Excursion sets of a sample signal-to-noise map for a 3.3 × 3.3 deg² field of SLICS for nine values t₁, …, t₉. The solid magenta ellipse highlights a connected component corresponding to a minimum of the signal-to-noise map; the solid orange and red ellipses each highlight a hole corresponding to a maximum. The dashed ellipses indicate the position of the features before their birth and after their death. The magenta feature is born at t₂ and dies at t₄ after being absorbed by older features that were born in t₁. This lifeline is described by the interval [t₂, t₄) in Dgm(H₀(𝕏)). Both the red and orange features are born at t₅. The orange one dies at t₇, while the red one, which corresponds to a sharper peak, persists longer and dies at t₉. Hence, they give rise to intervals [t₅, t₇) and [t₅, t₉) in Dgm(H₁(𝕏)).