In this paper a new methodology to recognize radk>larians is presented. This system is invariant to position, rotation and scale by using identity vectors signatures (Is) obtained for both the target and the problem image. In this application, / is obtained by means of a simplification of the main features of the original image in addition of the properties of the Fourier transform. Identity vectors signatures are compared using nonlinear correlation. This new methodology recognizes objects in a more simple way. It has a low computational cost of approximately 0.02 s per image. In addition, the statistics of Euclidean distances is used as an alternative methodology for comparison of the identity vectors signatures. Also, experiments were carried out in order to find the noise tolerance. The discrimination coefficient was used as a metric in performance evaluation in presence of noise. The invariant to position, rotation and scale of this digital system was tested with 20 different species of radiolarians and with 26 different species of phytoplankton (real images). The results obtained have a confidence level above 95.4%.