1. A directional interpolation method for increasing resolution of an image, the image consisting of pixels arranged in rows and columns, the directional interpolation method adding a plurality of pixels to increase resolution of the image, any of the pixels added being located on a position in the image, the method comprising: a texture analysis step, which obtains a monotone variation area by taking the position as a center, the monotone variation area being a union of same-sized regions where pixels of an upper monotone variation area faces to pixels of a lower monotone variation area one-to-one, the upper monotone variation area being obtained by performing both a high-pass filtering on pixels centered in a closest upper row to the position and a region determination process on the pixels after being high-pass filtered, the lower monotone variation area being obtained by performing both a high-pass filtering on pixels centered in a closest lower row to the position and a region determination process on the pixels after being high-pass filtered; a texture variance consistence step, which computes all directional texture variances in the closest upper and the closest lower rows of pixels within the monotone variation area in the case of taking the position as a center and accordingly finds two pixels having texture variance consistence; and an interpolation step, in which the interpolation step finds a value of pixel to be interpolated to the position by filtering in accordance with the two pixels found at the texture variance consistence step.