The goal of the works described in this paper is to improve results produced by an object detector operating independently on each frame of a video document in order to generate a more robust index. Results of the object detector are ”smoothed” along the time dimension using a temporal window. For a given frame, we count the number of occurrences of each object in the previous and next frames, and then only the objects whose number of appearance is above a threshold are validated. In this paper, we present a probabilistic approach for theoretically computing these thresholds. This approach is well suited to limit the number of false alarms provided by the static detector, and its principle of detection generalization also allows some detections that can be missed by the detector.