Image Processing Reference
In-Depth Information
1 Introduction
Traditionally, private information is considered as passwords and personal identiication
numbers (PINs) among the society, which is easy to use but vulnerable to the risk of exposure
and being stolen or forgoten. Biometrics [ 1 , 2 ], however, has been atracting researchers' and
industry's atention more and more as it is believed that biometrics is a promising alternat-
live to the traditionally used password or PIN-based authentication techniques [ 3 ] . Nowadays,
there are several different biometrics systems under research such as face recognition, finger
print, palm print, voice recognition, iris recognition, and so on [ 1 , 4 - 7 ] . There are two main
challenges in terms of biometrics systems. The first one is that the main element by which the
identity is verified or identified is accessible and forgeable, and the second one is that the rate
of reliability of the mentioned systems in terms of having a satisfactory accuracy rate is not
acceptable. For instance, finger and palm prints are usually frayed; iris images and voice sig-
nature are easily forged; face recognition could be considered difficult and unreliable when
there are occlusions or face-lifts. Finger vein recognition [ 8 - 11 ] , however, is more secure and
convenient and has none of the mentioned drawbacks because of the following three reasons:
(1) human veins are mostly invisible and located inside the body; therefore, it is difficult to be
forged or stolen, (2) it is more acceptable for the user as capturing finger vein images is nonin-
vasive and contactless, and (3) the finger vein data can only be captured from a live individual.
It is thus a convincing proof that the subject whose finger vein [ 12 ] is successfully captured is
Because the data in finger vein recognition are “image,” there are several methods for ana-
lyzing and classifying the images in such a recognition system. Principal component analysis
(PCA) [ 3 , 13 ] is one of the common and powerful methods of patern recognition and feature
extraction which has been used a lot in biometrics. There have been several improvements on
PCA such as kernel PCA (KPCA) [ 13 , 14 ], and kernel entropy PCA (KECA) [ 15 - 17 ] so far. See
the topic [ 18 ] for kernel methods in patern analysis. One-dimensional (1D) KPCA [ 19 ] and
KECA [ 20 , 21 ] have been proposed for finger vein recognition which led to promising results
[ 22 ] . The main drawback of 1D PCA, however, is that after converting the 2D matrix to 1D,
the dimension of the data is too high which results in having a very time-consuming and even
inaccurate system. A highlighted improvement on 1DPCA is 2DPCA [ 23 - 26 ] in which the im-
age matrix is not converted to 1D. This method has two main advantages over 1DPCA which
are being much faster, and having higher accuracy. After proposing 2DPCA, kernel 2DPCA
[ 25 ] was introduced in which the data are first mapped to another space using different kernel
methods and then 2DPCA is implemented on the mapped data. It is believed that by trans-
forming the data into the appropriate space first and applying 2DPCA on the mapped data,
the accuracy rate will have a dramatic increase. This work is an extension of Ref. [ 27 ] presen-
ted in IPCV 2014 conference. As 2DPCA is applied on 2D image matrixes directly, there has
been a great amount of research on the direction of the analysis. 2DPCA can be applied in row
direction, column direction, or both. In this paper, however, different directions of the mat-
rixes for mapping the data into kernel space are argued. We chose kernel polynomial degree
one as mapping function and applied input images in row and column directions. The direc-
tion of mapping is important in our system because 2DPCA is applied on the mapped data
and extracts as many eigenvectors as the dimension of the mapped data, meaning that if we
have an ( N × N ) matrix, we will have N eigenvectors and their corresponding eigenvalues. For
example, assuming our input matrixes are 60 × 180, applying the mapping function in row and
column directions will result in 60 × 60 and 180 × 180 matrixes, respectively. Applying 2DPCA
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