UV-parameterized Gaussian Splatting (UVGS) maps an unstructured set of 3D Gaussians to a regular UV tensor, enabling compact storage and explicit control of representation capacity. Existing UVGS, however, uses a deterministic spherical pro- jection to assign Gaussians to UV locations. Because this mapping ignores the global Gaussian distribution, it often leaves many UV slots empty while causing frequent collisions in dense regions. We reinterpret UV mapping as a capacity-allocation problem under a fixed UV budget and propose OT-UVGS, a lightweight, separable one-dimensional optimal-transport-inspired mapping that globally couples assignments while preserving the original UVGS representation. The method is implemented with rank-based sorting, has O(N log N) complexity for N Gaussians, and can be used as a drop-in replacement for spherical UVGS. Across 184 object-centric scenes and the Mip-NeRF dataset, OT-UVGS consistently improves peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) under the same UV resolution and per-slot capacity (K=1). These gains are accompanied by substantially better UV utilization, including higher non-empty slot ratios, fewer collisions, and higher Gaussian retention. Our results show that revisiting the mapping alone can unlock a significant fraction of the latent capacity of UVGS.

翻译：UV参数化高斯溅射（UVGS）将无序的三维高斯集合映射为规则UV张量，实现紧凑存储与表示容量的显式控制。然而，现有UVGS采用确定性球面投影将高斯分配至UV位置。由于该映射忽略全局高斯分布，常导致大量UV槽位空置，同时在密集区域引发频繁碰撞。我们将UV映射重新诠释为固定UV预算下的容量分配问题，提出OT-UVGS——一种轻量级、可分离的一维最优传输启发式映射方法，在保持原始UVGS表示的同时实现全局关联分配。该方法基于秩排序实现，对N个高斯具有O(N log N)复杂度，可直接替代球面UVGS。在184个物体中心场景及Mip-NeRF数据集上，在相同UV分辨率与单槽容量（K=1）条件下，OT-UVGS持续提升峰值信噪比（PSNR）、结构相似性（SSIM）及学感知图像块相似度（LPIPS）指标。这些增益伴随着显著的UV利用率提升，包括更高非空槽位比率、更少碰撞及更高高斯保留率。结果表明，仅通过重新审视映射机制即可充分释放UVGS的潜在容量。