1. An interactive projector capable of receiving an instruction of a user to a projected screen with a pointing element, comprising: a projection section adapted to project the projected screen on a screen surface; an imaging section adapted to take an image of an area of the projected screen; a correlation value calculation section adapted to calculate a correlation value by a pixel between each of template images different from each other used to detect the pointing element and a taken image taken by the imaging section and including the pointing element using the template images to generate a first correlation value for each of the template images; a correlation value map generation section adapted to generate a correlation value map representing the correlation values between the plurality of template images and the taken image based on the plurality of first correlation values generated for the respective template images; and a pointing element detection section adapted to extract a high correlation value area having the correlation value equal to or higher than a predetermined threshold value in the correlation value map, and calculate a centroid of the correlation values in the high correlation value area with an accuracy corresponding to a value smaller than one pixel to thereby detect a tip position of the pointing element based on the centroid.