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Our research focuses on finding mathematical representations of biometric features that are not only distinctive, but also invariant to projective transformations. We have chosen hand geometry technology to work with, because it has wide public awareness and acceptance and most important, large space for improvement. Unlike the traditional hand geometry technologies, the hand descriptor in our hand geometry system is constructed using projective-invariant features. Hand identification can be accomplished by a single view of a hand regardless of the viewing angles. The noise immunity and the discriminability possessed by a hand feature vector using different types of projective invariants are studied. We have found an appropriate symmetric polynomial representation of the hand features with which both noise immunity and discrimminability of a hand feature vector are considerably improved. Experimental results show that the system achieves an equal error rate (EER) of 2.1% by a 5-D feature vector on a database of 52 hand images. The EER reduces to 0.00% when the feature vector dimension increases to 18. In this paper, we extend the concept of hand geometry from a geometrical size-based technique that requires physical hand constraints to a projective invariant-based technique that allows free hand motion.