Thanks to its Bargmann representation, a Gaussian STFT can be factorized so as to be described by its zeros. This paves the way for a new approach that exploits the (usually ignored) zeros of the transform. Zeros can serve as centers for Voronoi cells whose statistics is investigated in terms of density, area, and shape. They can also be connected via a Delaunay triangulation, whose characterization in the noise-only situation permits, a contrario, to identify signals embedded in noise from “silent” points.