1. A line figure connecting apparatus comprising: digitizing means for digitizing line figure image data into a first value indicating pixel data on line figure and a second value indicating background pixel data; background figure skeletonizing means, connected to said digitizing means, for skeletonizing the background pixel data of the input image data by a predetermined number of steps; gap filling means, connected to said background figure skeletonizing means, for converting into the pixel data on line figure a pixel area in which the skeletonized background pixel data has a 1-dot line width; connection picture element detecting means, connected to said background figure skeletonizing means, for skeletonizing the picture element data on line figure obtained by said gap filling means, by a predetermined number of steps, and for detecting pixels each having a 1-dot line length; connection candidate detecting means, connected to said digitizing means and said gap filling means, for calculating pixel data around the pixel data on line figure of the image data input from said digitizing means to detect a connection candidate area; connection pixel thickening means, connected to said connection pixel detecting means and said connection candidate detecting means, for thickening the connection pixels detected by said connection pixel detecting means within the connection candidate area; and logical sum means, connected to said image input means and said connection pixel thickening means, for combining the pixel data on line figure from said connection pixel thickening means and the image data input from said digitizing means.