CN111310545A - Method for measuring handwriting simulation complexity in online handwriting authentication - Google Patents

Abstract

The invention relates to the field of information security, and discloses a method for measuring handwriting simulation complexity in online handwriting authentication, which comprises the following steps: calculating the writing speed and the rotation angle information of the given handwriting, calculating a simulation complexity index related to attention, a simulation complexity index related to memory, a simulation complexity index related to hand-eye coordination and a simulation complexity index related to observation, and fusing the four calculated simulation complexity indexes to obtain the overall simulation complexity of the handwriting. The invention discloses a method for measuring handwriting imitation complexity in online handwriting authentication, which quantitatively measures the imitation complexity of handwriting from four capabilities such as attention, memory, eye coordination, observation and the like so as to achieve the purpose of further estimating the shortest exercise time required by successfully imitating the handwriting with the given imitation complexity and lay a foundation for improving the overall safety of an online handwriting authentication system.

Description

Method for measuring handwriting simulation complexity in online handwriting authentication

Technical Field

The invention relates to the field of information security, in particular to a method for measuring handwriting simulation complexity in online handwriting authentication.

Background

In the field of on-line signature handwriting authentication, a system judges whether templates and test handwriting come from the same writer or not by comparing the handwriting of the user with the handwriting of the user name. The template handwriting is online handwriting which is submitted by a user with known identity and is related to the name of the user in a registration stage; the test handwriting refers to online handwriting submitted by a user with unknown identity in a test stage; the online handwriting is a time sequence signal sequence obtained by adopting special data acquisition equipment to acquire the movement track of a pen point in the handwriting process in real time through a sensor, and information acquired by the sensor at each sampling moment comprises information such as two-dimensional position information of the pen point, forward pressure applied by the pen point on a writing plane and the like; the online signature handwriting specifically refers to a time sequence signal sequence acquired by data acquisition equipment in the process of writing own name characters by a user.

In the authentication process using signature handwriting, such a dilemma is often encountered: namely, because the signature of some users is too simple, the signature handwriting such as "wang-wai-xiao" is easy to copy, so that the system faces higher misjudgment risk. Analysis has found that the reason for this problem is not classification algorithms, but rather that the space for variation of features contained in the easily imitated signature script is too small. If the handwritten signature handwriting submitted by the user is measured according to the imitation complexity in the registration stage, registration applications which are easy to imitate are rejected, so that the overall security of the system is improved.

The daily life experience tells us that the difficulty degree of handwriting imitation is objective, and the difficulty degree of different handwriting imitation is obviously different; it is not obvious to give a quantitative measure of the ease of simulation. It has been found that the complexity of the simulation is the minimum effort required to overcome the limitations of the ability of the person to successfully simulate handwriting (e.g., observation, memory, coordination, attention, etc.), for example, to recite short texts. Each specific handwriting has a certain imitation complexity, for example, it requires the imitator to have a strong observation power to perceive the handwriting detail characteristics (pen-moving mode, pen power variation, proportion collocation relationship, etc.) as much as possible; strong memory to remember the information; strong hand-eye coordination ability to write handwriting with specified characteristics; strong attention is also required to inhibit self-power setting of writing. The combination of all of the above capabilities determines how easily the handwriting is to be copied. The more a given handwriting requires for the above capabilities, the higher the corresponding emulation complexity; conversely, the lower.

Disclosure of Invention

The invention aims to provide a method for measuring handwriting imitation complexity in online handwriting authentication, which carries out quantitative measurement on the imitation complexity of the handwriting from four capabilities of attention, memory, hand-eye coordination, observation and the like so as to achieve the purpose of further estimating the shortest exercise time required for successfully imitating the handwriting with the given imitation complexity and lay a foundation for improving the overall safety of an online handwriting authentication system.

