1. An image processing apparatus comprising: a color separating unit configured to separate a color image into a plurality of color components to generate images of respective colors; a periodicity determining unit configured to determine, for each of the images of the respective colors, 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 pixel values of the respective colors of a pixel using a first interpolation method; a second pixel value generating unit configured to generate pixel values of the respective colors 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 pixel values of the respective colors of the target pixel; and a pixel value combining unit configured to combine candidate pixel values which are the pixel values of the respective colors of the target pixel and which are generated by the first or second pixel value generating unit determined by the control unit to calculate a combined pixel value for interpolating the target pixel.