Context. The advent of large scale multi-epoch surveys raises the need for automated light curve (LC) processing. This is particularly true for eclipsing binaries (EBs), which form one of the most populated types of variable objects. The Gaia mission, launched at the end of 2013, is expected to detect of the order of few million EBs over a five-year mission.

Aims. We present an automated procedure to characterize EBs based on the geometric morphology of their LCs with two aims: first to study an ensemble of EBs on a statistical ground without the need to model the binary system, and second to enable the automated identification of EBs that display atypical LCs.

Methods. We modeled the folded LC geometry of EBs using up to two Gaussian functions for the eclipses and a cosine function for any ellipsoidal-like variability that may be present between the eclipses. The procedure is applied to the OGLE-III data set of EBs in the Large Magellanic Cloud (LMC) as a proof of concept. The Bayesian information criterion is used to select the best model among models containing various combinations of those components, as well as to estimate the significance of the components.

Results. Based on the two-Gaussian models, EBs with atypical LC geometries are successfully identified in two diagrams, using the Abbe values of the original and residual folded LCs, and the reduced χ². Cleaning the data set from the atypical cases and further filtering out LCs that contain non-significant eclipse candidates, the ensemble of EBs can be studied on a statistical ground using the two-Gaussian model parameters. For illustrative purposes, we present the distribution of projected eccentricities as a function of orbital period for the OGLE-III set of EBs in the LMC, as well as the distribution of their primary versus secondary eclipse widths.