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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Palmprints have been widely studied for biometric recognition for many years. Traditionally, a white light source is used for illumination. Recently, multispectral imaging has drawn attention because of its high recognition accuracy. Multispectral palmprint systems can provide more discriminant information under different illuminations in a short time, thus they can achieve better recognition accuracy. Previously, multispectral palmprint images were taken as a kind of multi-modal biometrics, and the fusion scheme on the image level or matching score level was used. However, some spectral information will be lost during image level or matching score level fusion. In this study, we propose a new method for multispectral images based on a quaternion model which could fully utilize the multispectral information. Firstly, multispectral palmprint images captured under red, green, blue and near-infrared (NIR) illuminations were represented by a quaternion matrix, then principal component analysis (PCA) and discrete wavelet transform (DWT) were applied respectively on the matrix to extract palmprint features. After that, Euclidean distance was used to measure the dissimilarity between different features. Finally, the sum of two distances and the nearest neighborhood classifier were employed for recognition decision. Experimental results showed that using the quaternion matrix can achieve a higher recognition rate. Given 3000 test samples from 500 palms, the recognition rate can be as high as 98.83%.

There are two main categories in the automatic traditional personal identification area: token-based methods that rely on personal identification such as driver licenses, passports, and other IDs; and knowledge-based methods that rely on signatures or password-protected access [

Among these features, palmprints are widely studied [

To address the issue of limited information, we have applied multispectral imaging which can provide several images of the same scene with different illuminations for enhanced biometrics applications that include face recognition [

The concept of quaternion was first proposed in 1843 by the Irish mathematician William Rowan Hamilton [

The rest of the paper is organized as follows: a multispectral imaging device is briefly described in Section 2. The proposed method is outlined in Section 3. Experimental results are reported in Section 4. Finally, the conclusions are given in Section 5.

The key components of the multispectral palmprint imaging device include a CCD camera, lens, and A/D converter. To ensure a semi-closed environment, the box containing the camera is made of opaque plastic and the central part of the device panel is hollow. The multispectral images were captured with four different wavelengths: NIR (880 nm), red (660 nm), green (525 nm) and blue (470 nm) [

Before extracting palmprint features, a region of interest (ROI) of a palmprint image is selected first. A coordinate system to reduce rotation and translation effects is built from the given image and then a 128 × 128 ROI [

To fully utilize the information of the multispectral palmrpint images, the multispectral palmprint images are represented by a quaternion matrix. In mathematics, quaternions are a noncommutative number system. A quaternion is a linear combination of a real scalar and three imaginary units:
^{2} = ^{2} = ^{2} =

The conjugate of a quaternion is:

In

In this study, two kinds of features are extracted from a quaternion matrix, quaternion PCA (QPCA) [

To speed up computation and reduce memory cost [_{m}_{×}_{n}_{1} _{2}…_{n}

Given the matrix _{m}_{×}_{n}_{m}_{×}_{m}_{m}_{×}_{m}_{n}_{×}_{n}_{n}_{×}_{n}

Matrix _{B}_{B}_{n}_{×}_{n}

Eigenvalues of _{n}_{×}_{n}_{c}_{n}_{×}_{n}_{n}_{×}_{n}_{m}_{×}_{m}_{m}_{×}_{m}_{m}_{×}_{m}

Eigenvalues _{x}^{th} eigenvalue. Given an energy ratio, the number of the eigenvalues

For an input quaternion sample _{QPCA}

After one scale decomposition, four groups of coefficients will be generated [

Given a quaternion sample ^{Q}_{1} and _{2} are two filters specifically designed by He and Li for QDWT [

To get stable features, the quaternion matrix is divided into non-overlapping blocks. Each block is with size of z × z. The

For each block:

The standard deviation of this block is a quaternion constructed by the standard deviation of each band in the block.
_{l}^{th} block. Then a quaternion vector is built by concatenating all standard deviations and this quaternion vector is used as the QDWT feature:

