1. An image processing apparatus comprising: a periodicity determining unit to determine whether an image region including a target pixel whose pixel value is to be interpolated is a periodic region in which pixel values vary periodically; a first pixel value generating unit to generate a pixel value of a pixel using a first interpolation method; a second pixel value generating unit to generate a pixel value of a pixel using a second interpolation method different from the first interpolation method; a control unit to determine, based on the determination result obtained by the periodicity determining unit, which one of the first and second pixel value generating units is to be used for generating a pixel value of the target pixel; and a pixel value inserting unit to insert, to the target pixel, the pixel value generated by one of the first and second pixel value generating units determined by the control unit, wherein the periodicity determining unit includes a cycle estimating unit to estimate, using pixel values of respective pixels within the image region including the target pixel, a variation cycle of the pixel values, wherein at least one of the first and second pixel value generating units generates the pixel value of the target pixel using the variation cycle of the pixel values estimated by the cycle estimating unit, and wherein the first pixel value generating unit determines a size of a template used in a pattern matching method, based on the variation cycle of the pixel values estimated by the cycle estimating unit.