Given a sequence of tasks T subject to precedence constraints between adjacent tasks, and given a set of fixed intervals I, the TaskIntersection (T,I,o,inter) constraint restricts the overall intersection of the tasks of T with the fixed intervals of I to be greater than or equal (o= ‘≥’) or less than or equal (o= ‘≤’) to a given limit inter. We provide a bound(ℤ)-consistent cost filtering algorithm wrt the starts and the ends of the tasks for the TaskIntersection constraint and evaluate the constraint on the video summarisation problem.