Method and apparatus for comparing a test handwritten signature with a reference signature by using information relative to curvilinear and angular velocities of the signature

• US 5,101,437 A
• Filed: 02/11/1991
• Issued: 03/31/1992
• Est. Priority Date: 02/11/1991
• Status: Expired due to Term

• Current Assignee: Sign Matrix Incorporated
• Original Assignee: Ecole polytechnique
• Inventors: Plamondon, Rejean
• Primary Examiner(s): Boudreau, Leo H.
• Assistant Examiner(s): Stellrecht, Barry
• Application Number:
  US07/653,656
• Time in Patent Office: 414 Days
• Field of Search: 382/3, 382/13
• US Class Current: 382/122
• CPC Class Codes: G06V 40/30 Writer recognition; Reading and verifying signatures
• CPC Class Codes: G07C 9/35 by means of a handwritten signature

Abstract

Apparatus and method for comparing a test handwriting signature with a reference signature where each of the test and reference signatures have been acquired by generating three electrical digital position signals characterizing a trajectory of a handwriting signature. The apparatus comprises a device for calculating variations of simple dynamic parameters of the test signature with respect to the simple dynamic parameters of the reference signature, by calculating a first evaluating function C1; a device for comparing C1 with a first threshold value, and rejecting said test signature if C1 passes the first threshold value; a device for calculating local intrinsic correlations of V.sub.σ and V.sub.θ values of the test and reference signatures for each pair of characteristic segments, by calculating a second evaluating function C2; a device for comparing C2 with a third threshold value, and rejecting the test signature if C2 passes the third threshold value; a device for calculating a classifying function C_b ; and a device for comparing the classifying function C_b with a fourth threshold value, and rejecting the test signature if C_b passes the fourth threshold value.

Claims

1. Apparatus for comparing a test handwritten signature with a reference signature where each of said test and reference signatures have been acquired by:

means for generating three electrical digital position signals characterizing a trajectory of a handwritten signature by means of a pencil provided with a point and an analog-to-digital tablet, said three signals being D_x (t), D_y (t) and D_z (t), where D_x (t) and D_y (t) are respectively position signals according to X and Y axes of a cartesian reference with respect to time, and D_x (t) is a discrete signal indicating whether or not said point is contacting said tablet;

means for low-pass filtering said D_x (t) and D_y (t) electrical signals;

means for taking the derivative of said D_x (t) and D_y (t) electrical signals for generating V_x and V_y electrical components which represent respectively speeds of said point according to X and Y axes of a cartesian reference;

means for calculating V.sub.σ and

V.sub.θ

values from V_x and V_y components where;

##EQU39## where V.sub.θ

has a sign determined by;

##EQU40## means for calculating handwritten components and handwritten strings, where each of said handwritten components is delimited by two successive liftings of said point along said trajectory, and each of said handwritten strings is delimited by two successive portions of said trajectory where said V.sub.θ

value is higher than a predetermined angular speed value and where said V.sub.σ

value is lower than a predetermined curvilinear speed value, said handwritten strings and components having beginnings and ends defining temporal marks along said trajectory by which duration of said handwriting signature is determined;

means for calculating simple dynamic parameters characterizing said test and reference signatures;

means for applying respectively a first predetermined rotating operator and a second predetermined rotating operator to said D_x (t) and D_y (t) signals for correcting inclination of said trajectory and aligning a base line of said trajectory with a horizontal base line; and

means for scaling said D_x (t) signal according to said X cartesian axis, and scaling said D_y (t) signal according to said Y cartesian axis, said apparatus comprises;

means for calculating variations of said simple dynamic parameters of said test signature with respect to said simple dynamic parameters of said reference signature, by calculating a first evaluating function C1 where;

