Patent Publication Number: US-7913090-B2

Title: Authentication systems and authentication method

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority to Japanese Patent Document No. 2004-239439 filed in Japan on Aug. 19, 2004, the contents of which are herein incorporated by reference. 
     BACKGROUND 
     The present invention relates to an authentication system for biometric authentication authenticating a biometric subject based on a characteristic quantity acquired from the related biometric subject and a method of same. 
     In a communication system for communication via a network and a predetermined processing system etc., it is sometimes authenticated whether or not the user is a legitimate user. 
     Such authentication includes for example biometric authentication reading biometric data such as fingerprints and vein patterns from the user and performing the authentication based on correlation values of inspected characteristic data showing characteristic features inherent to the user extracted from the biometric data and previously held comparative characteristic data. 
     In such biometric authentication, how a threshold value of the correlation value set as the standard for judging whether or not the user is the true person or another person is determined is important for achieving a high reliability. 
     Namely, the probability of erroneously judging another person as the true person, that is, a False Acceptance Rate (FAR), and the probability of erroneously judging a true person as if he were not the true person, that is, a False Rejection Rate (FRR), are determined according to the method of determination of the threshold value. 
     The method of determination of the threshold value includes a variety of methods such as the method shown in the following Patent Document 1. 
     Patent Document 1: Japanese Patent No. 3439359 
     SUMMARY 
     The reliability of the authentication systems explained above depends upon how the above threshold value is determined. 
     At present, there is a demand for further raising the reliability of the authentication according to the authentication systems explained above. 
     Further, there is a demand for realizing a desired false acceptance rate FAR and the false rejection rate FRR in accordance with the characteristics etc. of the service for which the authentication is used. 
     The present invention has as its object to solve the problems of the prior art explained above by providing an authentication system and an authentication method enabling authentication with a high reliability in comparison with the prior art. 
     Further, another object of the present invention is to provide an authentication system and an authentication method able to realize a desired false acceptance rate or false rejection rate in accordance with the characteristics etc. of the service for which the authentication is used. 
     To solve the problems of the prior art explained above and achieve the above object, the authentication system of a first aspect of the invention is an authentication system for comparing a correlation value between inspected characteristic data of biometric data acquired from a biometric subject being inspected and comparative data linked with the predetermined biometric subject and a predetermined threshold value linked with the predetermined biometric subject to authenticate whether or not the biometric subject being inspected is the predetermined biometric subject, including: a storing means for storing a threshold value defined so that a value obtained by dividing an absolute value of a difference between a first mean value of a plurality of first correlation values generated by detecting correlation with the comparative data for a plurality of first characteristic data previously acquired from the predetermined biometric subject and the threshold value by a standard deviation of the plurality of first correlation values and values obtained by dividing an absolute value of a difference between a second mean value of a plurality of second correlation values generated by detecting correlation with the comparative data for a plurality of second characteristic data previously acquired from a biometric subject other than the predetermined biometric subject and the threshold value by the plurality of second correlation values coincide; and an authenticating means for comparing the inspected characteristic data and the threshold value read out from the storing means to authenticate whether or not the biometric subject being inspected is the predetermined biometric subject. 
     The mode of operation of the authentication system of the first aspect of the invention is as follows. 
     The authenticating means authenticates whether or not the biometric subject being inspected is the predetermined biometric subject by comparing the inspected characteristic data and the threshold value read out from the storing means. 
     An authentication method of a second aspect of the invention is an authentication method comparing a correlation value between inspected characteristic data of a biometric subject acquired from the biometric subject being inspected and comparative data linked with a predetermined biometric subject and a predetermined threshold value linked with the predetermined biometric subject to authenticate whether or not the biometric subject being inspected is the predetermined biometric subject, including: a first step of determining a threshold value so that a value obtained by dividing an absolute value of a difference between a first mean value of a plurality of first correlation values generated by detecting correlation with the comparative data for a plurality of first characteristic data previously acquired from the predetermined biometric subject and the threshold value by a standard deviation of the plurality of first correlation values and values obtained by dividing an absolute value of a difference between a second mean value of a plurality of second correlation values generated by detecting correlation with the comparative data for a plurality of second characteristic data previously acquired from a biometric subject other than the predetermined biometric subject and the threshold value by the plurality of second correlation values coincide; and a second step of authenticating whether or not the biometric subject being inspected is the predetermined biometric subject by comparing the inspected characteristic data and the threshold value determined at the first step. 
     An authentication system of a third aspect of the invention is an authentication system comparing a correlation value between inspected characteristic data of a biometric subject acquired from the biometric subject being inspected and comparative data linked with a predetermined biometric subject and a predetermined threshold value linked with the predetermined biometric subject to authenticate whether or not the biometric subject being inspected is the predetermined biometric subject, including: an inputting means for inputting a false rejection rate showing a probability of certifying that the biometric subject being inspected who is the predetermined biometric subject is not the predetermined biometric subject; a threshold value determining means for determining the threshold value so as to satisfy the false rejection rate input by the inputting means by assuming that a plurality of correlation values generated by detecting correlation with the comparative data for the plurality of characteristic data previously acquired from the predetermined biometric subject are according to a normal profile; and an authenticating means for authenticating whether or not the biometric subject being inspected is the predetermined biometric subject by comparing the correlation value of the inspected characteristic data and the comparative data and the threshold value determined by the threshold value determining means. 
     A mode of operation of the authentication system of the third aspect of the invention is as follows. 
     The inputting means inputs a false rejection rate showing the probability of certifying that a biometric subject being inspected which is the predetermined biometric subject is not the predetermined biometric subject. 
     Next, the threshold value determining means determines the threshold value so as to satisfy the false rejection rate input by the inputting means by assuming that a plurality of correlation values generated by detecting correlation with the comparative data for the plurality of characteristic data previously acquired from the predetermined biometric subject are according to a normal profile. 
