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In this paper, we adopt a unified viewpoint to represent local ridge orientation (LRO) and local ridge frequency (LRF) and extract important features (including cores, deltas, and minutiae) by using PGBF-based approach. Based on the continuity of ridge structures, a local fingerprint image is represented by a principal Gabor basis functions (PGBF) because PGBF only has large response values with similar LRO and LRF. Owing to the discontinuity of ridge structures, on the contrast, the positions of important points have small response values than their surroundings. Owing to the unified PGBF-based viewpoint, therefore, fewer steps are applied for important points extraction in fingerprint enrollment. To speed up the procedure of minutiae matching in fingerprint verification, besides, we propose a different procedure to directly check the positions of minutiae in gray-level fingerprint images from coarse level to fine level. So some time-consuming overall pixel-level computations are avoided, and then an efficient fingerprint matching is achieved.