##EQU41## FC1_i (RC1_i) is a function representative of the variations of a particular dynamic parameter where i indicates the parameter in question, and p_i is a weight given to a particular parameter of said simple dynamic parameters;

means for comparing C1 with a first threshold value, and rejecting said test signature if C1 passes said first threshold value;

means for calculating a classifying function C_a where;

space="preserve" listing-type="equation">C.sub.a =a1·

C1

where a1 is a weight given to said first evaluating function C1;

means for comparing said classifying function C_a with a second threshold value, and rejecting said test signature if C_a passes said second threshold value;

first means for comparing durations of said test and reference signatures, and effectuating temporal expansion of the temporal marks of the signature having the shortest duration so that its duration matches the duration of the other signature;

second marks for comparing sequences of said temporal marks of said test and reference signatures and for coupling temporal marks of said test and reference signatures if and only if two corresponding temporal marks have between them a minimal temporal distance which is reciprocally the shortest between the sequences in question, and said minimal distance is shorter than a predetermined distance so that coupled temporal marks form a pair of characteristic segments of said test and reference signatures;

means for processing in an iterative manner remaining temporal marks, that have not been coupled, of said test and reference signatures for forming additional pairs of characteristic segments by means of said first and second means for comparing until not characteristic segment is coupled;

means for calculating local intrinsic correlations of said V.sub.σ and

V.sub.θ

values of said test and reference signatures for each of said pairs of characteristic segments, by calculating a second evaluating function C2 where;

##EQU42## where FC2_i (RC2_i) is a function representative of the local intrinsic correlation of either said V.sub.σ

or V.sub.θ

values for said pairs of characteristic segments where i indicates the component in question, and p_i is a weight given to the particular component in question;

means for comparing C2 with a third threshold value, and rejecting said test signature if C2 passes said third threshold value;

means for calculating a classifying function C_b where;

space="preserve" listing-type="equation">C.sub.b =a.sub.1 C1+a.sub.2 C2

where a₂ is a weight given to said second evaluating function C2; and

means for comparing said classifying function C_b with a fourth threshold value, and rejecting said test signature if C_b passes said fourth threshold value.

2. Apparatus according to claim 1, wherein said simple dynamic parameters consist of:

a first simple dynamic parameter P₁ consisting of a period of time of said trajectory during which said point of said pencil is contacting said tablet;

a second simple dynamic parameter P₂ consisting of a percentage representative of a period of time of said trajectory during which said point is lifted;

a third simple dynamic parameter P₃ consisting of a percentage representative of a period of time of said trajectory during which said point is stopped; and

a fourth simple dynamic parameter P₄ consisting of a percentage representative of a period of time of said trajectory during which said V.sub.θ

value is positive.

3. Apparatus according to claim 2, comprising means for comparing said simple dynamic parameters of said test signature with the corresponding simple dynamic parameters of the reference signature, and rejecting said test signature if said simple dynamic parameters are the same.

4. Apparatus according to claim 1, further comprising:

means for calculating variations of D_x and D_y components of said test and reference signatures for each of said pairs of characteristic segment, by calculating a third evaluating function C3 where;

space="preserve" listing-type="equation">C3=FC3(RC3),ε

[-1,1]

where FC3(RC3) is a function representative of variations of D_x and Dy components for said pairs of characteristic segments;

means for comparing C3 with a fifth threshold value, and rejecting said test signature if C3 passes said fifth threshold value;

means for calculating a classifying function C_c where;

space="preserve" listing-type="equation">C.sub.c a.sub.1 C1+a.sub.2 C2+a.sub.3 C3

where a₃ is a weight given to said third evaluating function C3; and

means for comparing said classifying function C_c with a sixth threshold value REJ, and either rejecting said test signature if C_c is higher than said sixth threshold value REJ, or emitting a signal indicating that no conclusive result has been achieved if C_c is within a range of values limited by REJ and a threshold value UNC, or accepting said test signature if C_c is lower than UNC.

5. Apparatus according to claim 4, comprising means for calculating RC1₁, RC1₂, RC1₃ and RC1₄ where:

RC1₁ =(P₁ of said test signature P₁ of said reference signature)/P₁ of said reference signature;

RC1₂ =P₂ of said test signature-P₂ of said reference signature;

RC1₃ =P₃ of said test signature-P₃ of said reference signature; and

RC1₄ =P₄ of said test signature-P₄ of said reference signature.

