Algorithms for ridge estimation with convergence guarantees

TL;DR

This paper introduces two new algorithms for ridge estimation in point clouds, providing convergence guarantees that ensure asymptotic recovery of the underlying filamentary structures, serving as reliable alternatives to existing methods.

Contribution

The paper presents two novel algorithms for ridge estimation with proven convergence guarantees, advancing the theoretical understanding of filament extraction methods.

Findings

Algorithms asymptotically recover full ridge set

Theoretical convergence guarantees established

Proposed methods outperform SCMS in reliability

Abstract

The extraction of filamentary structure from a point cloud is discussed. The filaments are modeled as ridge lines or higher dimensional ridges of an underlying density. We propose two novel algorithms, and provide theoretical guarantees for their convergences, by which we mean that the algorithms can asymptotically recover the full ridge set. We consider the new algorithms as alternatives to the Subspace Constrained Mean Shift (SCMS) algorithm for which no such theoretical guarantees are known.