  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. We consider the new algorithms as
alternatives to the Subspace Constraint Mean Shift (SCMS) algorithm that do not
suffer from a shortcoming of the SCMS that is also revealed in this paper.