6. Apparatus according to claim 5, comprising:

means for calculating FC1_i (RC1_i) for each of said four dynamic parameters where RC1_i is the variation of a particular dynamic parameter, where;

FC1_i (RC1_i)=0 if RC1_i <

SC1_Ei where SC1_Ei is a seventh predetermined threshold value for a particular dynamic parameter,

FC1_i (RC1_i)=((e^h(RC 1_i)-1)/(e-1))^Ni

if SC1_Ei <

RC1_i <

SC1_Ri where SC1_Ri is an eighth predetermined threshold value for a particular dynamic paramater, or

FC1_i (RC1_i)=1 if SC1_Ri ≦

RC1_i ;

where h(RC1_i) =(RC1_i -SC1_Ei)/(SC1_Ri -SC1_Ei), and where Ni is a growth factor for a particular dynamic parameter; and

means for generating a signal indicative of a rejection of said test signature if FC1_i (RC1_i)=1.

7. Apparatus according to claim 6, comprising means for calculating RC2₁ and RC2₂ where:

##EQU43## where N is the number of pairs of characteristic segments, l_r is the number of samples used for acquiring said reference signature, j identifies a particular pair of said pairs of characteristic segments, l_j is the number of samples used for acquiring a particular segment of said reference signature, CV.sub.σ

j is a partial intrinsic local correlation of said V.sub.σ

value for a particular pair of said pairs of characteristic segments, and CV.sub.θ

j is a partial intrinsic local correlation of said V.sub.θ

component for a particular pair of said pairs of characteristic segments.

8. Apparatus according to claim 7, comprising:

means for calculating FC2_i (RC2.sub. i) for each of said V.sub.θ and

V.sub.θ

values of said pairs of characteristic segments where RC2.sub. i is an intrinsic local correlation of either said V.sub.σ

or V.sub.θ

value for said pairs of characteristic segments, where;

FC2_i (RC2.sub. i)=1 if RC2_i <

SC2_Ri where SC2_Ri is a ninth predetermined threshold value,

space="preserve" listing-type="equation">FC2.sub.i (RC2.sub.i)=((e.sup.h1(RC2.sub.i)-1)/(e-1)).sup.N1i

if SC2_Ri <

RC2_i <

SC2_Ei where SC2_Ei is a tenth predetermined threshold value,

space="preserve" listing-type="equation">FC2.sub.i (RC2.sub.i)=(((e.sup.h2(RC2.sub.i)-1)/(e-1)).sup.N2i -1)

if SC2_Ei ≦

RC2.sub. i, or

FC2i(RC2.sub. i)=0 if SC2_Ai RC2_i where SC2_Ai is an eleventh threshold value;

where h1(RC2_i)=(SC2_Ei -RC2_i)/(SC2_Ei -SC2_Ri), h2(RC2_i)=(SC2_Ai -RC2_i)/(SC2_Ai -SC2_Ei), and N1i and N2i are predetermined growth factors;

means for generating a signal indicative of a rejection of said test signature if FC2_i (RC2_i)=1; and

means for generating a signal indicative of an acceptation of said test signature if FC2_i (RC2_i)=0.

9. Apparatus according to claim 8, comprising means for calculating RC3 where:

##EQU44## where RC3_ii is a minimal residual distance of said D_x and D_y components between the characteristic segments of a particular pair of said pairs of characteristic segments ##EQU45## where ##EQU46## q(1,1)=d(1,1);

D_xT and D_xR are respectively said D_x component of said test and reference signatures of a particular pair of characteristic segments;

D_yT and D_yR are respectively said Dy components of said test and reference signatures of a particular pair of characteristic segments; and

Δ

is a linear operator of difference.

10. Apparatus according to claim 9, comprising:

means for calculating FC3(RC3) for each of said D_x and D_y components of said pairs of characteristic segments where RC3 is representative of a minimal residual distance of said D_x and D_y components between said characteristic segments of each of said pairs of characteristic segments, where;

FC3(RC3)=1 if RC3>

SC3R where SC3R is a twelfth threshold value,

space="preserve" listing-type="equation">FC3(RC3)=((e.sup.h1(RC3) -1)/(e-1)).sup.N1

if SC3_E <

RC3<

SC3_R where SC3_E is a thirteenth threshold value,

space="preserve" listing-type="equation">FC3(RC3)=(((e.sup.h2(RC3) -1)/(e-1)).sup.N2 -1)

if SC3_A <

RC3<

SC3_E where SC3_A is a fourteenth threshold value, or

FC3(RC3)=0 if RC3<

SC3_A ;

where h1(RC3)=(RC3-SC3_E)/(SC3_R -SC3_E), h2(RC3)=(SC3_A -RC3)/(SC3_A -SC3_E), and N1 and N2 are predetermined growth factors;

means for generating a signal indicative of a rejection of said test signature if FC3(RC3)=1; and

means for generating a signal indicative of an acceptation of said test signature if FC3(RC3)=0.

