The global interpolation method we propose evaluates segment pattern continuity and connectedness to produce characters with smooth edges while interpreting blank or missing segments based on global label connectivities, e.g, in extracting a handwritten character overlapping a border, correctly. Conventional character segmentation involving overlapping a border concentrates on removing the thin border based on known format information rather than extracting the character. This generates discontinuous segments which produce distortion due to thinning and errors in direction codes, and is the problem to recognize the extracted character. In our method, characters contacting a border are extracted after the border itself is labeled and removed automatically by devising how to extract wavy and oblique borders involved in fax communication. The absence of character segments is then interpolated based on segment continuity. Interpolated segments are relabeled and checked for matching against the original labeled pattern. If a match cannot be made, segments are reinterpolated until they can be identified. Experimental results show that global interpolation interprets the absence of character segments correctly and generates with smooth edges.