In order to achieve the above object, the present invention provides a method for measuring handwriting simulation complexity in online handwriting authentication, comprising the following steps:

A) beginning: let W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) The method comprises the steps that (1) a time sequence of the handwriting to be measured, which is acquired by a sensor, is defined, wherein x and y represent two-dimensional position information of a pen point, which is acquired by the sensor, and f represents pen point pressure information, which is acquired by the sensor;

B) calculating writing speed information of handwriting W: is provided with L_W＝{l₁,l₂,...,l_nRepresents the writing speed time series of the handwriting W,

representing the speed information of the pen point at the kth moment, wherein k is more than 1 and less than or equal to n, l₁＝0；

C) Calculating the rotation angle information of the handwriting W: let A_W＝{a₁,a₂,...,a_nDenotes the time sequence of the rotation angle of the handwriting W, is set

Indicates the k-th timeInformation of the angle of rotation of the pen tip, wherein_k,l_k+1Represents the velocity of the nib, D, at time k, k +1_k＝dx_k×dx_k+1+dy_k×dy_k+1， dx_k＝x_k-x_k-1，dx_k+1＝x_k+1-x_k，dy_k＝y_k-y_k-1，dy_k+1＝y_k+1-y_k，1＜k＜n，b₁＝0， b_nFinally, the direction of the rotation angle is determined, i.e. if the sampling point (x) is set to 0_k+1,y_k+1) Such that the equation of the line f (x, y) is greater than zero, then a_k＝b_k(ii) a Otherwise, a_k＝-b_k(ii) a Wherein f (x, y) represents the sum of the values of the slave point (x)_k-1,y_k-1) To (x)_k,y_k) Linear equation of vector definition of direction, -pi ≦ a_k≤π，1≤k≤n；

D) Calculating a simulation complexity index related to attention: calculating to obtain a simulation complexity index P1 related to attention by taking the number of sampling points of the handwriting time sequence W as an input parameter;

E) calculating a memory-related simulation complexity index: using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And rotation angle time series A_W＝{a₁,a₂,...,a_nCalculating to obtain a simulation complexity index P2 related to memory;

F) calculating a simulation complexity index related to the hand-eye coordination force and the observation force; using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And writing speed time series L_W＝{l₁,l₂,...,l_nInvoking a simulation complexity index calculation method related to the hand-eye coordination force and the observation force, which is disclosed in the patent document, as an input parameter; obtaining simulation complexity indexes P3 and P4 related to the hand-eye coordination force and the observation force;

G) calculating the imitation complexity index P of the handwriting W as P1 × P2 × P3 × P4;

H) finishing; and returning the copy complexity index P of the handwriting W.

Preferably, in the step D), the step of calculating the imitation complexity index related to attention comprises the following steps:

D1) starting; taking the number n of sampling points of the handwriting time sequence W as an input parameter;

D2) calculating a simulation complexity index related to attention:

wherein x represents the time for writing the handwriting, and the unit is second; x is n/F, wherein n represents the number of sampling points in the handwriting W, and F represents the sampling frequency of the handwriting board for collecting the handwriting W;

D3) and (4) ending: returning the tracing complexity index P1 ═ c (x) of the handwriting W in relation to attention.

Preferably, in the step E), the step of calculating the memory-related simulation complexity index comprises the following steps:

E1) beginning: using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And rotation angle time series A_W＝{a₁,a₂,...,a_nAs input parameters;

E2) segmenting the handwriting W according to strokes: extracting key points K ═ K in W₀,k₁,k₂,...,k_m-1,k_mIn which k is_iI is more than or equal to 0 and less than or equal to m, k represents the serial number of the key point in the handwriting W₀＝1，k_m＝n，k_i＜k_i+1I is more than or equal to 0 and less than m, and the handwriting W is divided into m strokes by the key points; wherein the ith stroke is

E3) Initializing a loop variable x to 1;

E4) calculating the number of the intersection points of the x-th stroke and other strokes in the handwriting W: let c_xRepresenting the number of intersection points of the x-th stroke and other strokes in the handwriting W;

E5) calculating the number of subsegments with the same rotation angle sign in the x-th stroke: the sub-segments with the same rotation angle sign indicate that the rotation angle signs of all sampling points in the sub-segments are all non-positive or all non-negative sub-segments, and d is set_xThe number of the subsegments with the same rotation angle sign in the x-th stroke is represented;

E6) calculating the stroke complexity index P of the x-th segment_x＝1+c_x/2+d_x；

E7) If x is equal to x +1 and is less than or equal to m, jumping to step E4), reading the stroke complexity index of the next segment, otherwise, jumping to step E8);

E8) calculating a memory-related simulation complexity index: weighted average of stroke complexity indices for all segments

Obtaining a stroke complexity index of the handwriting W;

E9) and (4) ending: returning the copy complexity index P2 of the handwriting W relative to memory.

