Soft Anisotropic Diagrams for Differentiable Image Representation

MIT researchers (Iinbor, Dou, Matusik) have published a paper on Soft Anisotropic Diagrams (SAD), a novel differentiable image representation that outperforms existing methods like Image-GS and Instant-NGP at matched bitrates. SAD parameterizes images with adaptive sites that each define an anisotropic metric and additively weighted distance score. Pixel colors are computed via a softmax blend over a small per-pixel top-K subset of sites, enabling clear, content-aligned boundaries while preserving informative gradients for training. The method induces a soft anisotropic additively weighted Voronoi partition (Apollonius diagram) with learnable per-site temperatures.

On standard benchmarks, SAD achieves 46.0 dB PSNR on Kodak with only 2.2 seconds encoding time, compared to 28 seconds for Image-GS, representing a 4-19x end-to-end training speedup over state-of-the-art baselines. The GPU-first pipeline uses gradient-weighted initialization, Adam optimization, and adaptive budget control through densification and pruning. SAD's top-K propagation scheme, inspired by jump flooding with stochastic injection, provides probabilistic global coverage while maintaining GPU-friendly, fixed-size local computation. The method demonstrates seamless integration with differentiable pipelines for both forward and inverse problems, efficient random access, and compact storage, making it a promising approach for neural rendering, image compression, and computer vision applications.