1. A computer implemented image processing method for an image processing apparatus that generates an output image having a resolution the same as or higher than that of an original image, the image processing method comprising: converting, by a computer, the resolution of the original image into the same resolution as the output image so as to generate an output resolution image; converting, by a computer, the resolution of the original image into a resolution different from that of the output image so as to generate an intermediate resolution image; detecting, by a computer, a plurality of similar areas, in a block in the intermediate resolution image corresponding to a predetermined partial area in the output resolution image, that resemble the partial area, and generating similarity information including a position of each of the plurality of similar areas in the intermediate resolution image and a weight of the position; generating, by a computer, a texture image by combining high-frequency components of the intermediate resolution image at the position indicated in the similarity information in accordance with the weight indicated in the similarity information; and blending, by a computer, the output resolution image and the texture image so as to generate the output image.