Fast and exact visibility on digitized shapes and application to saliency-aware normal estimation

2026-03-12

AI Summary

This work addresses the challenges of accuracy and efficiency in visibility computation and normal vector estimation for digital geometry by introducing a novel representation of digital shapes based on integer interval lists. The proposed method enables, for the first time, the efficient and exact construction of complete visibility graphs, which are subsequently leveraged for robust normal vector field estimation. The framework guarantees algorithmic convergence and high precision while effectively preserving sharp geometric features of the input models. By maintaining salient structural details, the approach achieves a significant improvement in computational efficiency without compromising geometric fidelity.

Technology Category

• Computer Vision: Other Foundations of Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Security and Privacy: Data transparency and provenance

Abstract

Computing visibility on a geometric object requires heavy computations since it requires to identify pairs of points that are visible to each other, i.e. there is a straight segment joining them that stays in the close vicinity of the object boundary. We propose to exploit a specic representation of digital sets based on lists of integral intervals in order to compute eciently the complete visibility graph between lattice points of the digital shape. As a quite direct application, we show then how we can use visibility to estimate the normal vector eld of a digital shape in an accurate and convergent manner while staying aware of the salient and sharp features of the shape.

Problem

• visibility
• digital shape
• normal estimation
• saliency-aware
• visibility graph

Innovation

• visibility graph
• digital shape
• integral intervals
• normal estimation
• saliency-aware