11. Apparatus according to claim 10, wherein more than one reference signatures are acquired, and compared among themselves, taken two by two, to obtain several groups of RC1₁, RC1₂, RC1₃, RC1₄, RC2₁, RC2₂ and RC3 values, said apparatus further comprising:

means for comparing each of said RC1₁, RC1₂, RC1₃, RC1₄ and RC3 values with other corresponding values of its own group, and determining maximum values of each group which constitutes respectively personalized threshold values SP1₁, SP1₂, SP1₃, SP1₄ and SP3; and

means for comparing each of said RC2₁ and RC2₂ values with other corresponding values of its own group, and determining minimum values of each group which constitutes respectively personalized threshold values SP2₁ and SP2₂ ;

means for calculating SC1_Ei =MAX (cte,p(SC1_pi)) ε

[ 0%,SC1_Ri [, and SC1_Ri `MAX (cte,q(SC1_pi)) ε

]SC1_Ei,∞

], where p(SC1_pi) and q(SC1_pi) are linear functions of the type y=a·

SC1_pi +b, where SC1_pi is the personalized threshold value "i" which is respectively SP1₁, SP1₂, SP1₃ or SP1₄, a, b and cte being predetermined constants;

means for calculating SC2_Ei =MAX (cte,p(SC2_pi)) ε

]SC2_Ri, SC2_Ai [, SC2_Ri =MIN (cte,q(SC2_pi))ε

[8%,SC2_Ei [, and SC2_Ai =MIN (cte,r(SC2_pi)) ε

]SC2_Ei, 100%], where p(SC2_pi), q(SC2_pi) and r(SC2_pi) are linear functions of the type y=a.SC2_pi +b, where SC2_pi is the personalized threshold value "i" which is respectively SP2₁ or SP2₂, a, b and cte being predetermined constants; and

means for calculating SC3_E =MIN (cte,p(SC3_p)) ε

]SC3_A, SC3_R [, SC3_R =MAX (cte,q(SC3_p)) ε

]SC3_E, ∞

], and SC3_A =MAX (cte,r(SC3_p)) ε

[0, SC3_E [, where p(SC3_p), q(SC3_p) and r(SC3_p) are linear functions of the type y=a·

SC3p+b, where SC3_p is the personalized threshold value SP3, a, b and cte being predetermined constants.

12. Apparatus according to claim 1, comprising means for rejecting said test signature when said first evaluating function C1 equals zero and said second evaluating function C2 equals 1.

13. Apparatus according to claim 4, comprising means for rejecting said test signature when said first evaluating function C1 equals zero and said third evaluating function C3 equals zero.

14. Method for comparing a test handwritten signature with a reference signature where each of said test and reference signatures have been acquired by:

generating three electrical digital position signals characterizing a trajectory of a handwritten signature by means of a pencil provided with a point and an analog-to-digital tablet, said three signals being D_x (t), D_y (t) and D_z (t) where D_x (t) and D_y (t) are respectively position signals according to X and Y axes of a cartesian reference with respect to time, and D_z (t) is a discrete signal indicating whether or not said point is contacting said table;

low-pass filtering said D_x (t) and D_y (t) electrical signals;

taking the derivative of said D_x (t) and D_y (t) electrical signals for generating V_x and V_y electrical components which represent respectively speeds of said point according to X and Y axes of a cartesian reference;

calculating V.sub.σ and

V.sub.θ

values from V_x and V_y components where;

##EQU47## where V.sub.θ

has a sign determined by;

