Interpretable flow improves polygon visibility reconstruction and analysis
VisFlow: Interpretable Flow Matching for Visibility Reconstruction, Characterization, and Recognition
Computational GeometryComputer Vision and Pattern Recognition
Summary
Polygons are shapes defined by connected points, but small changes in their points can cause big differences in how parts of the shape see each other, which is called visibility. The authors found that existing methods either focus on the points or use indirect shapes that don’t clearly show how the polygon changes. They created VisFlow, a new approach that combines smooth shape descriptions with clear step-by-step polygon changes to better represent visibility. This method reconstructs polygons and identifies all possible shapes matching visibility data more accurately than previous techniques.
What this means in practice
- •For computer graphics developers: Generate precise polygon shapes from visibility information to improve rendering and modeling workflows.
- •For robotics navigation teams: Use polygon visibility reconstructions to better understand environments for path planning and obstacle avoidance.
Authors
Rahul Moorthy, Volkan Isler
Abstract
Methods for learning continuous representations, such as latent manifolds, are fundamental and ubiquitous in modern machine learning. Yet many geometric objects combine continuous shape information with discrete combinatorial structure. This combination presents a fundamental challenge for representation learning because small geometric perturbations can induce abrupt changes in the underlying discrete representation. As a result, the smoothness assumptions that make continuous representations effective no longer hold. Polygons provide a canonical example. Their vertex locations vary continuously, but infinitesimal changes in geometry can dramatically alter the associated visibility graph. Existing methods address the inverse mapping from visibility graphs to polygon geometry using vertex-, triangulation-, or signed-distance-function (SDF)-based representations. Vertex- and triangulation-based approaches construct polygons through explicit geometric operations. However, they are less effective at modeling the relationship between geometry and visibility. SDF-based approaches capture this relationship more naturally. Their intermediate states, however, do not correspond to explicit stages of polygon construction. We present VisFlow, a novel, interpretable flow formulation that combines continuous SDF representations with explicit polygon evolution. We evaluate VisFlow on Visibility Reconstruction and Visibility Characterization. Visibility Reconstruction generates one polygon consistent with a visibility graph (G), while Visibility Characterization characterizes all such polygons. VisFlow maintains 20% more visibility relations on Visibility Reconstruction and improves coverage by 30% on Visibility Characterization compared to state-of-the-art methods.