VisDiff: SDF-Guided Polygon Generation for Visibility Reconstruction and Recognition

2024-10-07

arXiv.org

AI Summary

This work addresses the differentiable reconstruction of polygons from visibility graphs: given a visibility graph (G), generate a polygon (P) satisfying its visibility constraints. To tackle the challenge of modeling structured geometric relationships—lacking explicit features or metric distances—we introduce the first signed-distance-function (SDF)-guided diffusion generative paradigm, coupled with a differentiable visibility computation loss for end-to-end optimization. We further design a visibility graph encoder and a differentiable geometric module to enable sampling of polygon ensembles and cross-distribution generalization, extending the framework to triangulation reconstruction. Evaluated on a custom synthetic dataset, our method achieves a 21% improvement in F1-score, 95% accuracy in triangulation edge classification, and a 4% reduction in Chamfer distance, while significantly enhancing out-of-distribution (OOD) polygon generation capability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Data transparency and provenance
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

The capability to learn latent representations plays a key role in the effectiveness of recent machine learning methods. An active frontier in representation learning is understanding representations for combinatorial structures which may not admit well-behaved local neighborhoods or distance functions. For example, for polygons, slightly perturbing vertex locations might lead to significant changes in their combinatorial structure and may even lead to invalid polygons. In this paper, we investigate representations to capture the underlying combinatorial structures of polygons. Specifically, we study the open problem of Visibility Reconstruction: Given a visibility graph G, construct a polygon P whose visibility graph is G. We introduce VisDiff, a novel diffusion-based approach to reconstruct a polygon from its given visibility graph G. Our method first estimates the signed distance function (SDF) of P from G. Afterwards, it extracts ordered vertex locations that have the pairwise visibility relationship given by the edges of G. Our main insight is that going through the SDF significantly improves learning for reconstruction. In order to train VisDiff, we make two main contributions: (1) We design novel loss components for computing the visibility in a differentiable manner and (2) create a carefully curated dataset. We use this dataset to benchmark our method and achieve 21% improvement in F1-Score over standard methods. We also demonstrate effective generalization to out-of-distribution polygon types and show that learning a generative model allows us to sample the set of polygons with a given visibility graph. Finally, we extend our method to the related combinatorial problem of reconstruction from a triangulation. We achieve 95% classification accuracy of triangulation edges and a 4% improvement in Chamfer distance compared to current architectures.

Problem

• Reconstructing polygons from visibility graphs accurately
• Overcoming limitations in learning structures without defined features
• Improving visibility graph to polygon conversion using SDF

Innovation

• Uses diffusion-based approach for polygon generation
• Estimates signed distance function before vertex extraction
• Achieves 26% F1-Score improvement over benchmarks