1. An apparatus responsive to an input binary image signal for outputting data for generating a connected element which is an area including a same label in a label image, comprising: binary image storage means for storing therein the input binary image signal as binary image data; labeling means for performing label processing on the binary image data and generating the label image; rectangle calculation means, based on the label image data, for calculating a rectangle circumscribing a same label and rectangle definition data defining the rectangle by the label and a position in the label image; overlap determination means based on the rectangle definition data for determining whether a rectangle calculated by said rectangle calculation means is an overlapping or non-overlapping rectangle depending on whether or not the rectangle overlaps with other rectangles; and output means for outputting data comprising the binary image data, the rectangle definition data and the label image data of the overlapping rectangle, as the data for generating the connected element.