In this paper we derive a Maximum Likelihood (ML) framework for photon counting-based fluorescence lifetime estimation in Fluorescence Lifetime Imaging Microscopy (FLIM) from the biophysical phenomenon and instrument models. Data collected at a given pixel consist of photon counts exponentially decreasing along time and are assumed to follow Poisson statistics. Both pointwise approaches and a neighborhood-wise approach are proposed to take explicitly into account the spatial correlation of data. Evaluations and comparisons are presented on simulated as well as on experimental biological image data.