From ex(p) to poly: Gaussian Splatting with Polynomial Kernels

Recent advancements in 3D Gaussian Splatting (3DGS) have shifted the focus toward balancing reconstruction fidelity with computational efficiency. In this work, we propose ImprovedGS+, a high-performance, low-level reinvention of the ImprovedGS strategy, implemented natively within the LichtFeld-Studio framework. By transitioning from high-level Python logic to hardware-optimized C++/CUDA kernels, we achieve a significant reduction in host-device synchronization and training latency. Our implementation introduces a Long-Axis-Split (LAS) CUDA kernel, custom Laplacian-based importance kernels with Non-Maximum Suppression (NMS) for edge scores, and an adaptive Exponential Scale Scheduler. Experimental results on the Mip-NeRF360 dataset demonstrate that ImprovedGS+ establishes a new Pareto-optimal front for scene reconstruction. Our 1M-budget variant outperforms the state-of-the-art MCMC baseline by achieving a 26.8% reduction in training time (saving 17 minutes per session) and utilizing 13.3% fewer Gaussians while maintaining superior visual quality. Furthermore, our full variant demonstrates a 1.28 dB PSNR increase over the ADC baseline with a 38.4% reduction in parametric complexity. These results validate ImprovedGS+ as a scalable, high-speed solution that upholds the core pillars of Speed, Quality, and Usability within the LichtFeld-Studio ecosystem.

3D Gaussian Splatting (3DGS) achieves state-of-the-art rendering quality at real-time speeds but suffers from "model bloat" - a large number of redundant, low-opacity Gaussians that inflate memory usage and training costs. This inefficiency stems from the standard "densify-then-prune" paradigm, which expands the model aggressively before relying on pruning to achieve compactness. To mitigate this problem, we present an efficient training framework that builds an intrinsically compact representation, replacing the conventional densify-then-prune cycle. Our method leverages a synergistic design: an L2 reconstruction loss to provide error-proportional gradients that stabilize optimization, and a novel Polarized Opacity Prior (POP) to actively manage the Gaussian population. POP steers informative primitives toward full opacity and uninformative ones toward transparency, enabling natural pruning and accelerating rendering through Early Ray Termination. Experiments on three public datasets demonstrate that our approach consistently achieves accelerated 3DGS training with significantly fewer Gaussians while maintaining comparable visual reconstruction quality. These results show that the proposed framework provides a simple and effective path toward fast and inherently compact 3DGS training.

3D Gaussian Splatting (3DGS) has significantly advanced real-time novel view synthesis by representing scenes as dense collections of anisotropic 3D Gaussian primitives. However, the irregular spatial distribution of Gaussians often leads to poor GPU utilization, as warp divergence and redundant computation degrade rendering performance. To address this, we present Local-GS, a warp-coherent rendering paradigm that, organizes Gaussian primitives with respect to SIMT (Single Instruction, Multiple Threads) execution boundaries rather than scene geometry. Specifically, we propose three warp-coherent stages: a hoisting stage that precomputes shared parameters at tile level, a culling stage that discards warps with no contribution, and a blending stage that replaces per-pixel branching with a uniform instruction stream. Across extensive benchmarks on multiple datasets, Local-GS improves efficiency without compromising quality. As a plug-and-play optimization, it provides additional performance gains to all tested baselines, culminating in a $7.76\times$ speedup on Deep Blending scenes.