1. An information processing apparatus comprising: a display unit configured to display an object on a display screen; a first detecting unit configured to detect a two-dimensional contact position of an operator's pointer on the display screen; a second detecting unit configured to detect a three-dimensional position of the operator's pointer in three-dimensional space above the display screen; and a control device coupled with said display unit, said first detection unit and said second detection unit, wherein said control device causes said display unit to display at least one selectable object on the display screen; specifies, when said first detecting unit detects contact on the display screen, an object selected by the operator's pointer based on the two-dimensional contact position detected by said first detecting unit, and determines, among pointers in the three-dimensional space detected by said second detecting unit, one pointer which is closest to the two-dimensional contact position detected by said first detecting unit, as a pointer to be tracked by said second detecting unit for determining a three-dimensional gesture for designating processing on the specified object.