In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas-liquid two-phase flows through geometrical variables. The contribution is twofold. First it participates in the theoretical design of a unified reduced-order model for the description of two regimes: a disperse phase in a carrier fluid and two separated phases. The first idea is to propose a statistical description of the interface relying on geometrical properties such as the mean and Gauss curvatures and define a Surface Density Function (SDF). The second main idea consists in using such a formalism in the disperse case, where a clear link is proposed between local statistics of the interface and the statistics on objects, such as the number density function in Williams-Boltzmann equation for droplets. This makes essential the use of topolog-ical invariants in geometry through the Gauss-Bonnet formula and allows to include the works conducted on sprays of spherical droplets. It yields a statistical treatment of populations of non-spherical objects such as ligaments, as long as they are home-omorphic to a sphere. Second, it provides an original angle and algorithm in order to build statistics from DNS data of interfacial flows. From the theoretical approach, we identify a kernel for the spatial averaging of geometrical quantities preserving the topological invariants. Coupled to a new algorithm for the evaluation of curvatures and surface that preserves these invariants, we analyze two sets of DNS results conducted with the ARCHER code from CORIA with and without topological changes and assess the approach.