Incremental Noising and its Fractal Behavior
This work addresses a theoretical problem in shape analysis, but it appears incremental as it builds on existing noising concepts.
The paper investigates incremental noising as an extension of noising for global methods in curvature estimation and vertex localization, revealing a surprising connection to progressive smoothing through fractal and space-filling properties.
This manuscript is about further elucidating the concept of noising. The concept of noising first appeared in \cite{CVPR14}, in the context of curvature estimation and vertex localization on planar shapes. There are indications that noising can play for global methods the role smoothing plays for local methods in this task. This manuscript is about investigating this claim by introducing incremental noising, in a recursive deterministic manner, analogous to how smoothing is extended to progressive smoothing in similar tasks. As investigating the properties and behavior of incremental noising is the purpose of this manuscript, a surprising connection between incremental noising and progressive smoothing is revealed by the experiments. To explain this phenomenon, the fractal and the space filling properties of the two methods respectively, are considered in a unifying context.