1. An image processing apparatus, comprising: an edge image generating unit configured to detect edges in an original image and to generate an edge image formed by the detected edges; a connection pixel extracting unit configured to extract connection pixel sets in the edge image; a binary image generating unit configured to classify the connection pixel sets by colors and generate respective character images which are binary images corresponding to the colors; a background image generating unit configured to generate a background image of the original image on the basis of the character images; and an image compressing unit configured to compress image data of the character images and image data of the background image using respective different compressing methods; wherein regarding plural character areas in the character image of each color, the image compressing unit is further configured to include one of the character areas from which a distance to another one of the character areas is either equal to or larger than a predetermined threshold value into a character image other than the character image in which the other one of the character areas is included, and to compress image data of the other one of the character areas separately from other image data; wherein the image compressing unit is further configured to classify the plural character areas into character groups so as to make the character areas between which a distance is short belong to one character group and make the character areas between which a distance is long belong to respective different character groups on the basis of the threshold value, and to separately compress the character groups as respective pieces of image data of character images.