Introduction

Given a scalar field φ : Rd → R and a constant σ ∈ R, the set {x : φ(x) = σ} is called a level set1 of φ. We use the notation φ−1(σ) to represent the level set {x : φ(x) = σ}. If φ is a continuous function, then the level set φ−1(σ) separates Rd into two sets of points, those with scalar value above σ and those with scalar value below σ.