1. An image processing apparatus comprising: a periodicity determining unit configured 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 configured to generate a pixel value of a pixel using a first interpolation method; a second pixel value generating unit configured to generate a pixel value of a pixel using a second interpolation method different from the first interpolation method; a control unit configured 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 configured 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 at least one of: a cycle estimating unit configured to estimate, using pixel values of respective pixels within the image region including the target pixel, a variation cycle of the pixel values; and a partial region periodicity determining unit configured to determine whether each of regions positioned at left and right sides of the target pixel is the periodic region, and wherein at least one of the first and second pixel value generating units generates the pixel value of the target pixel using at least one of the variation cycle of the pixel values estimated by the cycle estimating unit and the determination result determined by the partial region periodicity determining unit.