# Soft Anisotropic Diagrams for Differentiable Image Representation

arXiv: https://arxiv.org/abs/2604.21984 · HTML: https://mlsanity.com/paper/2604.21984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 71 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Builds on (most cited first, 30 of 30)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Variable Bitrate Neural Fields](https://mlsanity.com/paper/2206.07707/) (2022)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [ReLU Fields: The Little Non-linearity That Could](https://mlsanity.com/paper/2205.10824/) (2022)
- [COIN++: Neural Compression Across Modalities](https://mlsanity.com/paper/2201.12904/) (2022)
- [Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field](https://mlsanity.com/paper/2304.11605/) (2023)
- [Image-GS: Content-Adaptive Image Representation via 2D Gaussians](https://mlsanity.com/paper/2407.01866/) (2024)
- [Large Images are Gaussians: High-Quality Large Image Representation with Levels of 2D Gaussian Splatting](https://mlsanity.com/paper/2502.09039/) (2025)
- [Coverage Axis: Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2110.00965/) (2021)
- [Instant GaussianImage: A Generalizable and Self-Adaptive Image Representation via 2D Gaussian Splatting](https://mlsanity.com/paper/2506.23479/) (2025)
- [Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram](https://mlsanity.com/paper/2210.13676/) (2022)
- [Differentiable Surface Triangulation](https://mlsanity.com/paper/2109.10695/) (2021)
- [Spherical Voronoi: Directional Appearance as a Differentiable Partition of the Sphere](https://mlsanity.com/paper/2512.14180/) (2025)
- [VoronoiNet: General Functional Approximators with Local Support](https://mlsanity.com/paper/1912.03629/) (2019)
- [Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2401.12946/) (2024)
- [Tetrahedron Splatting for 3D Generation](https://mlsanity.com/paper/2406.01579/) (2024)
- [Medial Skeletal Diagram: A Generalized Medial Axis Approach for 3D Shape Representation](https://mlsanity.com/paper/2310.09395/) (2023)
- [MATTopo: Topology-preserving Medial Axis Transform with Restricted Power Diagram](https://mlsanity.com/paper/2403.18761/) (2024)
- [Cellular Topology Optimization on Differentiable Voronoi Diagrams](https://mlsanity.com/paper/2204.10313/) (2022)
- [2D Neural Fields with Learned Discontinuities](https://mlsanity.com/paper/2408.00771/) (2024)
- [Fast 2DGS: Efficient Image Representation with Deep Gaussian Prior](https://mlsanity.com/paper/2512.12774/) (2025)

## Abstract (arXiv)

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.