1. An image analysis device comprising: a first point detection unit that moves an original image including a designated image region which is rotationally symmetric with respect to a first point relative to a reference image which is obtained by rotating the original image about a second point on the original image, calculates a correlation value between the original image and the reference image at each relative position, and detects the position of the first point in the original image, according to a geometric model indicating a relative positional relationship between the first point and the second point in the original image, on the basis of the amount of rotation of the reference image about the second point at a relative position between the original image and the reference image where the correlation value is the maximum and a vector indicating a deviation between the second point of the original image and the second point of the reference image; and a region specifying unit that specifies a range of the designated image region in the original image, based on the detected position of the first point and a distribution of brightness values of pixels in the original image.