     Next, the authenticating means authenticates whether or not the biometric subject being inspected is the predetermined biometric subject by comparing the correlation value of the inspected characteristic data and the comparative data and the threshold value determined by the threshold value determining means. 
     An authentication method of a fourth aspect of the invention is an authentication method comparing a correlation value between inspected characteristic data of a biometric subject acquired from the biometric subject being inspected and comparative data linked with a predetermined biometric subject and a predetermined threshold value linked with the predetermined biometric subject to authenticate whether or not the biometric subject being inspected is the predetermined biometric subject, including: a first step of inputting a false rejection rate showing the probability of certifying that the biometric subject being inspected which is the predetermined biometric subject is not the predetermined biometric subject; a second step of determining the threshold value so as to satisfy the false rejection rate input in the first step by assuming that a plurality of correlation values generated by detecting correlation with the comparative data for the plurality of characteristic data previously acquired from the predetermined biometric subject are according to a normal profile; and a third step of authenticating whether or not the biometric subject being inspected is the predetermined biometric subject by comparing the correlation value of the inspected characteristic data and the comparative data and the threshold value determined in the second step. 
     An authentication system of a fifth aspect of the invention is an authentication system comparing a correlation value between inspected characteristic data of a biometric subject acquired from the biometric subject being inspected and comparative data linked with a predetermined biometric subject and a predetermined threshold value linked with the predetermined biometric subject to authenticate whether or not the biometric subject being inspected is the predetermined biometric subject, including: an inputting means for inputting a false acceptance rate showing the probability of certifying that the biometric subject being inspected who is not the predetermined biometric subject is the predetermined biometric subject; a threshold value determining means for determining the threshold value so as to satisfy the false acceptance rate input by the inputting means by assuming that a plurality of correlation values generated by detecting correlation with the comparative data for the plurality of characteristic data previously acquired from the predetermined biometric subject are according to a normal profile; and an authenticating means for authenticating whether or not the biometric subject being inspected is the predetermined biometric subject by comparing the correlation value of the inspected characteristic data and the comparative data and the threshold value determined by the threshold value determining means. 
     A mode of operation of the authentication system of the fifth aspect of the invention is as follows. 
     The inputting means inputs a false acceptance rate showing the probability of certifying that a biometric subject being inspected which is not a predetermined biometric subject is the predetermined biometric subject. 
     Next, the threshold value determining means determines the threshold value so as to satisfy the false acceptance rate input by the inputting means by assuming that a plurality of correlation values generated by detecting correlation with the comparative data for the plurality of characteristic data previously acquired from the predetermined biometric subject are according to a normal profile. 
     Next, the authenticating means compares a correlation value of the inspected characteristic data and the comparative data and the threshold value determined by the threshold value determining means to authenticate whether or not the biometric subject being inspected is the predetermined biometric subject. 
     An authentication method of a sixth aspect of the invention is an authentication method for comparing a correlation value between inspected characteristic data of a biometric subject acquired from the biometric subject being inspected and comparative data linked with a predetermined biometric subject and a predetermined threshold value linked with the predetermined biometric subject to authenticate whether or not the biometric subject being inspected is the predetermined biometric subject, including: a first step of inputting a false acceptance rate showing the probability of certifying that the biometric subject being inspected which is not the predetermined biometric subject is the predetermined biometric subject; a second step of determining the threshold value so as to satisfy the false acceptance rate input in the first step by assuming that a plurality of correlation values generated by detecting correlation with the comparative data for the plurality of characteristic data previously acquired from the predetermined biometric subject are according to a normal profile; and a third step of authenticating whether or not the biometric subject being inspected is the predetermined biometric subject by comparing the correlation values of the inspected characteristic data and the comparative data and the threshold value determined in the second step. 
     According to the first and second aspects of the invention, an authentication system and the authentication method able to perform authentication with a higher reliability in comparison with the conventional ones can be provided. 
     According to the third to sixth aspects of the invention, authentication systems and the authentication methods able to realize an input false acceptance rate or a false rejection rate can be provided. 
     Additional features and advantages of the present invention are described in, and will be apparent from, the following Detailed Description and the Figures. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is a view of the overall configuration of an authentication system of a first embodiment of the present invention. 
         FIG. 2  is a flow chart for explaining processing of a threshold value determination unit shown in  FIG. 1 . 
         FIG. 3  is a flow chart for explaining the processing of step ST 3  shown in  FIG. 2 . 
         FIG. 4  is a diagram for explaining characteristics of another profile. 
         FIG. 5  is a diagram for explaining characteristics of another profile where a skewness is negative. 
         FIG. 6  is a diagram for explaining characteristics of a deformed other profile where the skewness is negative. 
         FIG. 7  is a diagram for explaining a threshold value when using a deformed other profile where the skewness is negative. 
         FIG. 8  is a diagram for explaining characteristics of another profile where the skewness is positive. 
         FIG. 9  is a diagram for explaining characteristics of a deformed other profile where the skewness is positive. 
         FIG. 10  is a diagram for explaining the threshold value when using a deformed other profile where the skewness is positive. 
         FIG. 11  is a view of the overall configuration of an authentication system of a second embodiment of the present invention. 
         FIG. 12  is a flow chart for explaining the processing of step ST 3  shown in  FIG. 2  in the authentication system shown in  FIG. 11 . 
         FIG. 13  is a view of the overall configuration of an authentication system of a third embodiment of the present invention. 
         FIG. 14  is a diagram for explaining relationships of another profile and a true profile and FRR and FAR. 
         FIG. 15  is a diagram for explaining a normal profile table data TABLE stored in a memory shown in FIG.  13 . 
         FIG. 16  is a flow chart for explaining pre-processing of the threshold value determination unit of the authentication system shown in  FIG. 15 . 
         FIG. 17  is a flow chart for explaining the processing of the threshold value determination unit of the authentication systems shown in  FIG. 15 . 
         FIG. 18  is a diagram for explaining an example of an experiment of the authentication system shown in  FIG. 15 . 
     
