Rendering Separoid Information: Rate-Distortion Reconstruction of Convex Apartness Scenes

This paper treats a convex scene as a carrier of discrete relational information: which groups of convex bodies are mutually apart, and which cross. Instead of optimizing for visual fidelity alone, the authors model rendering as an encoder for a separoid table, then decode that structure from the image as if it were a noisy channel.

The practical twist is a rate–distortion framing for “apartness-preserving” rendering. They define a differentiable geometric code length for the scene and a closure-aware distortion term that weights separations by how many downstream consequences they control. A support-function formulation turns separability into a soft directional margin, which lets them estimate a lower bound on apartness mutual information and reason about viewpoint selection.

For developers, the interesting part is less the math jargon and more the design goal: renderings that preserve relational structure, not just appearance. That matters for procedural geometry tools, CAD-like editors, collision/visibility analysis, and any pipeline where the scene’s combinatorial structure is as important as the final image. The paper suggests you can trade a bit of geometric precision for stronger guarantees about recoverable structure.

Their experiments on planar convex scenes are strong: recovery from the apartness table alone reaches 99.9% bit accuracy, and the certificate skeleton already determines the full table. They also show a clean rate–distortion frontier under coordinate quantization, with certificate distortion stricter than plain Hamming error, and report that 48×48...