Locality-Aware Density Control for Efficient Gaussian-based Image Representation

3D Gaussian Splatting has emerged as a powerful scene representation for real-time novel-view synthesis. However, its standard adaptive density control relies on screen-space positional gradients, which do not distinguish between geometric misplacement and frequency aliasing, often leading to either over-blurred high-frequency textures or inefficient over-densification. We present a structure-aware densification framework. Our key insight is that the decision to subdivide a Gaussian should be driven by an explicit comparison between its projected screen-space extent and the local structure of the texture it seeks to represent. We introduce a multi-scale frequency analysis combining structure tensors with Laplacian scale space analysis to estimate the dominant frequency at each pixel, enabling robust supervision across varying texture scales. Based on this analysis, we define $η$, a per-Gaussian, per-axis frequency violation metric that indicates when a primitive may be under-resolving local texture details. Unlike methods that perform isotropic splitting (e.g., splitting each Gaussian into two smaller ones with uniform shape), our approach performs anisotropic splitting. For each axis with high $η$, we compute a split factor to better resolve the local frequency content. We further introduce a multiview consistency criterion that aggregates $η$ observations across multiple views. By performing densification early and faster, we skip the lengthy iterative densification phases required by baseline methods and achieve significantly faster convergence. Experiments on standard benchmarks demonstrate that our method also achieves superior reconstruction quality, particularly in high-frequency regions.

3D Gaussian Splatting (3DGS) achieves high-fidelity novel view synthesis in real-time; however its training efficiency and representation compactness are hindered by excessive primitive proliferation. To address this challenge, we formulate the structural evolution of 3DGS as a global budget-constrained optimization problem and derive an optimality condition, which requires the marginal utility of structural resources to be balanced across spatial regions under a finite primitive budget. Based on this formulation, we propose SPARE-GS, a general plug-and-play framework that dynamically aligns the distribution of 3D Gaussian primitives with regional representational demand. SPARE-GS estimates capacity-normalized regional demand, assigns adaptive target quotas, and uses regional budget deviations to coordinate densification, pruning and adaptive termination toward a more balanced structural allocation. Extensive experiments across standard, accelerated, and structure-enhanced 3DGS pipelines demonstrate that SPARE-GS reduces the Gaussian count and training time by an average of 30.38% and 23.81%, respectively, while improving the average PSNR. Moreover, the resulting compact representations reduce downstream processing time and improve the rate-distortion performance of diverse compression and pruning methods, demonstrating the broad applicability of global structural budget regulation.

2D Gaussian splatting provides an efficient explicit representation for image reconstruction, but existing methods still require costly per-image iterative optimization or rely on handcrafted priors for primitive allocation. We present AIR, a self-supervised feed-forward framework that amortizes iterative Gaussian fitting into a single network pass, eliminating per-image test-time optimization. AIR adopts a stage-wise residual architecture that progressively predicts additional Gaussian primitives from reconstruction residuals, together with an explicit Stage Control mechanism that activates new primitives only in under-reconstructed regions. A Predict--Optimize--Distill training strategy stabilizes multi-stage prediction by distilling short-horizon optimized Gaussian increments back into the predictor. The stabilized predictor is then jointly finetuned across stages and equipped with an image-adaptive quantizer for compact Gaussian storage. Experiments on Kodak and DIV2K show that AIR achieves better reconstruction quality than representative Gaussian-based baselines while reducing encoding time to 160--300,ms. Code: https://github.com/whoiszzj/AIR.git