Background modeling is a core task of video-based surveillance systems used to facilitate the online analysis of real-world scenes. Nowadays, GMM-based background modeling approaches are widely used, and several versions have been proposed to improve the original one proposed by Stauffer and Grimson. Nonetheless, the cost function employed to update the GMM weight parameters has not received major changes and is still set by means of a single binary reference, which mostly leads to noisy foreground masks when the ownership of a pixel to the background model is uncertain. To cope with this issue, we propose a cost function based on Euclidean divergence, providing nonlinear smoothness to the background modeling process. Achieved results over well-known datasets show that the proposed cost function supports the foreground/background discrimination, reducing the number of false positives, especially, in highly dynamical scenarios