    
    
     DESCRIPTION OF NOTATIONS 
       10  . . . biometric subject,  12  . . . biometric data reading unit,  14  . . . characteristic extraction unit,  16  . . . correlation value calculation unit,  18  . . . memory,  20  . . . authentication unit,  22 ,  122 ,  222  . . . threshold value determination unit,  221  . . . input unit, TP . . . true profile, OP, OPA . . . other profile, FAR . . . false acceptance rate, FRR . . . false rejection rate. 
     DETAILED DESCRIPTION 
     Below, authentication systems according to embodiments of the present invention will be explained. 
     First Embodiment 
     Below, this embodiment will be explained with reference to  FIG. 1  to  FIG. 3 . 
     First, the correspondence between components of the present embodiment and components of the present invention will be explained. 
     A memory  18  corresponds to the storing means of the first aspect of the invention, an authentication unit  20  corresponds to the authenticating means of the first aspect of the invention, and a threshold value determination unit  22  corresponds to the threshold value determining means of the first aspect of the invention. 
     True person sample data Ct 1  to Ctn correspond to the first characteristic data of the first aspect of the invention, other sample data Co 1  to Com correspond to the second characteristic data of the first aspect of the invention, correlation data Ft correspond to the first correlation values of the first aspect of the invention, and correlation data Fo correspond to the second correlation values of the first aspect of the invention. 
     Further, a mean value μt corresponds to the first mean value of the first aspect of the invention, and a mean value μo corresponds to the second mean value of the first aspect of the invention. 
     Further, a threshold value Xth corresponds to the threshold value of the first aspect of the invention. 
       FIG. 1  is a view of the configuration of an authentication system  1  according to an embodiment of the present invention. 
     As shown in  FIG. 1 , the authentication system  1  has for example a biometric data reading unit  12 , characteristic extraction unit  14 , correlation value calculation unit  16 , memory  18 , authentication unit  20 , and threshold value determination unit  22 . 
     The characteristic extraction unit  14 , correlation value calculation unit  16 , memory  18 , authentication unit  20 , and threshold value determination unit  22  are realized by executing a program by dedicated hardware such as an electronic circuit or processing circuit. 
     The biometric data reading unit  12  reads for example the fingerprint or vein pattern or other the biometric data from a human finger or other biometric subject  10  and outputs the related read biometric data S 12  to the characteristic extraction unit  14 . 
     The characteristic extraction unit  14  extracts inspected characteristic data S 14  showing a characteristic feature such as a branch point and end point of a fingerprint and vein pattern from the biometric data S 12  input from the biometric data reading unit  12  and outputs this to the correlation value calculation unit  16 . 
     The correlation value calculation unit  16  detects correlation data Ft indicating the correlation value of the inspected characteristic data S 14  input from the characteristic extraction unit  14  and the reference characteristic data Cref read out from the memory  18  and outputs this to the authentication unit  20 . 
     The memory  18  stores the reference characteristic data Cref and a threshold value Xth written from the threshold value determination unit  22 . 
     The authentication unit  20  judges whether or not the correlation value indicated by the correlation data Ft input from the correlation value calculation unit  16  is larger than the threshold value Xth, certifies that the biometric subject  10  is legitimate when judging that the correlation value is larger, and certifies that the biometric subject  10  is not legitimate when not judging so. 
     The threshold value determination unit  22  calculates the threshold value Xth as explained below based on the true sample data Ct 1  to Ctn of the characteristic data previously acquired from the biometric subject  10  a plurality of times and the other sample data Co 1  to Com of the characteristic data previously acquired from a biometric subject other than the biometric subject  10  (other person) a plurality of times and writes this into the memory  18 . 
       FIG. 2  is a flow chart for explaining the processing of the threshold value determination unit  22  shown in  FIG. 1 . 
     Step ST 1 : 
     The threshold value determination unit  22  receives as input the true sample data Ct 1  to Ctn from another apparatus via the memory  18  or the network etc. 
     Step ST 2 : 
     The threshold value determination unit  22  receives as input the other sample data Co 1  to Com from another apparatus via the memory  18  or the network etc. 
     Step ST 3 : 
     The threshold value determination unit  22  calculates the threshold value Xth based on the true sample data Ct 1  to Ctn input at step ST 1  and the other sample data Co 1  to Com input at step ST 2 . 
     Step ST 4 : 
     The threshold value determination unit  22  writes (sets) the threshold value Xth calculated at step ST 3  in the memory  18 . 
     Below, step ST 3  shown in  FIG. 2  will be explained in detail. 
       FIG. 3  is a flow chart for explaining step ST 3  shown in  FIG. 2 . 
     Step ST 11 : 
     The threshold value determination unit  22  calculates correlation data Ft 1  to Ftn indicating correlation values with the reference characteristic data Cref read out from the memory  18  for each of the true sample data Ct 1  to Ctn input at step ST 1  shown in  FIG. 2 . 
     Step ST 12 : 
     The threshold value determination unit  22  calculates correlation data Fo 1  to Fom indicating correlation values with the reference characteristic data Cref read out from the memory  18  for each of the other sample data Co 1  to Com input at step ST 2  shown in  FIG. 2 . 
     Step ST 13 : 
     The threshold value determination unit  22  calculates the mean value μt of n number of correlation data Ft 1  to Ftn calculated at step ST 11 . 
     Step ST 14 : 
     The threshold value determination unit  22  calculates the mean value μo of m number of correlation data Fo 1  to Fom calculated at step ST 12 . 
     Step ST 15 : 
     The threshold value determination unit  22  calculates the standard deviation σt of the correlation data for the true person based on the following equation (1) based on the correlation data Ft 1  to Ftn calculated at step ST 11  and the mean value μt calculated at step ST 13 . 
     
