1. An image processor comprising: an image input unit configured to input a multiple image including superimposed images, wherein the superimposed images comprise images of a subject which are superimposed on each other; a frequency transformation unit configured to perform frequency transformation processing with respect to the input multiple image; and an inter-superimposed-image displacement calculation unit configured to calculate a displacement amount between the images forming the superimposed images included in the input multiple image by using a frequency-transformed image subjected to the frequency transformation processing; wherein the inter-superimposed-image displacement calculation unit converts a length of one cycle of a waveform specified by a power spectrum of the frequency-transformed image into the displacement amount between the images; and wherein the inter-superimposed-image displacement calculation unit measures a cyclic structure of a sinusoidal wave represented by the power spectrum and converts a length of one cycle of the sinusoidal wave specified by the measured cyclic structure into the displacement amount between the images.