This paper proposes a framework for tracking multiple fluorescent objects in 2D + time video-microscopy. We present a novel batch-processing track-before-detect multiple object tracking approach based on a spatio-temporal marked point process model of ellipses. Our approach takes into account events such as births, deaths, splits and merges of objects which are motivated by the biological and physical considerations. We show the performance of the proposed model on synthetic biological data and a real total internal reflection fluorescence microscopy (TIRF) image sequence.