       
         
           
             
               
                 
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     Step ST 16 : 
     The threshold value determination unit  22  calculates the standard deviation σo of the correlation data for the other person based on the following equation (2) based on the correlation data Fo 1  to Fom calculated at step ST 12  and the mean value μo calculated at step ST 14 . 
     
       
         
           
             
               
                 
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     Step ST 17 : 
     The threshold value determination unit  22  calculates a value X satisfying the following equation (3) based on the mean value μt calculated at step ST 13  and the standard deviation σt calculated at step ST 15 . 
     Note that, in the following equation (3), the left side indicates a Mahalanobis distance according to the true profile, and the right side indicates the Mahalanobis distance according to the other profile. 
     When the following equation (4) is satisfied, the following equation (3) becomes like the following equation (5) and further can be modified as in the following equations (6) and (7). 
     Accordingly, the threshold value determination unit  22  calculates the value X based on the following equation (7). 
                   [       Equation     ⁢           ⁢   3     ]                                    X   -     μ   ⁢           ⁢   t              σ   ⁢           ⁢   t       =            X   -     μ   ⁢           ⁢   o              σ   ⁢           ⁢   o               (   3   )               [Equation 4] μt&gt;μO  (4)
 
                   [       Equation     ⁢           ⁢   5     ]                                 μ   ⁢           ⁢   t     -   X       σ   ⁢           ⁢   t       =       X   -     μ   ⁢           ⁢   o         σ   ⁢           ⁢   o               (   5   )               [Equation 6]   σo ( μt−X ) =σt ( X−μo )  (6)
 
     
       
         
           
             
               