Preferably, in the step F), calculating the simulation complexity index related to the hand-eye coordination force and the observation force comprises the following steps:

F1) beginning: using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And writing speed time series L_W＝{l₁,l₂,...,l_nAs input parameters;

F2) segmenting the handwriting W according to strokes: extracting key points K ═ K in W₀,k₁,k₂,...,k_m-1,k_mIn which k is_iI is more than or equal to 0 and less than or equal to m, k represents the serial number of the key point in the handwriting W₀＝1，k_m＝n，k_i＜k_i+1I is more than or equal to 0 and less than m, and the handwriting W is divided into m strokes by the key points, wherein the ith stroke is

F3) Calculating the length of each stroke

a_x＝atan(dy_x/dx_x)，

Get L ═ L₁,L₂,...,L_m}，A＝{a₁,a₂,...,a_mCalculating the mean and variance of the sets L and A respectively,

F4) calculating writing speed sequence L_W＝{l₁,l₂,...,l_nMaximum and minimum values of }: is provided with

Respectively representing the writing speed maximum and minimum value set, respectively calculating the mean value and variance of the writing speed maximum and minimum value,

F5) calculating writing force sequence F_W＝{f₁,f₂,...,f_nMaximum and minimum values of }: is provided with

Respectively representing the maximum and minimum value sets of the writing force, and respectively calculating the mean value and the variance of the maximum and minimum values of the writing force;

F6) calculating the intersection points between all strokes in the handwriting W: let C { (x)_i,y_j)|(x_i,y_j) Is the intersection point of the ith and j strokes, i is more than or equal to 1, j is less than or equal to m, represents the set of the intersection points between all strokes in the handwriting W, and B is { (x)_i,y_i) I belongs to K and represents the starting and stopping point set of all strokes, and D is C ∪ B;

F7) calculate the mean and variance of all intersection location information: the mean and variance over the x and y components of all sample points in the cross point set D are calculated,

F8) calculating a feature change complexity index: p₁＝DIV_L/AVG_L；P₂＝DIV_A/AVG_A，

P₇＝DIV_x/AVG_x，P₈＝DIV_y/AVG_y；

F9) Calculating a feature change complexity index of the handwriting W

F10) Clustering the intersection points in the handwriting: clustering all the cross points in the set C according to the position relation by adopting a clustering algorithm, and setting E { (d)₁,r₁),(d₂,r₂),...,(d_k,r_k) Expressing a clustering result returned by a clustering algorithm, wherein k expresses the number of obtained categories; d_i，r_iRepresenting the number of intersection points in the ith category and the intra-category distance of the ith category, wherein i is more than or equal to 1 and less than or equal to k;

F11) calculating a viewing power dependent copy complexity index

F12) And (4) ending: returning the handwriting W a simulation complexity index P3 related to hand-eye coordination and a simulation complexity index P4 related to observation.

Compared with the prior art, the invention has the following advantages: the method carries out quantitative measurement on the tracing complexity of the handwriting from four capabilities of attention, memory, eye coordination, observation and the like so as to achieve the purpose of further estimating the shortest exercise time required by successfully tracing the handwriting with the given tracing complexity, and lays a foundation for improving the overall safety of an online handwriting authentication system.

Drawings

FIG. 1 is a flow chart of a method for measuring handwriting simulation complexity in online handwriting authentication according to the present invention;

FIG. 2 is a detailed flowchart of step D) in FIG. 1;

FIG. 3 is a detailed flowchart of step E) of FIG. 1;

FIG. 4 is a detailed flowchart of step F) in FIG. 1.

Detailed Description

The invention is described in further detail below with reference to the figures and the specific embodiments.

