Hand-based verification is a key biometric technology with a wide range of potential applications both in industry and government. The focus of this work is on improving the efficiency, accuracy, and robustness of hand-based verification. In particular, we propose using high-order Zernike moments to represent hand geometry, avoiding the more difficult and prone to errors process of hand-landmark extraction (e.g., finding finger joints). The proposed system operates on 2D hand silhouette images acquired by placing the hand on a planar lighting table without any guidance pegs, increasing the ease of use compared to conventional systems. Zernike moments are powerful translation, rotation, and scale invariant shape descriptors. To deal with several practical issues related to the computation of highorder Zernike moments including computational cost and lack of accuracy due to numerical errors, we have employed an efficient algorithm that uses arbitrary precision arithmetic, a look-up table, and avoids recomputing the same terms multiple times [2]. The proposed hand-based authentication system has been tested on a database of 40 subjects illustrating promising results. Qualitative comparisons with state of the art systems illustrate comparable of better performance.

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Abstract. Zernike Moments are useful tools in pattern recognition and image analysis due to their orthogonality and rotation invariance property. However, direct computation of these moments is very expensive, limiting their use especially at high orders. There has been some efforts to reduce the computational cost by employing quantized polar coordinate systems, which also reduces the accuracy of the moments. In this paper, we propose an efficient algorithm to accurately calculate Zernike moments at high orders. To preserve accuracy, we do not use any form of coordinate transformation and employ arbitrary precision arithmetic. The computational complexity is reduced by detecting the common terms in Zernike moments with different order and repetition. Experimental results show that our method is more accurate than the other methods and it has comparable computational complexity especially in case of using large images and high order moments.

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