Fingerprints are scanned by a scanning system (13). Topological systems for coding and comparing fingerprints are described including a system for recording a description of fingerprints. In a preferred embodiment, a central point of the fingerprint is selected as a center of rotating scan line. The scan line is rotated to different topological characteristics. A code (T) representing the type of irregularity is recorded (16, 17). A measure (M) of the scanning position when encountering the irregularity is made (16, 17). In the case of a rotating scan line the angular cordinate (.theta.) is recorded. The ridge count (R) (16) is also recorded. A list of coordinate sets (T, .theta., R) specifies the topology of a sector. For fragmentary prints similar coordinate sets are generated. A fourth coordinate can be added corresponding to the radial distance (D) (16). A full set of coordinates (T, .theta., R, D) gives a complete topological and spatial description of a fingerprint. Comparison of fingerprints can then be conducted by a computer (20).