We introduce Soft Anisotropic Diagrams (SAD), an explicit and differentiable image representation parameterized by a set of adaptive sites in the image plane. In SAD, each site specifies an anisotropic metric and an additively weighted distance score, and we compute pixel colors as a softmax blend over a small per-pixel top-K subset of sites. We induce a soft anisotropic additively weighted Voronoi partition (i.e., an Apollonius diagram) with learnable per-site temperatures, preserving informative gradients while allowing clear, content-aligned boundaries and explicit ownership. Such a formulation enables efficient rendering by maintaining a per-query top-K map that approximates nearest neighbors under the same shading score, allowing GPU-friendly, fixed-size local computation. We update this list using our top-K propagation scheme inspired by jump flooding, augmented with stochastic injection to provide probabilistic global coverage. Training follows a GPU-first pipeline with gradient-weighted initialization, Adam optimization, and adaptive budget control through densification and pruning. Across standard benchmarks, SAD consistently outperforms Image-GS and Instant-NGP at matched bitrate. On Kodak, SAD reaches 46.0 dB PSNR with 2.2 s encoding time (vs. 28 s for Image-GS), and delivers 4-19 times end-to-end training speedups over state-of-the-art baselines. We demonstrate the effectiveness of SAD by showcasing the seamless integration with differentiable pipelines for forward and inverse problems, efficiency of fast random access, and compact storage.
Gaussian Splatting has emerged as a powerful representation for high-quality, real-time 3D scene rendering. While recent works extend Gaussians with learnable textures to enrich visual appearance, existing approaches allocate a fixed square texture per primitive, leading to inefficient memory usage and limited adaptability to scene variability. In this paper, we introduce adaptive anisotropic textured Gaussians (A2TG), a novel representation that generalizes textured Gaussians by equipping each primitive with an anisotropic texture. Our method employs a gradient-guided adaptive rule to jointly determine texture resolution and aspect ratio, enabling non-uniform, detail-aware allocation that aligns with the anisotropic nature of Gaussian splats. This design significantly improves texture efficiency, reducing memory consumption while enhancing image quality. Experiments on multiple benchmark datasets demonstrate that A TG consistently outperforms fixed-texture Gaussian Splatting methods, achieving comparable rendering fidelity with substantially lower memory requirements. Project page: http://github.com/Rickyeeeeee/A2TG.
Adaptive density control in 3D Gaussian Splatting (3DGS) repeatedly grows the Gaussian population through fixed-cardinality random splitting to discover useful scene structure. However, in vanilla 3DGS, its binary split operator requires many densification rounds to expose fine details, making it a bottleneck for efficient training schedules with fewer iterations. We introduce AdpSplit, an error-driven adaptive split operator that determines the number of split children and initializes the child parameters from L1-pixel-error region statistics, enabling fewer densification iterations, thus reduced training time, while preserving the rendering quality of full-schedule training. Across the MipNeRF360, Deep-Blending, and Tanks&Temples datasets, AdpSplit reduces the training time of multiple accelerated 3DGS pipelines by 9.2%-22.3% as a simple drop-in replacement for the standard split operator. With FastGS, AdpSplit matches the full-schedule PSNR on MipNeRF360 while reducing training time by 16.4%, corresponding to a 12.6x acceleration over vanilla 3DGS.
Gradient-based saliency methods reveal which input features most influence a neural network's output, and are a standard tool for model interpretability. We observe that differentiable renderers, which are conventionally used for parameter optimisation, produce an analogous form of saliency: given any scalar metric evaluated on a rendered image, a single reverse-mode differentiation pass yields per-parameter gradients that identify which scene elements most influence the metric. We call these gradient fields metric saliency maps. Unlike neural saliency, which propagates attribution through learned weights, metric saliency propagates through the image formation process itself, including multi-bounce light transport, capturing parameter dependencies that are semi-opaque to manual inspection. We compute metric saliency maps for qualitatively different objectives: psychovisual glare indices, mean scene luminance, and neural perceptual scores. The saliency rankings differ substantially across metrics for the same scene, with parameters that dominate one objective being negligible for another. The saliency map is specific to the metric, not an intrinsic property of the scene. Our results suggest that differentiable renderers produce derivative images that are as informative for scene understanding as the primal images they were designed to generate.