##EQU48## calculating handwritten components and handwritten strings, where each of said handwritten components is delimited by two successive liftings of said point along said trajectory, and each of said handwritten strings is delimited by two successive portions of said trajectory where said V.sub.θ

value is higher than a predetermined angular speed value and where said V.sub.σ

value is lower than a predetermined curvilinear speed value, said handwritten strings and components having beginnings and ends defining temporal marks along said trajectory by which duration of said handwriting signature is determined;

calculating simple dynamic parameters characterizing said test and reference signatures;

applying respectively a first predetermined rotating operator and a second predetermined rotating operator to said D_x (t) and D_y (t) signals for correcting inclination of said trajectory and aligning a base line of said trajectory with a horizontal base line; and

scaling said D_x (t) signal according to said X cartesian axis, and scaling said D_y (t) signal according to said Y cartesian axis, said apparatus comprises steps of;

calculating variations of said simple dynamic parameters of said test signature with respect to said simple dynamic parameters of said reference signature, by calculating a first evaluating function C1 where;

##EQU49## FC1_i (RC1_i) is a function representative of the variations of a particular dynamic parameter where i indicates the parameter in question, and p_i is a weight given to a particular parameter of said simple dynamic parameters;

comparing C1 with a first threshold value, and rejecting said test signature if C1 passes said first threshold value;

calculating a classifying function C_a where;

space="preserve" listing-type="equation">C.sub.a =a1·

C1

where a1 is a weight given to said first evaluating function C1;

comparing said classifying function C_a with a second threshold value, and rejecting said test signature if C_a passes said second threshold value;

comparing durations of said test and reference signatures, and effectuating temporal expansion of the temporal marks of the signature having the shortest duration so that its duration matches the duration of the other signature;

comparing sequences of said temporal marks of said test and reference signatures and coupling temporal marks of said test and reference signatures if and only if two corresponding temporal marks have between them a minimal temporal distance which is reciprocally the shortest between the sequences in question, and said minimal distance is shorter than a predetermined distance so that coupled temporal marks form a pair of characteristic segments of said test and reference signatures;

processing in an iterative manner remaining temporal marks, that have not been coupled, of said test and reference signatures for forming additional pairs of characteristic segments by repeating said steps of comparing durations and comparing until not characteristic segment is coupled;

calculating local intrinsic correlations of said V.sub.σ and

V.sub.θ

values of said test and reference signatures for each of said pairs of characteristic segments, by calculating a second evaluating function C2 where;

##EQU50## where FC2_i (RC2_i) is a function representative of the local intrinsic correlation of either said V.sub.σ

or V.sub.θ

values for said pairs of characteristic segments where i indicates the component in question, and p_i is a weight given to the particular component in question;

comparing C2 with a third threshold value, and rejecting said test signature if C2 passes said third threshold value;

calculating a classifying function C_b where;

space="preserve" listing-type="equation">C.sub.b =a.sub.1 C1+a.sub.2 C2

where a₂ is a weight given to said second evaluating function C2; and

comparing said classifying function C_b with a fourth threshold value, and rejecting said test signature if C_b passes said fourth threshold value.

15. Method according to claim 14, wherein said simple dynamic parameters consist of:

a first simple dynamic parameter P₁ consisting of a period of time of said trajectory during which said point of said pencil is contacting said tablet;

a second simple dynamic parameter P₂ consisting of a percentage representative of a period of time of said trajectory during which said point is lifted;

a third simple dynamic parameter P₃ consisting of a percentage representative of a period of time of said trajectory during which said point is stopped; and

a fourth simple dynamic parameter P₄ consisting of a percentage representative of a period of time of said trajectory during which said V.sub.θ

l value is positive;

16. Method according to claim 15, comprising steps of comparing said simple dynamic parameters of said test signature with the corresponding simple dynamic parameters of the reference signature, and rejecting said test signature if said simple dynamic parameters are the same.

17. Method according to claim 14, further comprising steps of:

calculating variations of D_x and D_y components of said test and reference signatures for each of said pairs of characteristic segment, by .calculating a third evaluating function C3 where;

space="preserve" listing-type="equation">C3=FC3(RC3),ε

[-1,1]

where FC3(RC3) is a function representative of variations of D_x and D_y components for said pairs of characteristic segments;

comparing C3 with a fifth threshold value, and rejecting said test signature if C3 passes said fifth threshold value;

calculating a classifying function C_c where;

space="preserve" listing-type="equation">C.sub.c =a1C1+a.sub.2 C2 a.sub.3 C3

where a₃ is a weight given to said third evaluating function C3; and

comparing said classifying function C_c with a sixth threshold value REJ, and either rejecting said test signature if C_c is higher than said sixth threshold value REJ, or emitting a signal indicating that no conclusive result has been achieved if C_c is within a range of values limited by REJ and a threshold value UNC, or accepting said test signature if C_c is lower than UNC.

