1. An interactive projector that projects a projected screen on a screen surface and that is capable of receiving an instruction of a user to the projected screen with a pointing element, comprising: an imaging device adapted to take a taken image of an area of the projected screen including the pointing element; and at least one processor that executes one or more programs stored in a non-transitory computer-readable storage medium to realize one or more functions of: a correlation value calculation section adapted to calculate a plurality of first correlation values for each of a plurality of pixels of the taken image by comparing each of a plurality of template images different from each other to the taken image pixel by pixel, such that each first correlation value for each pixel corresponds to the comparison between the taken image and one of the plurality of template images; a correlation value map generation section adapted to calculate a plurality of correlation value sums, each corresponding to one pixel of the plurality of pixels, by adding together the plurality of first correlation values calculated for the pixel, and generate a correlation value map representing the correlation value sums for each pixel; and a pointing element detection section adapted to extract a high correlation value area which includes pixels having correlation value sums equal to or higher than a predetermined threshold value in the correlation value map, and calculate a centroid of the correlation value sums 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.