This paper addresses the problems of fingerprint identification and verification when a query fingerprint is taken under conditions that differ from those under which the fingerprint of the same person stored in a database was constructed. This occurs when using a different fingerprint scanner with a different pressure, resulting in a fingerprint impression that is smeared and distorted in accordance with a geometric transformation (e.g., affine or even non-linear). Minutiae points on a query fingerprint are matched and aligned to those on one of the fingerprints in the database, using a set of absolute invariants constructed from the shape and/or size of minutiae triangles depending on the assumed map. Once the best candidate match is declared and the corresponding minutiae points are flagged, the query fingerprint image is warped against the candidate fingerprint image in accordance with the estimated warping map. An identification/verification cost function using a combination of distance map and global directional filterbank (DFB) features is then utilized to verify and identify a query fingerprint against candidate fingerprint(s). Performance of the algorithm yields an area of 0.99967 (perfect classification is a value of 1) under the receiver operating characteristic (ROC) curve based on a database consisting of a total of 1680 fingerprint images captured from 240 fingers. The average probability of error was found to be 0.713%. Our algorithm also yields the smallest false non-match rate (FNMR) for a comparable false match rate (FMR) when compared to the well-known technique of DFB features and triangulation-based matching integrated with modeling non-linear deformation. This work represents an advance in resolving the fingerprint identification problem beyond the state-of-the-art approaches in both performance and robustness.