A method for extracting and authenticating stroke dynamic characteristics in online handwriting authentication is shown in figure 1 and comprises the following steps:

a method for measuring handwriting simulation complexity in online handwriting authentication is shown in FIG. 1, and includes the following steps:

A) beginning: let W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) The method comprises the steps that (1) a time sequence of the handwriting to be measured, which is acquired by a sensor, is defined, wherein x and y represent two-dimensional position information of a pen point, which is acquired by the sensor, and f represents pen point pressure information, which is acquired by the sensor;

B) calculating writing speed information of handwriting W: is provided with L_W＝{l₁,l₂,...,l_nRepresents the writing speed time series of the handwriting W,

representing the speed information of the pen point at the kth moment, wherein k is more than 1 and less than or equal to n, l₁＝0；

C) Calculating the rotation angle information of the handwriting W: let A_W＝{a₁,a₂,...,a_nDenotes the time sequence of the rotation angle of the handwriting W, is set

Indicating the rotational angle information of the pen tip at the k-th time, where_k,l_k+1Represents the velocity of the nib, D, at time k, k +1_k＝dx_k×dx_k+1+dy_k×dy_k+1，dx_k＝x_k-x_k-1，dx_k+1＝x_k+1-x_k，dy_k＝y_k-y_k-1，dy_k+1＝y_k+1-y_k，1＜k＜n，b₁＝0， b_nFinally, the direction of the rotation angle is determined, i.e. if the sampling point (x) is set to 0_k+1,y_k+1) Such that the equation of the line f (x, y) is greater than zero, then a_k＝b_k(ii) a Otherwise, a_k＝-b_k(ii) a Wherein f (x, y) represents the sum of the values of the slave point (x)_k-1,y_k-1) To (x)_k,y_k) Linear equation of vector definition of direction, -pi ≦ a_k≤π，1≤k≤n；

D) Calculating a simulation complexity index related to attention: taking the number of sampling points of the handwriting time sequence W as an input parameter, calculating to obtain a simulation complexity index P1 related to attention, as shown in fig. 2, the calculating of the simulation complexity index related to attention includes the following steps:

D1) starting; taking the number n of sampling points of the handwriting time sequence W as an input parameter;

D2) calculating a simulation complexity index related to attention:

wherein x represents the time for writing the handwriting, and the unit is second; x is n/F, wherein n represents the number of sampling points in the handwriting W, and F represents the sampling frequency of the handwriting board for collecting the handwriting W;

D3) and (4) ending: returning the tracing complexity index P1 ═ C (x) of the handwriting W related to attention;

E) calculating a memory-related simulation complexity index: using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And rotation angle time series A_W＝{a₁,a₂,...,a_nCalculating a memory-related simulation complexity index P2 as an input parameter, as shown in fig. 3, wherein the calculating of the memory-related simulation complexity index includes the following steps:

E1) beginning: using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And rotation angle time series A_W＝{a₁,a₂,...,a_nAs input parameters;

E2) segmenting the handwriting W according to strokes: extracting key points K ═ K in W₀,k₁,k₂,...,k_m-1,k_mIn which k is_iI is more than or equal to 0 and less than or equal to m, k represents the serial number of the key point in the handwriting W₀＝1，k_m＝n，k_i＜k_i+1I is more than or equal to 0 and less than m, and the handwriting W is divided into m strokes by the key points; wherein the ith stroke is

E3) Initializing a loop variable x to 1;

E4) calculating the number of intersection points of the x-th stroke and other strokes in the handwriting W: let c_xRepresenting the number of intersection points of the x-th stroke and other strokes in the handwriting W;

E5) calculating the number of subsegments with the same rotation angle sign in the x-th stroke: the sub-segments with the same rotation angle sign indicate that the rotation angle signs of all sampling points in the sub-segments are all non-positive or all non-negative sub-segments, and d is set_xThe number of the subsegments with the same rotation angle sign in the x-th stroke is represented;

E6) calculating the stroke complexity index P of the x-th segment_x＝1+c_x/2+d_x；

E7) If x is equal to x +1 and is less than or equal to m, jumping to step E4), reading the stroke complexity index of the next segment, otherwise, jumping to step E8);

E8) calculating a memory-related simulation complexity index: weighted average of stroke complexity indices for all segments

Obtaining a stroke complexity index of the handwriting W;

E9) and (4) ending: returning a copy complexity index P2 of the handwriting W related to the memory;

F) calculating a simulation complexity index related to the hand-eye coordination force and the observation force; using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And writing speed time series L_W＝{l₁,l₂,...,l_nInvoking a simulation complexity index calculation method related to the hand-eye coordination force and the observation force, which is disclosed in the patent document, as an input parameter; obtaining the simulation complexity indexes P3 and P4 related to the hand-eye coordination power and the observation power, and calculating the simulation complexity indexes related to the hand-eye coordination power and the observation power as shown in FIG. 4 comprises the following steps:

