柔性各向异性图在可微分图像表征中的应用

摘要

我们提出软各向异性图（SAD）——一种由图像平面中自适应站点集合参数化的显式可微图像表示方法。在SAD中，每个站点定义了一个各向异性度量与加性加权距离评分，我们通过每个像素点对应的前K个站点子集进行softmax混合来计算像素颜色。该方法通过可学习的站点温度系数，诱导出软各向异性加权Voronoi划分（即阿波罗尼奥斯图），在保持信息梯度的同时形成清晰的内容对齐边界与显式归属关系。这种表述通过维护每个查询点的前K映射（该映射在相同着色评分下近似最近邻），实现了GPU友好的固定尺寸局部计算，从而达成高效渲染。我们采用受跳变扩散算法启发的Top-K传播方案更新该列表，并辅以随机注入机制确保概率性全局覆盖。训练过程采用GPU优先流程，包含梯度加权初始化、Adam优化器以及通过稠密化与剪枝实现的自适应预算控制。在标准测试集上，SAD在相同码率下持续超越Image-GS和Instant-NGP：在Kodak数据集上以2.2秒编码时间（Image-GS需28秒）达到46.0 dB PSNR，并实现比现有最优基线快4-19倍的端到端训练速度。我们通过展示SAD在正逆问题可微管道中的无缝集成、快速随机访问效率及紧凑存储优势，验证了其有效性。

English

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.

柔性各向异性图在可微分图像表征中的应用

Soft Anisotropic Diagrams for Differentiable Image Representation

摘要

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