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In this paper, we propose a hybrid computational geometry-gray scale algorithm that enhances fingerprint images greatly. The algorithm extracts the local minima points that are positioned on the ridges of a fingerprint, then, it generates a Delaunay triangulation using these points of interest. This triangulation along with the local orientations give an accurate distance and orientation-based ridge frequency. Finally, a tuned anisotropic filter is locally applied and the enhanced output fingerprint image is obtained. When the algorithm is applied to rejected fingerprint images from FVC2004 DB2 database by the veryfinger application, these images pass and experimental results show that we obtain a low false and missed minutiae rate with an almost uniform distribution over the database. Moreover, the application of the proposed algorithm enables the extraction of features from all low-quality fingerprint images where the equal error rate of verification is decreased from 6.50% to 5% using nondamaged low-quality images in the database.