A Comparison between Quaternion Euclidean Product Distance and Cauchy Schwartz Inequality Distance - Advances in Computational Science and Engineering - page 129

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

Di Liu, Dong-mei Sun, and Zheng-ding Qiu

Institute of Information Science, Beijing Jiaotong University, Beijing, China, 100044
[e-mail]

Abstract. 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 [1,2] and
CSID [11] these two 2D wavelet decomposition based distances for palm-
print authentication and face verification respectively. All two distances
could be constructed by quaternion which was introduced for reason-
able feature representation of physical significance, i.e. 4-feature parallel
fusion. Simultaneously, such quaternion representation enables to avoid
incompatibleness of multi-feature dimensionality space for fusion. How-
ever, a comparison between two distances is seldom discussed before.
Therefore, we give a comparison on 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.

1 Introduction

Biometrical information fusion community is flooded with a large number of
biometric fusion approaches. Traditionally, in field of the multi-feature biometric
fusion, it is well known that these schemes are categorized into four major levels,
namely (a) sensor level, i.e. data level, (b) feature level, (c) matching score
level, and (d) decision-making level [7]. Recently, it raises a heated research
on feature level, i.e. Feature Fusion Level (FLF) in the community of multi-
feature biometric recognition, because of (a) richer information which can be
acquired from raw data than other level fusion and (b) good performance without
independence assumption rather than decision-making level. And FLF classifies
into four aspects based on method fusion, namely serial fusion, parallel fusion,
weight fusion, and kernel fusion. Traditionally, serial fusion is a most common
used fusion method, yet it has two evident drawbacks: (1) the dimensionality
of feature vector after concatenation increases dramatically so that recognition
speed goes down sharply. (2) as to small sample size, e.g. face recognition, this
method usually gives rise to singularity which is an obstacle of feature extraction
of Fisher criterion. To avoid the problems, [10] proposed parallel fusion with a