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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/).

A hand biometric authentication method based on measurements of the user's hand geometry and vascular pattern is proposed. To acquire the hand geometry, the thickness of the side view of the hand, the K-curvature with a hand-shaped chain code, the lengths and angles of the finger valleys, and the lengths and profiles of the fingers were used, and for the vascular pattern, the direction-based vascular-pattern extraction method was used, and thus, a new multimodal biometric approach is proposed. The proposed multimodal biometric system uses only one image to extract the feature points. This system can be configured for low-cost devices. Our multimodal biometric-approach hand-geometry (the side view of the hand and the back of hand) and vascular-pattern recognition method performs at the score level. The results of our study showed that the equal error rate of the proposed system was 0.06%.

The rapidly growing biometric recognition industry [

Our study proposes a multimodal biometric approach integrating hand geometry and vascular patterns. Our proposed multimodal biometric system can be constructed as a low-cost device because our system uses only one image to extract the feature points. We perform multimodal biometrics by score-level fusion with z-score normalization, which results in improved recognition performance compared to that of unimodal biometrics consisting of each hand geometry (e.g., the side view of the hand and the back of hand) and vascular pattern.

The rest of this paper is organized as follows: in Section 2, we discuss the hand biometric recognition system and we talk about the proposed hand biometric recognition technique. In Section 3, we discuss the experimental results. We conclude in Section 4.

In this section, we discuss the hand biometric recognition system. A proposed user-authentication system using the side and back view of the hand is investigated. The implemented system is detailed in Section 2.1.1. Details of the acquisition device are provided in 2.1.2. The image segmentation and preprocessing are illustrated in Section 2.1.3.

The block diagram of the implemented system is shown in

An acquisition system has been developed for the collection of the side- and back-of-the-hand data and the vascular-pattern-of-the-hand data to acquire a single image. An acquisition device as shown in

The acquisition of a sample image is shown in

First, for hand recognition, the hand image is captured, and then preprocessing is performed. Preprocessing is conducted in two steps: (1) the gray image is transformed into a black and white one where the background is eliminated. The preprocessing for the side view of the hand is shown in

The Gaussian smoothing can be performed using standard convolution methods. The image has

The 2D Gaussian is expressed as:

The median filter is to compare these results to a threshold value. The input data is thereby converted to a binary value (0,1). The images of Vascular, Median filter are shown in

The median filter is expressed as:

The next step after preprocessing is the extraction of the feature points. The extraction of the feature-points process includes the thickness of the side view of the hand, the K-curvature [

This section addresses the algorithm used for hand biometric recognition. We detail the extraction of feature and verifier. The side view of the hand is detailed in Section 2.2.1. The back-of-the-hand view is provided in Section 2.2.2. The VPE are illustrated in Section 2.2.3.

To establish the thickness of the side view of the hand, the heights of the middle finger, the index finger, and the palm are collected and calculated in the following order: (1) find a line at the base of the palm; (2) next, find the starting point perpendicular to the palm base line; (3) then, calculate the thickness of the side view the hand from the starting point to the end point. The location of the endpoint is predetermined by the acquisition device. The profile of thickness is _{side}

The curvature can define a curve intwo-dimensional space. The curvature of the discrete data in a digital image using a suitable approximation is obtained. The concept of K-curvature is such that a continuous curvature is represented by a discrete function.

In this study, the K-curvature uses the curvature of the boundaries of the hands and the background as feature vectors. The K-curvature is calculated in the following order: (1) The chain code representation of the hand surface pattern is obtained. The traces of chain code are represented by blue in

The K-curvature is expressed as:

The curvature at a point _{i}_{i}_{i}f_{i}

The traces of the K-curvature are represented by red in

The first feature of the hand geometry is the divided K-curvatures. The original K-curvature is split into components that can be characterized. These components consist of _{1}_{2}_{3}_{4}

The second feature of the hand geometry is the length and the angle of the finger valley that is calculated by the K-curvature. Valley points consist of _{1}_{2}_{3}_{4}_{1}_{2}_{1}_{2}_{2}_{3}_{3}_{3}_{4}_{1} is the angle between _{1}_{3}_{2}_{2} is the angle between _{2}_{4}_{3}

