A Comparison in Handmetric between Quaternion Euclidean Product Distance and Cauchy Schwartz Inequality Distance

This paper proposes a comparison in handmetrics between quaternion Euclidean product distance (QEPD) and Cauchy-Schwartz inequality distance (CSID), where "handmetrics" refers to biometrics on palmprint or finger texture. Previously, we proposed QEPD and CSID these two 2D wavelet decomposition based distances for palmprint authentication and face verification respectively. All two distances could be constructed by quaternion which was introduced for reasonable feature representation of physical significance, i.e. 4-feature parallel fusion. Simultaneously, such quaternion representation enables to avoid incompatibleness of multi-feature dimensionality of quaternion fusion. However, a comparison between two distances is seldom discussed before. Therefore, we give a comparison on both theoretical and experimental aspects for providing a conclusion which algorithm is better. From the result, we can conclude the performance of QEPD is better than CSID and finger texture is a better discriminative biometric than palmprint for QEPD or CSID.