Interval Volumes

The region between two level sets is called an interval volume. Formally, the interval volume for a function φ : R3 → R is defined as

Iφ(σ0, σ1) = {x ∈ R3 : σ0 ≤ φ(x) ≤ σ1}, where σ0, σ1 ∈ R and σ0 < σ1.