Incremental Noising and its Fractal Behavior

TL;DR

This paper explores incremental noising, revealing its fractal behavior and connection to progressive smoothing, and investigates its potential role in shape analysis tasks.

Contribution

It introduces the concept of incremental noising, demonstrating its fractal properties and its relation to progressive smoothing in shape analysis.

Findings

Incremental noising exhibits fractal and space-filling properties.

A surprising connection between noising and smoothing is experimentally demonstrated.

Fractal analysis unifies the behaviors of noising and smoothing.

Abstract

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.