Global Vertices and the Noising Paradox

TL;DR

This paper introduces a global perspective on shape vertices, revealing that noise can paradoxically improve vertex localization, supported by theoretical analysis and experimental validation.

Contribution

It presents a novel global approach to vertex detection that leverages noise to enhance localization accuracy, challenging traditional curvature-based methods.

Findings

Noise can improve vertex localization in certain cases.

Global descriptors combined with noise aid in detecting vertices.

Experimental results validate the theoretical advantage of noising.

Abstract

A theoretical and experimental analysis related to the identification of vertices of unknown shapes is presented. Shapes are seen as real functions of their closed boundary. Unlike traditional approaches, which see curvature as the rate of change of the tangent to the curve, an alternative global perspective of curvature is examined providing insight into the process of noise-enabled vertex localization. The analysis leads to a paradox, that certain vertices can be localized better in the presence of noise. The concept of noising is thus considered and a relevant global method for localizing "Global Vertices" is investigated. Theoretical analysis reveals that induced noise can help localizing certain vertices if combined with global descriptors. Experiments with noise and a comparison to localized methods validate the theoretical results.