18. Method according to claim 17, comprising a step of calculating RC1₁, RC1₂, RC1₃ and RC1₄ where:

RC1₁ =(P₁ of said test signature-P₁ of said reference signature)/P₁ of said reference signature;

RC1₂ =P₂ of said test signature-P₂ of said reference signature;

RC1₃ =P₃ of said test signature-P₃ of said reference signature; and

RC1₄ =P₄ of said test signature-P₄ of said reference signature.

19. Method according to claim 18, comprising steps of:

calculating FC1_i (RC1_i) for each of said four dynamic parameters where RC1_i is the variation of a particular dynamic parameter, where;

FC1_i (RC1_i (=0 if RC1_i <

SC1_Ei where SC1_Ei is a seventh predetermined threshold value for a particular dynamic parameter,

FC1_i (RC1_i)=((e^h(RC1.sbsp.i.sup.) -1)/(e-1))^Ni

if SC1_Ei <

RC1_i <

SC1_Ri where SC1_Ri is an eighth predetermined threshold value for a particular dynamic paramater, or

FC1_i (RC1_i)=1 if SC1_Ri ≦

RC1_i ;

where h(RC1_i)=(RC1_i -SC1_Ei)/(SC1_Ri -SC1_Ei), and where Ni is a growth factor for a particular dynamic parameter; and

means for generating a signal indicative of a rejection of said test signature if FC1_i (RC1_i)=1.

20. Method according to claim 19, comprising a step of calculating RC2₁ and RC2₂ where:

##EQU51## where N is the number of pairs of characteristic segments, l_r is the number of samples used for acquiring said reference signature, j identifies a particular pair of said pairs of characteristic segments, l_j is the number of samples used for acquiring a particular segment of said reference signature, CV.sub.σ

j is a partial intrinsic local correlation of said V.sub.σ

component for a particular pair of said pairs of characteristic segments, and CV.sub.θ

j is a partial intrinsic local correlation of said V.sub.θ

value for a particular pair of said pairs of characteristic segments.

21. Apparatus according to claim 20, comprising steps of:

calculating FC2_i (RC2.sub. i) for each of said V.sub.σ and

V.sub.θ

values of said pairs of characteristic segments where RC2.sub. i is an intrinsic local correlation of either said V.sub.σ

or V.sub.θ

value for said pairs of characteristic segments, where;

FC2_i (RC2.sub. i)=1 if RC2_i <

SC2_Ri where SC2_Ri is a ninth predetermined threshold value,

space="preserve" listing-type="equation">FC2.sub.i (RC2.sub.i)=((e.sup.h1(RC2.sub.i)-1)/(e-1)).sup.N1i

if SC2_Ri <

RC2_i <

SC2_Ei where SC2_Ei is a tenth predetermined threshold value,

space="preserve" listing-type="equation">FC2.sub.i (RC2.sub.i)=(((e.sup.h2(RC2.sub.i)-1)/(e-1)).sup.N2i -1)

if SC2_Ei ≦

RC2_i, or

FC2i(RC2.sub. i)=0 if SC2_Ai RC2_i where SC2_Ai is an eleventh threshold value;

where h1(RC2_i)=(SC2_Ei -RC2_i)/(SC2_Ei -SC2_Ri), h2(RC2_i)=(SC2_Ai -RC2_i)/(SC2_Ai -SC2_Ei), and N1i and N2i are predetermined growth factors;

generating a signal indicative of a rejection of said test signature if FC2_i (RC2_i)=1; and

generating a signal indicative of an acceptation of said test signature if FC2_i (RC2_i)=0.

