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This paper proposes a novel technique to analyze the infrared vein patterns in the back of the hand for biometric purposes. The technique utilizes the minutiae features extracted from the vein patterns for recognition, which include bifurcation points and ending points. Similar to fingerprints, these feature points are used as a geometric representation of the shape of vein patterns. Analysis of a database of infrared vein patterns shows a trend that for each hand vein pattern image, there are, on average, 13 minutiae points in each vein pattern image, including 7 bifurcation and 6 ending points. The modified Hausdorff distance algorithm is proposed to evaluate the discriminating power of these minutiae for person verification purposes. Experimental results show the algorithm reaches 0% of equal error rate (EER) on the database of 47 distinct subjects, which indicates the minutiae features of the vein pattern can be used to perform personal verification tasks. The paper also presents the preprocessing techniques to obtain the minutiae points as well as in-depth study on their tolerance to processing errors, such as loss of features and geometrical displacement.