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

TL;DR

This paper introduces an efficient method for computing exact visibility graphs on digitized shapes using interval-based digital representations, enabling accurate normal estimation that preserves salient features.

Contribution

It presents a novel interval-based digital shape representation for fast, exact visibility computation and applies it to saliency-aware normal estimation.

Findings

Efficient visibility graph computation for digital shapes.

Accurate normal estimation preserving salient features.

Convergent method for shape normal estimation.

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.