F1) beginning: using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And writing speed time series L_W＝{l₁,l₂,...,l_nAs input parameters;

F2) segmenting the handwriting W according to strokes: extracting key points K ═ K in W₀,k₁,k₂,...,k_m-1,k_mIn which k is_iI is more than or equal to 0 and less than or equal to m, k represents the serial number of the key point in the handwriting W₀＝1，k_m＝n，k_i＜k_i+1I is more than or equal to 0 and less than m, and the handwriting W is divided into m strokes by the key points, wherein the ith stroke is

F3) Calculating the length of each stroke

a_x＝atan(dy_x/dx_x)，

Get L ═ L₁,L₂,...,L_m}，A＝{a₁,a₂,...,a_mCalculating the mean and variance of the sets L and A respectively,

F4) calculating writing speed sequence L_W＝{l₁,l₂,...,l_nMaximum and minimum values of }: is provided with

Respectively representing the writing speed maximum and minimum value set, respectively calculating the mean value and variance of the writing speed maximum and minimum value,

F5) calculating writing force sequence F_W＝{f₁,f₂,...,f_nMaximum and minimum values of }: is provided with

Respectively representing the maximum and minimum value sets of the writing force, and respectively calculating the mean value and the variance of the maximum and minimum values of the writing force;

F6) calculating the intersection points between all strokes in the handwriting W: let C { (x)_i,y_j)|(x_i,y_j) Is the intersection point of the ith and j strokes, i is more than or equal to 1, j is less than or equal to m, represents the set of the intersection points between all strokes in the handwriting W, and B is { (x)_i,y_i) I belongs to K and represents the starting and stopping point set of all strokes, and D is C ∪ B;

F7) calculate the mean and variance of all intersection location information: the mean and variance over the x and y components of all sample points in the cross point set D are calculated,

F8) calculating a feature change complexity index: p₁＝DIV_LAVG_L；P₂＝DIV_AAVG_A，

P₇＝DIV_x/AVG_x，P₈＝DIV_y/AVG_y；

F9) Calculating a feature change complexity index of the handwriting W

F10) Clustering the intersection points in the handwriting: clustering all the cross points in the set C according to the position relation by adopting a clustering algorithm, and setting E { (d)₁,r₁),(d₂,r₂),...,(d_k,r_k) Expressing a clustering result returned by a clustering algorithm, wherein k expresses the number of obtained categories; d_i，r_iRepresenting the number of intersection points in the ith category and the intra-category distance of the ith category, wherein i is more than or equal to 1 and less than or equal to k;

F11) calculating a viewing power dependent copy complexity index

F12) And (4) ending: returning a simulation complexity index P3 related to hand-eye coordination of the handwriting W and a simulation complexity index P4 related to observation power;

G) calculating the imitation complexity index P of the handwriting W as P1 × P2 × P3 × P4;

H) finishing; and returning the copy complexity index P of the handwriting W.

In the present example, quantitative analysis was performed from the following four aspects:

A. memory power

Each stroke in the handwriting comprises information such as the position, the length, the azimuth angle, the shape and the like of a starting point and an ending point, and also comprises information such as arc length, rotated angle, direction and the like if the stroke is wound, so that the more the number of strokes is, the larger the information amount is, and the higher the requirement on the memory is.

B. Coordination of hand and eye

In unit time, the more strokes are, the more writing actions are, and the higher the requirement on the coordination force of hands and eyes is; if the stroke category number is more in a certain stroke sequence, the requirement on the coordination force of hands and eyes is higher.

C. Observation power

The shorter the stroke length in the handwriting, the less easy to attract attention; the higher the degree of stroke aggregation, e.g., crossing strokes, overlapping strokes, etc., the less likely it is to find features therein, and the more careful observation is required.

D. Attention to

It was found experimentally that the high concentration state of attention is not permanent and that after a certain increase in duration, e.g. 6 ± 2 seconds, attention will not be dispersed autonomously. Therefore, the longer the handwriting writing time, the higher the attention requirement.