22. Apparatus according to claim 21, comprising means for calculating RC3 where:

where RC3_ii is a minimal residual distance of said D_x and D_y components between the characteristic segments of a particular pair of said pairs of characteristic segments where;

##EQU52## where ##EQU53## q(1,1)=d(1,1);

D_xT and D_xR are respectively said D_x component of said test and reference signatures of a particular pair of characteristic segments;

D_yT and D_yR are respectively said Dy components of said test and reference signatures of a particular pair of characteristic segments; and

Δ

is a linear operator of difference.

23. Apparatus according to claim 22, comprising:

means for calculating FC3(RC3) for each of said D_x and D_y components of said pairs of characteristic segments where RC3 is representative of a minimal residual distance of said D_x and D_y components between said characteristic segments of each of said pairs of characteristic segments, where;

FC3(RC3)=1 if RC3>

SC3R where SC3R is a twelfth threshold value,

space="preserve" listing-type="equation">FC3(RC3)=((e.sup.h1(RC3) -1)/(e-1)).sup.N1

if SC3_E <

RC3<

SC3_R where SC3_E is a thirteenth threshold value,

space="preserve" listing-type="equation">FC3(RC3)=(((e.sup.h2(RC3) -1)/(e-1)).sup.N2 -1)

if SC3_A <

RC3<

SC3_E where SC3_A is a fourteenth threshold value, or

FC3(RC3)=0 if RC3<

SC3_A ;

where h1(RC3)=(RC3-SC3_E)/(SC3_R -SC3_E), h2(RC3)=(SC3_A -RC3)/(SC3_A -SC3_E), and N1 and N2 are predetermined growth factors;

generating a signal indicative of a rejection of said test signature if FC3(RC3)=1; and

means for generating a signal indicative of an acceptation of said test signature if FC3(RC3)=0.

24. Apparatus according to claim 23, wherein more than one reference signatures are acquired, and compared among themselves, taken two by two, to obtain several groups of RC1₁, RC1₂, RC1₃, RC1₄, RC2₁, RC2₂ and RC3 values, said apparatus further comprising:

comparing each of said RC1₁, RC1₂, RC1₃, RC1₄ and RC3 values with other corresponding values of its own group, and determining maximum values of each group which constitutes respectively personalized threshold values SP1₁, SP1₂, SP1₃, SP1₄ and SP3; and

comparing each of said RC2₁ and RC2₂ values with other corresponding values of its own group, and determining minimum values of each group which constitutes respectively personalized threshold values SP2₁ and SP2₂ ;

calculating SC1_Ei =MAX (cte,p(SC1_pi)) ε

[ 0%,SC1_Ri [, and SC1_Ri `MAX (cte,q(SC1_pi)) ε

]SC1_Ei,∞

], where p(SC1_pi) and q(SC1_pi) are linear functions of the type y=a·

SC1_pi +b, where SC1_pi is the personalized threshold value "i" which is respectively SP1₁, SP1₂, SP1₃ or SP1₄, a, b and cte being predetermined constants;

calculating SC2_Ei =MAX (cte,p(SC2_pi)) ε

]SC2_Ri, SC2_Ai [, SC2_Ri =MIN (cte,q(SC2_pi))ε

[8%,SC2_Ei [, and SC2_Ai =MIN (cte,r(SC2_pi)) ε

]SC2_Ei, 100%], where p(SC2_pi), q(SC2_pi) and r(SC2_pi) are linear functions of the type y=a.SC2_pi +b, where SC2_pi is the personalized threshold value "i" which is respectively SP2₁ or SP2₂, a, b and cte being predetermined constants; and

means for calculating SC3_E =MIN (cte,p(SC3_p)) ε

]SC3_A, SC3_R [, SC3_R =MAX (cte,q(SC3_p)) ε

]SC3_E, ∞

], and SC3_A =MAX (cte,r(SC3_p)) ε

[0, SC3_E [, where p(SC3_p), q(SC3_p) and r(SC3_p) are linear functions of the type y=a·

SC3p+b, where SC3_p is the personalized threshold value SP3, a, b and cte being predetermined constants.

25. Method according to claim 17, comprising a step of rejecting said test signature when said first evaluating function C1 equals zero and said third evaluating function C3 equals zero.

26. Method according to claim 14, comprising a step of rejecting said test signature when said first evaluating function C1 equals zero and said second evaluating function C2 equals 1.