                 
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     Step ST 18 : 
     The threshold value determination unit  22  modifies the value X calculated at step ST 17  to the threshold value Xth. 
     Namely, the threshold value determination unit  22  assumes that the true profile defined by the correlation data Ft 1  to Ftn and the other profile defined by the correlation data Fo 1  to Fom are normal profiles and calculates the threshold value Xth based on the mean values μt and μo and standard deviations σt and σo of these. 
     Below, the operation of the authentication system  1  shown in  FIG. 1  will be explained. 
     The threshold value determination unit  22  shown in  FIG. 1  generates the threshold value Xth as explained by using  FIG. 2  and  FIG. 3  and writes this into the memory  18 . 
     At the time of the inspection, the biometric data reading unit  12  reads biometric data such as a fingerprint or vein pattern from a human finger or other biometric subject  10  and outputs the read biometric data S 12  to the characteristic extraction unit  14 . 
     Next, the characteristic extraction unit  14  extracts the inspected characteristic data S 14  indicating a characteristic feature such as a branch point or end point of a fingerprint or vein pattern from the biometric data S 12  input from the biometric data reading unit  12  and outputs this to the correlation value calculation unit  16 . 
     Next, the correlation value calculation unit  16  detects the correlation data Ft indicating the correlation value of the inspected characteristic data S 14  input from the characteristic extraction unit  14  and the reference characteristic data Cref read out from the memory  18  and outputs this to the authentication unit  20 . 
     Next, the authentication unit  20  judges whether or not the correlation value indicated by the correlation data Ft input from the correlation value calculation unit  16  is larger than the threshold value Xth, certifies that the biometric subject  10  is legitimate when judging that the correlation value is larger, and certifies that the biometric subject  10  is not legitimate when not judging so. 
     As explained above, according to the authentication system  1 , the threshold value determination unit  22 , as shown at step ST 17  shown in  FIG. 3  and above equation (3), determines the threshold value Xth (X) so that it indicates the Mahalanobis distance according to the true profile and it coincides with the Mahalanobis distance according to the other profile. 
     Due to this, the false acceptance rate FAR and the false rejection rate FRR can be made to schematically coincide and balanced high precision authentication can be performed. 
     Second Embodiment 
     In the present embodiment, the true profile TP corresponds to the first normal profile of the first aspect of the invention, the other profile OP corresponds to the second normal profile of the first aspect of the invention, and the deformed other profile corresponds to the third normal profile of the first aspect of the invention. 
     In the above first embodiment, the threshold value determination unit  22  calculated the mean value μo and the standard deviation σo by using the other profile defined according to the correlation data Fo 1  to Fom as it was. 
     In the present embodiment, the other profile is deformed by using the skewness, calculates the mean value μo and the standard deviation σo based on the deformed other profile, and stably suppresses the FAR/FRR low. 
     Here, the skewness is the value expressing the left and right symmetry of the profile, becomes zero in the case of the left and right symmetry as in the normal profile, becomes the profile biased to the right as shown in for example  FIG. 4A  in the case of a negative value, and becomes the profile biased to the left as shown in for example  FIG. 4B  in the case of a positive value, and the spread of the profile becomes the inverse direction thereof. 
     Here, when the mean value of m correlation data Fo 1  to Fom is Fave and a non-biased dispersion is ν, the skewness Sk becomes as in the following equation (8). 
     
       
         
           
             
               
                 
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     First, the case where the other profile OP is biased to the right with reference to  FIG. 5  will be explained. 
     For example, when performing personal authentication based on the true profile TP and the other profile OP shown in  FIG. 5 , when considering at which position to take the threshold value for distinguishing the true person and the other person, the Mahalanobis distance from the center OP_C of the other profile OP is used, but as shown in  FIG. 5 , when the other profile OP has a biased profile, it becomes possible to lower the FAR without raising the FRR by utilizing that eccentricity. 
     As seen from  FIG. 5 , the frequency is sharply lowered on the right side from the profile center of the other profile OP and there is no spread of the profile. On the other hand, on the left side, the frequency gently falls in comparison with the right side and also the spread of profile is large. In the conventional case, the standard deviation of the other profile OP is calculated by using these left and right data, but in confirming the true property, by using only the data on the true side, that is, the sharply changing data, to calculate the standard deviation again, it becomes possible to obtain the true side other profile data in a conscious form. In the case of a profile inclined to the true side (right) in this way, the skewness becomes negative. 
     First, consider the case where the skewness is negative. When using only the spread on the true side of the other profile OP and reform the other profile OP again considering another person with respect to the true person, the profile becomes like the other profile OPA shown in  FIG. 6 . Note that, the center of the other profile OP on the true side is set at a position where the degree of the other profile becomes the maximum value. 
     Accordingly, when the data composing the other profile OP is xi (i=1 to m) and the data composing the data composing the other profile on the true side is xj (j=1 to s), the profile σc 2  is indicated by the following equation (9). 
     
       
         
           
             
               
                 
