1. A fingerprint recognition and retrieval method comprising, I. establishing a machine searchable library of fingerprints by, for each file fingerprint, (a) locating a central reference point and projecting a line in a predetermined direction through the said central point to intersect ridge lines to each side of said centrally located reference point, (b) from the point of crossing of said projected line with each ridge, and in a predetermined order, tracing each side of said ridge crossings from said projected line to the first occurring topological event and assigning a type code (T) to the event, and measuring the distance (D) from the projected line crossing to the event, and (c) recording each type code (T) and distance (D) in said predetermined order as a topological data vector for each file fingerprint in a machine searchable database, II. with respect to unknown latent or rolled fingerprints, locating a central reference point on said unknown latent or rolled fingerprint and projecting a line through the said central point to intersect ridge lines to each side of said centrally located reference point, from the point of crossing of said projected line with each ridge, and in a predetermined order, tracing each side of said ridge crossings from said projected line to the first occurring topological event and assigning a type code (T.sub.u) to the event, and measuring the distance (D.sub.u) from the projected line crossing to the event, forming a code vector comprised of said type codes and said distances, and III. comparing said code vector with such code vectors machine searchable library of file fingerprints in order to identify which file fingerprint in the said file collection corresponds to the said unknown fingerprint, with respect to measured distances D and D.sub.u at apparently matching events, and in addition to comparing the absolute distances D and D.sub.u, performing at least one further comparison of said measured distances selected from (1) a predetermined differential distance tolerance between events on adjacent ridges on the same side of said projected line, respectively, and (2) predetermined summed distance tolerance of the pairs of ridge events to each side of said ridge crossings, respectively.