1. An image processing apparatus for converting an original image stored on a predetermined recording medium into an enlarged image on which enlargement processing has been performed with respect to a reference point, as the center, set within a screen displaying the original image, comprising: a selection processing unit that treats, as a starting point, a coordinate point which is the farthest from the reference point and selects a processing-target pixel from among pixels constituting the enlarged image; a calculation processing unit that calculates a coordinate point of the original image which is mapped to the coordinate point of the processing-target pixel selected by the selection processing unit; a reading processing unit that reads the pixel value of a pixel of the original image from the recording medium in accordance with the coordinate point of the original image calculated by the calculation processing unit; an interpolation processing unit that interpolates the pixel value of the processing-target pixel using the pixel value of the pixel of the original image read by the reading processing unit; and a writing processing unit that writes the pixel value of the processing-target pixel which has been interpolated by the interpolation processing unit into an area, on the recording medium, other than a storage area in which the pixel value of each of pixels of the original image has been stored, the pixels of the original image being positioned at the same coordinate points as pixels of the enlarged image, each of which has not been selected as the processing-target pixel.