We propose a new spatio-temporal autologistic centered model for binary data on a lattice. Centering allows the self-regression coefficients to be interpreted by separating the large-scale structure from the small-scale structure. One of the coefficients determines the overall level (or average) of the process, the second determines the spatial autocorrelation. We discuss the existence of the joint distribution of the process and carry out numerical studies to highlight the interest of this type of centering. We suggest using the estimator that maximises the Pseudo Likelihood (denoted Maximum Pseudo Likelihood Estimator (MPLE) in the following) and we give a method for choosing the neighbourhood structure. We run simulations studies that show that the estimation method and model selection method work well. The method is applied to model and fit epidemiological data on Esca disease in a vineyard in the Bordeaux region.