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     When viewing the other profile OP and the distance of the true profile TP from the deformed other profile OPA by using the standard deviation as a measure, they become as shown in  FIG. 7 . 
     In  FIG. 7 , consider the change of the threshold value according to the Mahalanobis distance by using the above deformed other profile OPA. 
     In  FIG. 7 , a threshold value thr 1  indicates the distance 3 times the standard deviation from the center of the other profile and a threshold value thr 2  indicates the distance 4.27 times the standard deviation from the profile center of the other person. 
     When using the threshold value thr 2 , the FAR becomes 0.001% when converted from the normal profile table. 
     When using the threshold value thr 2  defined based on the other profile OP, the threshold value thr 2  fully enters into the true profile and the false rejection rate FRR becomes relatively large. On the other hand, when determining the threshold value thr 2  based on the deformed other profile OPA, the false rejection rate FRR can be sufficiently, lowered with almost no rise of the false acceptance rate FAR. 
     Next, the case where the other profile OP is biased to the left will be explained with reference to  FIG. 8 . 
     For example, when using only the spread on the true side of the other profile OP even in the case shown in  FIG. 8  to reform the other profile OP again considering another person with respect to the true person, the profile becomes as in  FIG. 9 . Note that the center of the other profile OP on the true side is made the position where the degree of the other profile becomes the maximum value. 
     Then, when viewing the other profile OP and the distance of the true profile TP from the deformed other profile OPA by using the standard deviation as a measure, the profiles become as shown in  FIG. 9 . 
     In  FIG. 9 , consider the change of the threshold value according to the Mahalanobis distance by using the deformed other profile explained above. 
     In  FIG. 10 , the threshold value thr 1  indicates the distance 3 times the standard deviation from the center of the other profile, and the threshold value thr 2  indicates the distance 4.27 times the standard deviation from the profile center of the other person. 
     When the threshold value thr 2  is used, FAR becomes 0.001% when converted from the normal profile table. 
     When the threshold value thr 2  defined based on the other profile OP is used, the threshold value thr 2  is sufficiently apart from the true profile, and the false rejection rate FRR is sufficiently small. On the other hand, when the threshold value thr 2 A is determined based on the deformed other profile OPA, both of the false acceptance rate FAR and the false rejection rate FRR rise. That is, when the threshold value is determined by the whole profile, there is a worry of the set FAR and FRR insufficiently functioning. According to the present embodiment, the problem of a threshold value lower than the original threshold value being set and actually becoming an obstacle at the time of authentication can be solved. 
     Below, an authentication system  101  of the present embodiment for determining the threshold value Xth based on the other profile OPA obtained by deforming the other profile OP as explained above will be explained. 
       FIG. 11  is a view of the configuration of the authentication system  101  according to the embodiment of the present invention. 
     As shown in  FIG. 11 , the authentication system  101  has for example a biometric data reading unit  12 , characteristic extraction unit  14 , correlation value calculation unit  16 , memory  18 , authentication unit  20 , and threshold value determination unit  122 . 
     In  FIG. 11 , parts given the same notations as those of  FIG. 1  are the same as those explained in the first embodiment. 
     Namely, the authentication system  101  is different in the threshold value determination unit  122  from the threshold value determination unit  22  of the first embodiment. 
     The threshold value determination unit  122  is realized by running a program by dedicated hardware such as an electronic circuit or processing circuit. 
     Below, the threshold value determination unit  122  will be explained in detail. 
     The threshold value determination unit  122  calculates the threshold value Xth as will be explained below based on the true sample data Ct 1  to Ctn of the characteristic data previously acquired from a biometric subject  10  a plurality of times and the other sample data Co 1  to Com of the characteristic data previously acquired from a biometric subject other than the biometric subject  10  (other person) a plurality of times and writes this into the memory  18 . 
     In this case, as explained by using  FIG. 6 ,  FIG. 7 ,  FIG. 9 , and  FIG. 10 , the threshold value determination unit  122  does not use the other sample data Co 1  to Com as they are, but generates the other profile OPA which becomes linearly symmetric with the maximum degree about the other profile OP defined by the other sample data Co 1  to Com and calculates the threshold value Xth by using this other profile OPA. 
       FIG. 12  is a flow chart for explaining the processing of the threshold value determination unit  122 . 
     Step ST 32  shown in  FIG. 12  is the same as step ST 11  shown in  FIG. 3 . 
     Further, steps ST 34  to ST 39  shown in  FIG. 12  are the same as steps ST 13  to ST 18  shown in  FIG. 3 . 
     The threshold value determination unit  122  generates the other profile OPA which becomes linearly symmetric about the maximum degree in the other profile OP defined by the other sample data Co 1  to Com input at step ST 2  shown in  FIG. 2  as explained above. 
     Further, the threshold value determination unit  122 , at step ST 33 , calculates the correlation data Fo 1  to Fom indicating the correlation values with the reference characteristic data Cref read out from the memory  18  for each of the other sample data Co 1  to Com composing the other profile OPA generated at step ST 31 . 
     As explained above, according to the authentication system  101 , the threshold value determination unit  122  determines the threshold Xth based on the deformed other profile OPA by using the skewness of the other profile OP for the other profile OP, therefore the FAR/FRR can be stably suppressed low. 
     Third Embodiment 
     Below, the authentication system of the present embodiment will be explained by using  FIG. 13  to  FIG. 18 . 
     First, the correspondence between components of the present embodiment and components of the present invention will be explained. 
     The present embodiment corresponds to the third to sixth aspects of the invention. 
     An input unit  221  corresponds to the inputting means of the third and fifth embodiments, an authentication unit  20  corresponds to the authenticating means of the third and fifth aspects of the invention, and a threshold value determination unit  222  corresponds to the threshold value determining means of the third and fifth aspects of the invention. 
     Further, a memory  18  corresponds to the storing means of the third and fifth aspects of the invention. 
     Further, the false acceptance rate FAR corresponds to the false acceptance rate of the present invention, and the false rejection rate FRR corresponds to the false rejection rate. 
       FIG. 13  is a view of the configuration of an authentication system  201  according to this embodiment of the present invention. 
     As shown in  FIG. 13 , the authentication systems  201  has for example a biometric data reading unit  12 , characteristic extraction unit  14 , correlation value calculation unit  16 , memory  18 , authentication unit  20 , input unit  221 , and threshold value determination unit  222 . 
     In  FIG. 13 , parts given the same notations as those in  FIG. 1  are the same as those explained in the first embodiment. 
     Namely, the authentication system  201  has an input unit  221 . The threshold value determination unit  222  is different from the threshold value determination unit  22  of the first embodiment. 
     The threshold value determination unit  222  is realized by executing a program by dedicated hardware such as an electronic circuit or processing circuit. 
     The input unit  221  is an inputting means such as a keyboard and mouse and inputs a false acceptance rate or false rejection rate FRR in response to the operation of the user. 
     The threshold value determination unit  222  determines the threshold value Xth so as to satisfy the false acceptance rate FAR or the false rejection rate FRR input by the input unit  221  assuming that the true profile TP and the other profile OP are according to the normal profiles. 
     First, the relationships between the true profile TP and the other profile OP and the false acceptance rate FAR and the false rejection rate FRR will be explained with reference to  FIG. 14 . 
     In  FIG. 14 , the false acceptance rate FAR indicates the ratio with respect to the value obtained by integrating the other profile OP from the threshold value Xth to 1 for the entire other profile OP, that is, the ratio of the area of the right side in the figure from the threshold value Xth of the other profile OP. 
     On the other hand, the false rejection rate FRR indicates the ratio with respect to the value obtained by integrating the true profile TP from 0 to the threshold value Xth for the entire true profile TP, that is, the area of the left side in the figure from the threshold value Xth of the true profile TP. 
     
