The mathematics of multiple object tracking: from proportions correct to number of objects tracked

This paper examines the relation between proportions correct responses and the number of items tracked in multiple object tracking (MOT). It analyses two of the principle methods used in MOT. The mark all method, where the participants have to mark all the items, is shown to be equivalent to sampling without replacement. For the probe one method, where participants have to indicate whether a particular item belongs to the target set, formulas are derived as well. The paper shows that it is not possible to determine the tracked number of target items (m) and distractor items (v) from the proportions correct answers when employing only one of these two methods. A combination of the mark all and probe one methods does not yield a unique relation between the proportions correct and m and v either, because of the interchangeability between tracking targets and tracking distractors.