In this paper the authors propose a mathematical model of fingerprint images based on the vectors of ridge count values. The model takes into account the instability of the values of the ridge count in the region of the lines curvature and possible mutations of minutiae. This increases the stability of fingerprint template and reliability of identification. The vectors of ridge count are formed using topological descriptors, which are constructed for the neighborhood of all fingerprint minutiae. In the proposed model, a template of a fingerprint image keeps the list of minutiae, the list of topological vectors and the list of the ridge count vectors. The value of the ridge count can be represented as a fractional number.
