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In this paper, we propose a novel method for finger-vein recognition. We extract the features of the vein patterns for recognition. Then, the minutiae features included bifurcation points and ending points are extracted from these vein patterns. These feature points are used as a geometric representation of the vein patterns shape. Finally, the modified Hausdorff distance algorithm is provided to evaluate the identification ability among all possible relative positions of the vein patterns shape. This algorithm has been widely used for comparing point sets or edge maps since it does not require point correspondence. Experimental results show that these minutiae feature points can be used to perform personal verification tasks as a geometric representation of the vein patterns shape. Furthermore, by this developed method, we can achieve robust image matching under different lighting conditions.