Further, in a case of an image, different from sound, a digital image includes a step edge or the like in which a pixel value rapidly changes. In this case, a high frequency component exceeding a sampling theorem may be generated. When a digital image is shifted only by half a pixel, pixel values of respective processed pixels are obtained based on an average value or the like of the pixel values of peripheral pixels before the processing, thereby causing deterioration of the image quality due to occurrence of blurring or the like. That is, the digital image is not shift-invariant, different from digital sound.

• Patent Literature 1: Japanese Patent Application Laid-open No. 2015-188738
• Patent Literature 2: Japanese Patent Application Laid-open No. 2012-063945

However, it is desired to realize lossless free deformation including rotation with an arbitrary angle or shifting with an arbitrary distance with respect to a digital image.

The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a computer program, an image processing method, and an image processing apparatus that can avoid deterioration due to free deformation with respect to a digital image.