1. A method for generating a vector image in an image processing apparatus, the method comprising the steps of: obtaining an inclination of a character included in an image; obtaining apex pixels that form contours of the character; obtaining, from a portion that is supposed to be expressed by a single line segment among the contours of the character, an identical line segment candidate pixel group serving as a candidate for a pixel group of the apex pixels that are supposed to be positioned on the single line segment; extracting, based on the inclination, the identical line segment candidate pixel group thus obtained as an identical line segment pixel group that is the pixel group of the apex pixels that are supposed to be positioned on the single line segment; extracting, based on a position of each of the apex pixels of the identical line segment pixel group thus extracted, both-end pixels which are apex pixels located on both sides of the identical line segment pixel group from among the apex pixels of the identical line segment pixel group; approximating, by a line segment connecting between the both-end pixels thus extracted, a contour of the character in a portion corresponding to the both-end pixels; and approximating a portion among the contours of the character, excluding the portion that has been approximated by the line segment connecting between the both-end pixels, by a straight line or a curved line by performing an outlining process using apex pixels other than the apex pixels of the identical line segment pixel group.