An automatic flusher employs an infrared-light-type object sensor to provide an output on the basis of which a control circuit decides whether to flush a toilet. After each pulse of transmitted radiation, the control circuit pushes a new entry onto stack if the resultant percentage of reflected radiation differs significantly from the last, and it includes in that entry's direction field an indication of whether the percentage change was positive or negative. Otherwise, the control circuit increments the existing top entry's duration field. From the numbers of entries in a row having a given direction and the sums of the values in their duration fields, the control circuit determines whether a user has approached the facility and then withdrawn from it, and it operates the flusher's valve accordingly.