Ridges of Functions Defined on Manifolds

Abstract

In Section 5.1 we apply the definitions of Chapter 4 to finding height ridges of functions defined on manifolds. The first case is simplest where we construct 1dimensional ridges of a function defined on a 2—dimensional surface embedded in 1R³. The second case is the most general where we construct d—dimensional ridges of a function defined on an n—dimensional manifold embedded in IR^P. Section 5.2 provides an alternative definition for ridges based on principal curvatures and principal directions. Section 5.3 discusses a ridge definition which is an application of the definition of Section 5.2 to level sets.