Soft Anisotropic Diagrams for Differentiable Image Representation

arXiv cs.CV / 4/27/2026

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Key Points

The paper introduces Soft Anisotropic Diagrams (SAD), a fully explicit and differentiable image representation defined by learnable anisotropic sites and an additively weighted distance score.
SAD renders pixel colors via a softmax blend over a small per-pixel top-K subset of sites, forming a soft anisotropic additively weighted Voronoi (Apollonius) partition with learnable temperatures to preserve useful gradients and yield clear, content-aligned boundaries.
It improves efficiency by using a GPU-friendly fixed-size local computation through a per-query top-K map that approximates nearest neighbors under the same shading score, updated with a top-K propagation method inspired by jump flooding plus stochastic injection for wider global coverage.
In experiments, SAD outperforms Image-GS and Instant-NGP at matched bitrate and achieves strong Kodak results (46.0 dB PSNR) with much faster encoding time and reported end-to-end training speedups of 4–19×.
The method is demonstrated as integrating well with differentiable forward and inverse pipelines, while also offering fast random access and compact storage.

Abstract

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.