Analysis of Spatially and Temporally Overlapping Events with Application to Image Sequences

Counting spatially and temporally overlapping events in image sequences and estimating their shape-size and duration features are important issues in some applications. We propose a stochastic model, a particular case of the nonisotropic 3D Boolean model, for performing this analysis: the temporal Boolean model. Some probabilistic properties are derived and a methodology for parameter estimation from time-lapse image sequences is proposed using an explicit treatment of the temporal dimension. We estimate the mean number of germs per unit area and time, the mean grain size and the duration distribution. A wide simulation study in order to assess the proposed estimators showed promising results. The model was applied on biological image sequences of in-vivo cells in order to estimate new parameters such as the mean number and duration distribution of endocytic events. Our results show that the proposed temporal Boolean model is effective for obtaining information about dynamic processes which exhibit short-lived, but spatially and temporally overlapping events.