Euclidean distance between two quaternions

After feature extraction, one multispectral palmrpint sample has two different features, one QPCA feature _{QPCA}_{QDWT}_{QPCA}^{u}^{v}_{QDWT}

The final distance between two samples is the weighted fusion of the QPCA distance and the QDWT distance. Before fusion, we need to normalize QPCA and QDWT distances by dividing each of these distances by their respective standard deviation of the distances between the training samples, as expressed below [_{QPCA}_{DWT}_{=} 1-_{QPCA}

The experiments are based on a large multispectral palmprint database [

The database consists of 500 different palms, and each palm was sampled 12 times in two sessions with a time interval of about 5–15 days. In each session, the subjects were asked to provide six groups of images. Each group contained four images under four different illuminations, so there were 6,000 groups of palmprint images [

Recognition accuracy is obtained by matching each palmprint sample in the test set with all the samples in the training set.

To evaluate the performance of our method in the situation with less than four illuminations, we replace some bands with a zero-matrix.

From

The experiment is implemented using Matlab 7.0 on a PC with Windows XP (x64), Xeon 5160 CPU (3.0GHz), and 4-GB RAM. The execution time for preprocessing, feature extraction and feature matching is listed in

In this paper and to fully utilize the information of multispectral palmprint images, to the best of our knowledge, a quaternion model is employed for multispectral biometrics for the first time. QPCA is proposed for representing global features while QDWT is designed for extracting local features. Their fusion could achieve 98.83% recognition accuracy for 500 palms. The experimental results show that the proposed method is good enough for real applications and the quaternion model is an effective and efficient technique for multispectral biometrics. The special arrangement has shown that the quaternion matrix is still effective for multispectral palmprint in the situation with less than four illuminations.

In the future, we will try to apply the proposed method to other multispectral biometrics, such as face and iris recognition. We will also explore advanced feature extraction methods on the quaternion matrix, such as the kernel method [

The work is partially supported by National Science Foundation of China (No. 61101150, 61105011, 60872138), and the Specialized Research Fund for the Doctoral Program of Higher Education (No.20100203120010).

(

A typical multispectral palmprint sample. (

The framework of the proposed method.

ROI of

The ROIs of multispectral palmprint images under 4 different kinds of illuminations after the preprocessing and downsampling. (

A quaternion vector sample built using the input image in

A pair of multispectral palmprint images from the same palm but falsely recognized. (

Recognition Accuracy.

NIR PCA | 94.60% |

Red PCA | 96.30% |

Green PCA | 93.47% |

Blue PCA | 93.47% |

Image level fusion by PCA | 95.17% |

Matching score level fusion by PCA | 98.07% |

NIR DWT | 94.60% |

Red DWT | 95.20% |

Green DWT | 93.50% |

Blue DWT | 93.83% |

Image level fusion by DWT | 96.60% |

Matching level score fusion by DWT | 98.00% |

Recognition accuracy of different situations using QDWT.

1 | 1 | 0 | 0 | 97.17% |

1 | 0 | 1 | 0 | 98.10% |

1 | 0 | 0 | 1 | 98.13% |

0 | 1 | 1 | 0 | 97.23% |

0 | 1 | 0 | 1 | 97.33% |

0 | 0 | 1 | 1 | 94.87% |

1 | 1 | 1 | 0 | 98.03% |

1 | 1 | 0 | 1 | 97.90% |

1 | 0 | 1 | 1 | 98.13% |

0 | 1 | 1 | 1 | 97.10% |

Image correlation between different spectra.

1 | - | - | - | |

0.7470 | 1 | - | - | |

0.3690 | 0.5060 | 1 | - | |

0.4487 | 0.6829 | 0.7421 | 1 |

Execution Time.

Preprocessing | 20 |

QPCA feature extraction | 46 |

QDWT feature extraction | 547 |

QPCA feature matching | 0.42 |

QDWT feature matching | 0.43 |