In this paper, a computational definition of fingerprint singular points based on aligned tri-coloured pixel-wise directional image, called ATPDI, is presented. The traditional descriptive definitions, geometric definition, and ISO/IEC definition are explained in detail with discussion of their advantages and disadvantages. The quality of a singular point definition is measured by three factors: completeness, rotation sensibility, and precision. We used NIST-4 database for experimental tests, and the experimental results show the ATPDI does not leave cases undefined, is rotation insensitive, and can define singular points in a 2