-member adaptation to build nested anchors with persistent identities, and encodes their parameter changes relative to the full model in a compact residual atlas. At decoding, it interpolates the states of shared members and gradually introduces the rendering contributions of new members, connecting sparse anchors into a continuous-budget representation. Across 13 scenes, ParetoGS attains better average PSNR, SSIM, and LPIPS with fewer Gaussians than the compared prefix methods at 10% of each method's own full model. From a shared full model, it also outperforms FlexGS-imp at its trained 1%, 5%, and 10% budgets and NanoGS-imp at the 1% and 0.1% budgets. On Garden, its non-anchor quality approaches an empirical reference from independently optimized GNS models at higher retention ratios and exceeds it at some lower-budget points. Across 13 scenes, encoding reduces mean additional state from 390.0 to 85.7 MB with an average PSNR change of 0.01 dB. Project page: https://xiaobin2001.github.io/ParetoGS-Web/

2D Gaussian Splatting is an attractive direction for image representation due to its explicit formulation, fast rasterization, and favorable decoding efficiency. The representation quality of this paradigm depends on the proper allocation of Gaussian capacity to the demanding regions. However, existing methods fail to allocate Gaussian capacity efficiently during optimization: under-reconstructed content is often refined in a fragmented pixel-wise manner, while neighboring optimized Gaussians with similar attributes are redundantly retained. This inefficiency motivates the need for a density control framework that jointly addresses insufficient allocation in under-reconstructed regions and redundant allocation in over-reconstructed regions. Our key insight is that this framework should exploit two complementary forms of locality: the local continuity of reconstruction errors in image space for improved Gaussian allocation, and the local similarity of neighboring Gaussians in Gaussian space for redundant elimination. Based on this insight, we propose Locality-Aware Density Control (LocoADC), a plug-and-play framework that improves Gaussian capacity utilization through Region-wise Gaussian Densification (RGD) and Similarity-Driven Gaussian Merging (SDGM) strategies, together with a local color consistency constraint for more reliable merging. Extensive experiments on diverse datasets show that LocoADC consistently improves multiple baselines by enabling more effective local Gaussian allocation, including a 2.93 dB PSNR gain over GI on the CLIC dataset under the same 30k Gaussian budget. Code is available at: https://github.com/ChenJiaCong-1005/LocoADC.