       
         
           
             
               
                 
                   [ 
                   
                     
                       Equation 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
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                       F 
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     When the input unit  221  inputs the false rejection rate FRR (%), the threshold value determination unit  222  specifies a value near a value “FRR/100” corresponding to the false rejection rate FRR from the normal profile table data TABLE shown in  FIG. 15  and designates the specified value as a Mahalanobis distance dt. The normal profile table data TABLE is stored in for example the memory  18  shown in  FIG. 13 . 
     At this time, the threshold value Xth becomes the following equation (11).
 
[Equation 11]
 
 Xth=μt−σtdt   (11)
 
     On the other hand, when viewing the threshold value Xth in the above equation (11) for the other profile OP, the Mahalanobis distance do of the distance from the center of the other profile OP becomes as in the following equation (12). 
     
       
         
           
             
               
                 
                   [ 
                   
                     
                       Equation 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   do 
                   = 
                   
                     
                       Xth 
                       - 
                       
                         μ 
                         ⁢ 
                         
                             
                         
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                         o 
                       
                     
                     
                       σ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       o 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Then, the threshold value determination unit  222  specifies the false acceptance rate FAR as the value corresponding to the Mahalanobis distance do from the normal profile table data TABLE shown in  FIG. 15 . 
     Further, when the input unit  221  inputs the false acceptance rate FAR (%), the threshold value determination unit  222  specifies a value near a value “FAR/100” corresponding to the false acceptance rate FAR from the normal profile table data TABLE shown in  FIG. 15  and determines the specified value as the Mahalanobis distance do. 
     At this time, the threshold value Xth becomes as in the following equation (13).
 
[Equation 13]
 
 Xth=μo+σodo   (13)
 
     On the other hand, when viewing the threshold value Xth of the above equation (13) for the true profile TP, the Mahalanobis distance dt of the distance from the center of the true profile TP becomes as in the following equation (14). 
     
       
         
           
             
               
                 
                   [ 
                   
                     
                       Equation 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   dt 
                   = 
                   
                     
                       
