1. An image processing apparatus generating a thin line binary image and extracting vectors, comprising: a vector extracting unit configured to raster-scan the thin line binary image by using a pixel matrix including a plurality of pixels to extract a vector to which contour point information is added in accordance with a predetermined pattern of black and white pixels in the pixel matrix; and a coordinate correcting unit configured to detect that the vector has been extracted from a set of black pixels of 2 pixels×2 pixels in the pixel matrix by referring to the contour point information added to the vector and correct a coordinate of a core-line vector in accordance with coordinate correction information included in the contour point information, the core-line vector being produced by reducing the vector to a core line.