1. An image processing apparatus, comprising: an obtainment section to obtain an original image; a designation section to designate a final magnification ratio of the original image obtained by the obtainment section; a first separation section to separate a structure component and a texture component from the original image obtained by the obtainment section; an intermediate image generating section to generate magnify each of the structure component and the texture component separated from the original image by the first separation section by an intermediate magnification ratio smaller than the final magnification ratio, and to synthesize the magnified structure component and the magnified texture component to generate an intermediately magnified image; a second separation section to separate a structure component from the intermediately magnified image generated by the intermediate image generating section; a structure magnifying section to magnify the structure component separated from the intermediately magnified image by the second separation section to generate a finally magnified structure component which has the final magnification ratio to the original image in size; a texture magnifying section to magnify the texture component separated from the original image by the first separation section to generate a finally magnified texture component which has the final magnification ratio to the original image in size; and a final image generating section to synthesize the finally magnified structure component and the finally magnified texture component to generate a finally magnified image.