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 first structure component and a first texture component from the original image obtained by the obtainment section; an intermediate image generating section to generate a second structure component and a second texture component by magnifying each of the first structure component and the first texture component of the original image by an intermediate magnification ratio smaller than the final magnification ratio, and to synthesize the second structure component and the second texture component to generate an intermediately magnified image; a second separation section to separate a third structure component from the intermediately magnified image generated by the intermediate image generating section; a structure magnifying section to magnify the third structure component 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 first texture component 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.