1. An image processing apparatus comprising: a processor; and a memory storing computer readable code that, when executed, causes the processor to: calculate filtering coefficients for each of sample points in several of a plurality of first areas of an image, the image being partitioned into the plurality of first areas, the image being partitioned differently into a plurality of second areas, one of the plurality of second areas being enclosed by the sample points in the several of the plurality of first areas; calculate a convoluted image of the one of the plurality of second areas using the filtering coefficients calculated for a corresponding one of the sample points, the calculation of a convoluted image being executed repeatedly for all the sample points which enclose the one of the plurality of second areas; move pixels at a same position in convoluted images of the one of the plurality of second areas to positions of the sample points in the several of the plurality of first areas, respectively; and interpolate a pixel in the one of the plurality of second areas using the pixels moved to the positions of the sample points, by bilinear interpolation.