The invention discloses a method for measuring handwriting imitation complexity in online handwriting authentication, which quantitatively measures the imitation complexity of handwriting from four capabilities such as attention, memory, eye coordination, observation and the like so as to achieve the purpose of further estimating the shortest exercise time required by successfully imitating the handwriting with the given imitation complexity and lay a foundation for improving the overall safety of an online handwriting authentication system.

Claims (4)

1. A method for measuring handwriting simulation complexity in online handwriting authentication is characterized by comprising the following steps: the method comprises the following steps:

A) beginning: let W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) The method comprises the steps that (1) a time sequence of the handwriting to be measured, which is acquired by a sensor, is defined, wherein x and y represent two-dimensional position information of a pen point, which is acquired by the sensor, and f represents pen point pressure information, which is acquired by the sensor;

B) calculating the writing speed of handwriting WInformation: is provided with L_W＝{l₁,l₂,...,l_nRepresents the writing speed time series of the handwriting W,

representing the speed information of the pen point at the kth moment, wherein k is more than 1 and less than or equal to n, l₁＝0；

C) Calculating the rotation angle information of the handwriting W: let A_W＝{a₁,a₂,...,a_nDenotes the time sequence of the rotation angle of the handwriting W, is set

Indicating the rotational angle information of the pen tip at the k-th time, where_k,l_k+1Represents the velocity of the nib, D, at time k, k +1_k＝dx_k×dx_k+1+dy_k×dy_k+1，dx_k＝x_k-x_k-1，dx_k+1＝x_k+1-x_k，dy_k＝y_k-y_k-1，dy_k+1＝y_k+1-y_k，1＜k＜n，b₁＝0，b_nFinally, the direction of the rotation angle is determined, i.e. if the sampling point (x) is set to 0_k+1,y_k+1) Such that the equation of the line f (x, y) is greater than zero, then a_k＝b_k(ii) a Otherwise, a_k＝-b_k(ii) a Wherein f (x, y) represents the sum of the values of the slave point (x)_k-1,y_k-1) To (x)_k,y_k) Linear equation of vector definition of direction, -pi ≦ a_k≤π，1≤k≤n；

D) Calculating a simulation complexity index related to attention: calculating to obtain a simulation complexity index P1 related to attention by taking the number of sampling points of the handwriting time sequence W as an input parameter;

E) calculating a memory-related simulation complexity index: using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And rotation angle time series A_W＝{a₁,a₂,...,a_nAs inputCalculating parameters to obtain a copy complexity index P2 related to memory;

F) calculating a simulation complexity index related to the hand-eye coordination force and the observation force; using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And writing speed time series L_W＝{l₁,l₂,...,l_nInvoking a simulation complexity index calculation method related to the hand-eye coordination force and the observation force, which is disclosed in the patent document, as an input parameter; obtaining simulation complexity indexes P3 and P4 related to the hand-eye coordination force and the observation force;

G) calculating the imitation complexity index P of the handwriting W as P1 × P2 × P3 × P4;

H) finishing; and returning the copy complexity index P of the handwriting W.

2. The method for measuring the handwriting simulation complexity in the online handwriting authentication according to claim 1, wherein: in the step D), calculating the imitation complexity index related to attention comprises the following steps:

D1) starting; taking the number n of sampling points of the handwriting time sequence W as an input parameter;

D2) calculating a simulation complexity index related to attention:

wherein x represents the time for writing the handwriting, and the unit is second; x is n/F, wherein n represents the number of sampling points in the handwriting W, and F represents the sampling frequency of the handwriting board for collecting the handwriting W;

D3) and (4) ending: returning the tracing complexity index P1 ═ c (x) of the handwriting W in relation to attention.

