Global Vertices and the Noising Paradox
This work addresses shape analysis challenges in computer vision or geometry processing, offering a novel insight into noise utilization, though it appears incremental as it builds on existing vertex localization methods.
The paper tackles the problem of vertex localization in unknown shapes by introducing a global perspective on curvature, revealing that noise can paradoxically improve localization for certain vertices when combined with global descriptors, with experimental validation against localized methods.
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.