The third feature of the hand geometry is the length of the fingers. The peak points for K-curvature consist of _{1}_{2}_{3}_{4}_{1}_{1}_{5}_{1}_{6}_{2}_{7}_{1}_{8}_{1}_{4}_{1}_{5}_{2}_{6}_{3}_{7}_{4}_{8}_{5}

The fourth feature of hand geometry is the profile of the fingers. The starting points of the profile are the y-axis coordinates at the valley points. The end points of the profile are the y-axis coordinates at peak points. The starting point of the baseline consists of
_{1}(_{2}(_{3}(_{4}(_{5}(

The VPE algorithm is implemented by using the direction-based vascular-pattern extraction (DBVPE) method [

The VPE algorithm uses a noise-removal filter and an emphasizing filter. The VPE algorithm is shown in

The emphasizing filter is expressed as:
_{M}_{N}

The feature of hand recognition is illustrated in

In order to compare the different features of hand recognition, three kinds of verifier algorithms are used. The first algorithm is Euclidean distance. To establish the angle and length, the Euclidean distance algorithm was used. It performs its measurements with the following equation:
_{i}_{i}_{t}_{1},_{t}_{2},_{t}_{1},_{t}_{2},_{t}_{3},_{t}_{4},_{t}_{5},_{t}_{6},_{t}_{7},_{t}_{8}} ; and _{i}_{i}_{s}_{1},_{s}_{2},_{s}_{1},_{s}_{2},_{s}_{3},_{s}_{4},_{s}_{5},_{s}_{6},_{s}_{7},_{s}_{8}}.

The second algorithm is the distance measured for the polygonal curves. For the K-curvature and profile, the distance-measure algorithm was used. An approach to a distance measurement for polygonal curves is to make a comparison between the original curves and the target curves with the objective of minimizing some property under specific constraints on the possible mappings; this algorithm performs its measurements with the following equation:
_{i}

_{i}

For the K-curvature and profile, the number of scores is 10.

The third algorithm is a matching algorithm. The matching algorithm is used for the vascular pattern, and it obtains the maximum matching value between the source patterns and target patterns. The patterns consist of the vascular pattern and the background pattern. The matching of patterns is calculated by giving a weight of 1/4. The third algorithm performs its measurements with the following equation:

Three kinds of verifier algorithms compute 12 matching scores. The 12 matching scores are illustrated in

At the verifier state, the source templates are compared with the target template. A source or target template is represented by 21 feature vectors: one profile of thickness, four K-curvatures, two angles, eight lengths, five profiles of fingers, and one vascular pattern. Angle and length are grouped into a single matching score. The verifier between the source templates and the target templates consists of computing 12 matching scores between them.

For hand geometry recognition, we used a weighted sum between the Euclidean distance and the distance measurement for polygonal curves. The weights _{1} and _{2} are varied over the range [0,1] in steps of 0.01, such that the constraint _{1} + _{2} = 1 is satisfied. The best weights for the Euclidean distance and the distance measurements are 0.37 and 0.63. Measurements are performed using the following equation:

The VPE recognition performs its measurements with the following equation:

The false acceptance rate (FAR) is the error rate of accepting the wrong person; the false reject rate (FRR) is the error rate of rejecting own; the genuine acceptance rate (GAR) is 1 − FRR; and the equal error rate (EER) is the error rate when FRR is equal to the FAR.

