Generalized net model of a biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations

: In the current research work a multimodal biometric system is investigated. It combines the palm vein authentication and palm geometry recognition methods. The system will be used to manage the access control. The apparatus of generalized nets is applied to model the biometric authentication processes. The constructed generalized net model of biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations can be used for simulation of the real processes. The intuitionistic fuzzy evaluations are used to compare the user traits with the templates stored in database.


Introduction
The standard process of biometric pattern recognition problem contains a sequence different stages: acquisition, image quality assessment, preprocessing, region of interest (RoI) determination (templates), feature extraction and biometric comparison. Types of biometric authentication methods include face recognition, fingerprint recognition, eyes-retina-iris recognition, ear recognition, hand geometry recognition, odor identification, vein recognition, gait recognition, typing recognition, voice -speaker authentication, signature recognition and etc. Depending of the traits for capturing the algorithm can be modified. Hand-based biometric systems measure and analyze the structure, shape and proportions of the hand or extract characteristics of the skin surface of the palm. The scan devices are measuring and recording the length, width, thickness, and surface area of the hand of an individual. Hand geometry systems use a camera to capture a silhouette image of the hand. Palm vein authentication uses palm veins as the biometric feature. In the palm vein scan the infrared light maps the unique vein structure of the palm. The infrared light observes the palm vein, which is normally unobservable by the human eye. The similarity between the captured palm vein and the template stored in the database can be calculated using different methods. The resulting similarity score is verified using predetermined threshold [18].

Generalized net model of biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations
The theory of Genelarized Nets (GNs) is introduced in [1,6,7]. GN models for pattern recognition processes are published [2][3][4][5]10]. GN model of biometric access-control system and GN model of multimodal biometric systems are constructed [2,8]. The biometric methods as iris recognition [11,17], face recognition [14−16], fingerprints recognition [9] and signature verification [10], image classification [13] are already modeled using the apparatus of GNs. In the current paper a generalized net model of biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations is constructed using GNDraw software [12]. It contains 9 transitions and 39 places (Fig. 1). The set of transitions А has the following form: where the transitions describe the following processes: • Z1 -users; • Z2 -scanning the user traits: palm vein trait and palm geometry trait; • Z3 -image quality assessment and preprocessing the palm vein and palm geometry images; • Z4 -region of interest (RoI) determination and palm vein templates extracting; • Z5 -region of interest (RoI) determination and palm geometry templates extracting; • Z6 -storing templates and passwords in database; • Z6 -passwords validation; • Z8 -biometric comparison (pattern matching); • Z9 -calculating intuitionistic fuzzy evaluations.
Initially, there is one α14-token that is located in place L28 with initial characteristic: "database". In the next time-moments this token is split into two or more. The original α14-token will continue to stay in place l28, while the other α-tokens will move to the next transitions. The token α1 enters the net via place l1 with initial characteristic: "user".
The α-tokens that enter places l2 and l3 have the following characteristics: "user for scanning" in place l2, and "user for password" in place l3.
The token β1 enters the net via place l4 with initial characteristic: "scanning parameters". The transition Z2 has the form: • W8,5 = "there is scanned palm geometry"; • W8,6 = "there is scanned palm vein"; • W8,7 = "the user traits is needed to scan again"; The α-tokens that enter in the places l5, l6 and l7 have the following characteristics: • "scanned palm geometry" in place l5, • "scanned palm vein" in place l6, and • "the user traits to scan again" in place l7.
The token β2 enters the net via place l9 with initial characteristic: "parameters for preprocessing".
The transition Z3 has the form: The α-tokens that enter places l10 and l11 have the following characteristics: "preprocessed palm vein images" in place l10, and "preprocessed palm geometry images" in place l11. The token β3 enters the net via place l13 with initial characteristic: "parameters for palm vein templates extraction".
The transition Z4 has the form: The α-tokens that enter in the places l14 and l15 have the following characteristics: "extracted palm vein templates for comparison" in place l10 and "extracted palm vein templates for storing in database" in place l11. The token β4 enters the net via place l17 with initial characteristic: "parameters for palm geometry extraction".
The transition Z5 has the form: The α-tokens that enter places l18 and l19 have the following characteristics: "extracted palm geometry templates for storing in database" in place l18 and "extracted palm geometry templates for comparison" in place l19. The token β5 enters the net via place l21 with initial characteristic: "previously generated user traits data and passwords".
The α-tokens that enter places l22, l23, l24, l25, l26 and l27 have the following characteristics: • "demand of palm vein templates extraction" in place l22, • "templates for preprocessing" in place l23, • "palm vein templates for comparison" in place l24, • "palm geometry templates for comparison" in place l25, • "password" in place l26 and • "demand of palm geometry templates extraction" in place l27. The token β6 enters the net via place l29 with initial characteristic: "parameters for pattern matching". The transition Z7 has the form: l19, l24, l25, l29, l33, l34, l37}, {l30, l31, l32, l33, l39}  The α-tokens that enter in the places l30, l31, l32 and l39 have the following characteristics: • "palm vein patterns for intuitionistic fuzzy estimation" in place l30, • "palm geometry patterns for intuitionistic fuzzy estimation" in place l31, • "password for intuitionistic fuzzy estimation" in place l32 and • "result of pattern matching using intuitionistic fuzzy estimations" in place l39. The intuitionistic fuzzy evaluations of the images of palm vein, palm geometry and passwords are calculated using the following sets: − cardinality of the set of pixels is p; − cardinality of the common set of pixels in the two images t; − cardinality of the set containing the different pixels from the first image f . Therefore, the intuitionistic fuzzy estimations have the following form: The intuitionistic fuzzy evaluations are calculated for the palm geometry authentication, palm vein authentication and password identification.
The transition Z8 has the form: The α-token that enters place l34 has the following characteristics: "password".
The token β6 enters the net via place l36 with initial characteristic: "formulas for intuitionistic fuzzy evaluations".
The transition Z9 has the form: The α-token that enters in the place l37 has the following characteristics: "intuitionistic fuzzy evaluations".

Conclusion
In the present research work, a generalized net model of biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations is constructed. Palm geometry identification and palm vein matching are two of the main methods in the area of biometrics authentication. They are used in access control systems. The calculated intuitionistic fuzzy evaluations are used in the pattern matching phase. The constructed generalized net model of biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations can be applied for simulation of the real access control processes.