Soft Anisotropic Diagrams for Differentiable Image Representation

2026-04-23

AI Summary

This work proposes Soft Anisotropic Diagrams (SAD), a compact image representation that balances structural expressiveness with efficient differentiable optimization. By deploying adaptive sites across the image plane—each endowed with an anisotropic metric and weighted distance scores—SAD introduces, for the first time, a softened variant of anisotropic Apollonius diagrams into a differentiable rendering framework. Pixel colors are synthesized via a differentiable top-k nearest neighbor mechanism combined with softmax-based blending. The method incorporates learnable temperature parameters, gradient-weighted initialization, and dynamic budget control to enable GPU-friendly local computation while preserving sharp boundaries. Experiments demonstrate that SAD achieves 46.0 dB PSNR on the Kodak dataset with only 2.2 seconds of encoding time, significantly outperforming Image-GS (28 seconds) and Instant-NGP, and delivering 4–19× end-to-end training speedup.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• differentiable image representation
• anisotropic diagrams
• Voronoi partition
• image compression
• GPU acceleration

Innovation

• Soft Anisotropic Diagrams
• Differentiable Rendering
• Anisotropic Voronoi Partition
• Top-K Propagation
• GPU-Accelerated Optimization