Multi Target Tracking has many applications such as video surveillance and event recognition among others. In this paper, we present a multi object tracking (MOT) method based on point processes and random finite sets theory. The Probability Hypothesis Density (PHD) filter is a MOT algorithm that deals with missed, false and redundant detections. However, the PHD filter, as well as other conventional tracking-by-detection approaches, requires some sort of pre-processing technique such as non-maximum suppression (NMS) to eliminate redundant detections. In this paper, we show that using NMS is sub-optimal and therefore propose Determinantal Point Processes (DPP) to select the final set of detections based on quality and similarity terms. We conclude that PHD filter-DPP method outperforms PHD filter-NMS.