Keywords: ridges, filamentary structures, local PCA, kernel density estimation, geometric features
Filamentary structures, or ridges, are manifolds with higher density than surrounding areas. They have been used to model objects such as the cosmic web, fingerprints, road systems and blood vessels. In this talk I will describe a new algorithm using nonparametric methods to extract such filamentary structures from point clouds. The algorithm is driven by a measure of “ridgeness” based on the mathematical definition of ridges. One important ingredient in the algorithm is the close connection between local PCA and the Hessian of a density function, the theoretical foundation of which will be discussed.