Multimodal biometric uses various levels of fusion: matching-score level, decision level, and the feature-extraction level. In this paper, we used integration at the matching-score level. The matching-score level comprises two approaches: the classification approach and the combination approach. Because the combination approach performs better than some classification approaches [

The matching-score level needs normalization to transform the score into a common domain before combining it. In this paper, normalization uses a z-score [

The normalized scores are expressed as:

The distributions of the matching scores of the two modalities after z-score normalization are shown in

Once normalized, the normalized-scores obtained from hand geometric and vascular pattern are combined using a simple weighted-summation operation. The weighted-summation method is given by:
_{h}_{v}

The experimental database contains a total of 1,300 images (side-view-of-the-hand, back-of-the-hand and vascular-pattern-of-the-hand images) for 100 subjects,

In our experiments, we use summed score of all the scores from each unimodal matching as a final matching score. As the EER of unimodal biometrics, hand geometry, and VPE acquired 1.81%, and 1.19%. Our proposed approach is based on a score-level fusion with the unimodal biometrics approach. The score level was normalized as a z-score. The fusion of hand geometry and the VPE obtains the best EER of 0.06%.

We measured the speed of the proposed algorithm on a desktop computer with Intel Pentium (R) Dual CPU 2.00 GHz processor, with 2.00 GB of RAM The computational complexity of processing is summarized in

In this article, we have proposed a new multimodal biometric verification method based on the fusion of the hand geometry and the vascular pattern from a single hand image. The proposed hand recognition method was based on K-curvature, thickness of the side view of the hand, and VPE. The accuracy of the proposed multimodal biometrics method is better than that obtained using unimodal biometrics.

This work supported by the Nano IP/SoC Promotion Group of Seoul R&BD Program (10920) and the Converging Research Center Program through the Ministry of Education, Science and Technology (2012K001313).

Block diagram of the implemented system.

Acquisition of a sample image of the back of a hand.

Preprocessing for hand recognition. (

Gaussian filter. (

Median filter. (

Thickness search of the side view of the hand and the profile of the thickness.

(

The feature extraction for K-curvature.

The feature extraction for lengths and angles of finger valleys.

The feature extraction for the lengths of fingers.

The feature extraction for the profile of fingers.

The VPE algorithm processing.

Curvatures estimate. (

Distribution of genuine and impostor scores after z-score Normalization (

ROC curves of unimodal and multimodal biometrics.

Comparative biometric example (dorsum hand geometry, dorsum hand vascular pattern and multi-model biometrics).

1999 [ |
H | Contour coordinates | 53 | FAR = 1, FRR = 6 |

1999 [ |
H | Length, width, thickness and deviation | 20 | EER = 5 |

2006 [ |
H | Width and Curvature | 73 | EER = 3.6 |

2009 [ |
H | Fusion SVDD | 86 | EER = 1.5 |

1995 [ |
V | Sequential correlation | 20 | FAR = 0, FRR = 7.9 |

2004 [ |
V | Feature points of the vein patterns | 32 | EER = 2.3 |

2004 [ |
V | FFT based phase correlation | 25 | FAR = 0.73, FRR = 4 |

2005 [ |
V | Distance between feature points | 48 | FAR = 0, FRR = 0.9 |

2009 [ |
VK | Vascular structures and knuckle shape | 100 | EER = 1.14 |

2003 [ |
PH | Palm-print and Hand Geometry | 100 | FAR = 0, FRR = 1.41 |

2003 [ |
PH | Palm-print and Hand Geometry | 50 | FAR = 0.1818, FRR = 1 |

2010 [ |
VF | Vascular and geometry of finger | 102 | EER = 0.075 |

Our work | VH | Vascular and geometry of hand | 100 | EER = 0.06 |

H: Hand geometry, V: Vascular, K: Knuckle shape, P: Palm-print, F: Finger geometry.

The features of hand recognition.

The side view of the hand | _{side} |

The back-of-the-hand view | _{1}(_{2}(_{3}(_{4}( |

_{1}, _{2} | |

_{1}, _{2}, _{3}, _{4}, _{5}, _{6}, _{7}, _{8} | |

_{1}(_{2}(_{3}(_{4}(_{5}( | |

VPE |

The matching score.

Euclidean distance | |

Distance measurement for polygonal curves | _{1}, _{2}, _{3}, _{4}_{5}, _{6}, _{7}, _{8}, _{9}, _{10} |

matching |

The computational timing for processing.

Image Preprocessing | 112 |

Hand geometric Processing | 11 |

VPE Processing | 16 |