We present deep optical imaging of three face-on disk galaxies together with a detailed description of the reduction and calibration methods used, in order to measure the intrinsic shape of their outer stellar edges. Whereas it is now well accepted that disks of spiral galaxies are not infinite exponential beyond galactocentric distances of about 3-5 radial scalelengths, the genuine structure of the truncation region is not yet well known. Our data quantitatively establish a smooth truncation behaviour of the radial surface brightness profiles and is best described by a two-slope model, characterised by an inner and outer exponential scalelength separated at a relatively well defined break radius. This result disagrees with the frequently assumed sharply truncated nature of the radial surface brightness profiles and implies the presence of stars and even star-formation beyond the break radius. In addition, we do not find a strong influence of a nearby companion on the ratio of the break radius to the radial scalelength. Our results denote new observational constraints for the search of the physical explanation for these smooth disk truncations. Based on observations obtained at the German-Spanish Astronomical Center (DSAZ), Calar Alto, jointly operated by the Max-Planck-Institut für Astronomie Heidelberg and the Spanish National Commission for Astronomy.