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       t 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Then, the threshold value determination unit  222  specifies the false rejection rate FRR as the value corresponding to the Mahalanobis distance dt from the normal profile table data TABLE shown in  FIG. 15 . 
     Note that, in the above example, the case of using the normal profile table data TABLE stored in the memory  18  was exemplified, but the Mahalanobis distance may be calculated by approximation based on the input false acceptance rate FAR or the false rejection rate FRR. 
     As the approximation, use is made of the approximation formula of Hastings et al., Maclaurin expansion formula, Shenton continued fraction expansion formula, asymptotic expansion formula, Laplace continued fraction expansion formula, Williams approximation formula, Yamauchi approximation formula, Gauss-Legendre numerical integration, etc. 
     Below, an example of the operation of the threshold value determination unit  222  will be explained. 
       FIG. 16  is a flow chart for explaining the pre-processing of the threshold value determination unit  222  shown in  FIG. 13 . 
     The threshold value determination unit  222  performs the pre-processing shown in  FIG. 16  before the false acceptance rate FAR or the false rejection rate FRR is input. 
     Steps ST 51  to ST 56  shown in  FIG. 16  are the same as steps ST 11  to ST 16  explained in the first embodiment by using  FIG. 3 . 
       FIG. 17  is a flow chart for explaining the processing of the threshold value determination unit  222  when the false acceptance rate FAR or the false rejection rate FRR is input. 
     Step ST 61 : 
     The threshold value determination unit  222  judges whether or not the input unit  221  inputted the false rejection rate FRR, proceeds to step ST 62  when judging it did, and proceeds to step ST 64  when judging it did not. 
     Step ST 62 : 
     The threshold value determination unit  222  specifies the value near “FRR/100” from the normal profile table data TABLE stored in the memory  18  based on the input false rejection rate FRR and designates the specified value as the Mahalanobis distance dt. 
     Step ST 63 : 
     The threshold value determination unit  222  performs the computation according to above equation (11) by using the Mahalanobis distance dt acquired at step ST 62 , the standard deviation σt calculated at step ST 55  shown in  FIG. 16 , and the mean value μt calculated at step ST 53  to calculate the threshold value Xth. 
     Note that the threshold value determination unit  222  calculates the false acceptance rate FAR by using the threshold value Xth as previously explained and changes the FRR and newly calculates the threshold value Xth where this does not satisfy the predetermined condition. 
     Step ST 64 : 
     The threshold value determination unit  222  judges whether or not the input unit  221  inputted the false acceptance rate FAR, proceeds to step ST 65  when judging it did, and returns to step ST 61  when judging it did not. 
     Step ST 65 : 
     The threshold value determination unit  222  specifies the value near “FAR/100” from the normal profile table data TABLE stored in the memory  18  based on the input false acceptance rate FAR and designates the specified value as the Mahalanobis distance do. 
     Step ST 66 : 
     The threshold value determination unit  222  performs the computation according to equation (13) by using the Mahalanobis distance ot acquired at step ST 65 , the standard deviation σo calculated at step ST 56  shown in  FIG. 16 , and the mean value μo calculated at step ST 54  to calculate the threshold value Xth. 
     Note that, the threshold value determination unit  222  calculates the false acceptance rate FAR by using the threshold value Xth as previously explained and changes the FRR and newly calculates the threshold value Xth where this does not satisfy the predetermined condition. 
     As explained above, according to the authentication system  201 , the threshold value Xth can be set so as to realize the false acceptance rate FAR or false rejection rate FRR input via the input unit  221 . 
     For this reason, authentication tailored to the service for which the authentication of the authentication system  201  is used can be carried out. Namely, depending on the content of the service, the false acceptance rate FAR may be high, but the false rejection rate FRR is desired to be lowered. Alternatively, the false rejection rate FRR may be high, but the false acceptance rate FAR is desired to be lowered. Authentication tailored to these is possible. 
     Below, an example of an experiment according to the authentication system  201  will be explained. 
     An image emphasizing only the finger vein pattern from a finger vein pattern image was used as the characteristic quantity of the true person. The correlation values of the images of the characteristic quantities were used to differentiate the true person and another person. In  FIG. 18 , several sets of true data are collected from seven subjects (A to G). There are exactly the number of true reference data of the true data. Points concentrated on the left side represent the correlation with the other person data, and points dispersed on the right side mean the correlation with the true data. A middle of a bar at the other person data means an average of correlation values with the other person data and means distances of σ and 3σ from the mean value. 
     In the example shown in  FIG. 18 , the true person and another person can be reliably separated with the same threshold value for any subject. That is, they may be separated when setting the threshold value at approximately 0.43. This value is determined by viewing the lowest value of the correlation values of the subject E and the true person. When the threshold value is further lowered, it becomes the maximum value of the correlation values of the subject C with the other person. That is, when the threshold value is lowered in order to avoid false rejection of the subject E, false acceptance of the subject C will be permitted. In this way, irrespective of the characteristic values extracted with the same measure, a variation occurs according to subjects, and it may be difficult to unambiguously determine the threshold value. In the case of the subject C, the maximum value of the correlation values with the other person is high, but the minimum value of the correlation values with the true person is large. That is, limited to the subject C, differentiating between the true person and another person becomes easy even when the threshold value is larger than 0.43 explained before. Further, limited to the subject D, the mean value is a little high, but the dispersion is small, therefore the threshold value can be suppressed low. 
     The present invention is not limited to the above embodiments. 
     In above embodiments, the case where the threshold value Xth was determined in the threshold value determination units  22 ,  122 , and  222  in the authentication systems  1 ,  101 , and  201  was exemplified, but the threshold value determination units  22 ,  122 , and  222  may be assembled in apparatuses other than the authentication systems  1 ,  101 , and  201 , for example service apparatuses with which the authentication systems  1 ,  101 , and  201  communicate, and the authentication systems  1 ,  101 , and  201  may receive as input the threshold value Xth from the related apparatuses. 
     INDUSTRIAL APPLICABILITY 
     The present invention can be applied to a system for authentication based on biometric data. 
     It should be understood that various changes and modifications to the presently preferred embodiments described herein will be apparent to those skilled in the art. Such changes and modifications can be made without departing from the spirit and scope of the present invention and without diminishing its intended advantages. It is therefore intended that such changes and modifications be covered by the appended claims.