3. The method for measuring the handwriting simulation complexity in the online handwriting authentication according to claim 2, wherein: in the step E), the step of calculating the imitation complexity index related to the memory comprises the following steps:

E1) beginning: when writingThe sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And rotation angle time series A_W＝{a₁,a₂,...,a_nAs input parameters;

E2) segmenting the handwriting W according to strokes: extracting key points K ═ K in W₀,k₁,k₂,...,k_m-1,k_mIn which k is_iI is more than or equal to 0 and less than or equal to m, k represents the serial number of the key point in the handwriting W₀＝1，k_m＝n，k_i＜k_i+1I is more than or equal to 0 and less than m, and the handwriting W is divided into m strokes by the key points; wherein the ith stroke is

E3) Initializing a loop variable x to 1;

E4) calculating the number of intersection points of the x-th stroke and other strokes in the handwriting W: let c_xRepresenting the number of intersection points of the x-th stroke and other strokes in the handwriting W;

E5) calculating the number of subsegments with the same rotation angle sign in the x-th stroke: the sub-segments with the same rotation angle sign indicate that the rotation angle signs of all sampling points in the sub-segments are all non-positive or all non-negative sub-segments, and d is set_xThe number of the subsegments with the same rotation angle sign in the x-th stroke is represented;

E6) calculating the stroke complexity index P of the x-th segment_x＝1+c_x/2+d_x；

E7) If x is equal to x +1 and is less than or equal to m, jumping to step E4), reading the stroke complexity index of the next segment, otherwise, jumping to step E8);

E8) calculating a memory-related simulation complexity index: weighted average of stroke complexity indices for all segments

Obtaining a stroke complexity index of the handwriting W;

E9) and (4) ending: returning the copy complexity index P2 of the handwriting W relative to memory.

4. A method for measuring handwriting simulation complexity in online handwriting authentication according to claim 3, wherein: in the step F), calculating the simulation complexity index related to the hand-eye coordination force and the observation force comprises the following steps:

F1) beginning: using handwriting time sequence W { (x)₁,y₁,f₁),(x₂,y₂,f₂),...,(x_n,y_n,f_n) And writing speed time series L_W＝{l₁,l₂,...,l_nAs input parameters;

F2) segmenting the handwriting W according to strokes: extracting key points K ═ K in W₀,k₁,k₂,...,k_m-1,k_mIn which k is_iI is more than or equal to 0 and less than or equal to m, k represents the serial number of the key point in the handwriting W₀＝1，k_m＝n，k_i＜k_i+1I is more than or equal to 0 and less than m, and the handwriting W is divided into m strokes by the key points, wherein the ith stroke is

F3) Calculating the length of each stroke

a_x＝a tan(dy_x/dx_x)，

X is more than or equal to 1 and less than m, and L is ═ L₁,L₂,...,L_m}，A＝{a₁,a₂,...,a_mCalculating the mean and variance of the sets L and A respectively,

F4) calculating writing speed sequence L_W＝{l₁,l₂,...,l_nMaximum and minimum values of }: is provided with

Respectively representing the writing speed maximum and minimum value set, respectively calculating the mean value and variance of the writing speed maximum and minimum value,

F5) calculating writing force sequence F_W＝{f₁,f₂,...,f_nMaximum and minimum values of }: is provided with

Respectively representing the maximum and minimum value sets of the writing force, and respectively calculating the mean value and the variance of the maximum and minimum values of the writing force;

F6) calculating the intersection points between all strokes in the handwriting W: let C { (x)_i,y_j)|(x_i,y_j) Is the intersection point of the ith and j strokes, i is more than or equal to 1, j is less than or equal to m, represents the set of the intersection points between all strokes in the handwriting W, and B is { (x)_i,y_i) I belongs to K and represents the starting and stopping point set of all strokes, and D is C ∪ B;

F7) calculate the mean and variance of all intersection location information: computing a set of intersectionsThe mean and variance of all samples in D over the x and y components,

F8) calculating a feature change complexity index: p₁＝DIV_L/AVG_L；P₂＝DIV_A/AVG_A，

F9) Calculating a feature change complexity index of the handwriting W

F10) Clustering the intersection points in the handwriting: clustering all the cross points in the set C according to the position relation by adopting a clustering algorithm, and setting E { (d)₁,r₁),(d₂,r₂),...,(d_k,r_k) Expressing a clustering result returned by a clustering algorithm, wherein k expresses the number of obtained categories; d_i，r_iRepresenting the number of intersection points in the ith category and the intra-category distance of the ith category, wherein i is more than or equal to 1 and less than or equal to k;

F11) calculating a viewing power dependent copy complexity index

F12) And (4) ending: returning the handwriting W a simulation complexity index P3 related to hand-eye coordination and a simulation complexity index P4 related to observation.

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