Online Signature Authentication Method and System Based on Unconstrained Dynamic Time Programming

Abstract

The present invention discloses an online signature authentication method based on unconstrained dynamic time planning, which relates to the technical field of electronic signatures. A preprocessing module obtains discrete trajectory points of a sample signature and discrete trajectory points of a signature to be authenticated. A human muscle movement model fits a continuous trajectory function of the sample signature based on the discrete trajectory points of the sample signature, performs feature trajectory mapping, and obtains a feature trajectory function of the sample signature. A continuous trajectory function of the signature to be authenticated is fitted based on the discrete trajectory points of the signature to be authenticated, and performs feature trajectory mapping to obtain a feature trajectory function of the signature to be authenticated. A signature alignment path mapping function is constructed based on the feature trajectory functions of the sample signature and the continuous trajectory of the signature to be authenticated. The alignment path is initialized as a linear function, and the signatures are aligned end to end. A loss function is solved, and signature duration is used for normalization to obtain the difference between the signatures. The signature to be authenticated is then compared online based on the difference. The present invention can be applied to situations where high accuracy electronic signature recognition is required.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer information processing, and particularly relates to online signature authentication technology. Background Art

[0002] In the verification of electronic signatures, a large number of signature comparisons are involved. However, due to the signature device or the signature posture, the signature may be skewed, resulting in the loss of a lot of stroke feature information in the electronic signature verification and comparison, and the inaccurate obtained feature information, leading to a series of problems such as incorrect verification results and decreased accuracy. In a signature authentication system, it is often necessary to perform comparisons under different devices (mobile phones, tablets, and signature pads) and different writing methods (handwriting and pen writing). However, there are often large differences in the dynamic features under different devices and different writing methods. In some scenarios, effective dynamic features cannot be obtained. For example, some mobile phones cannot obtain the pressure value, and even the obtained time information is not accurate.

[0003] Traditional time dynamic programming algorithms make a series of assumptions for signature authentication: (1) Boundary: The beginning and end of two signatures must be aligned. (2) Continuity: There are no omitted or redundant strokes in the signature. (3) Monotonicity: There is no misaligned alignment between two signatures, that is, there are no reverse strokes. However, these assumptions are often not satisfied in Chinese signatures, resulting in an unsatisfactory signature alignment effect.

[0004] The Chinese patent application with the publication number CN108536314A and the name "User Identity Recognition Method and Device" segments the signature trajectory in three-dimensional space and calculates the similarity of stroke shape features using the DTW algorithm; the Chinese patent application with the publication number CN103927532A and the name "Stroke Feature-Based Handwriting Registration Method" uses the DTW algorithm to align the signature trajectory to obtain corresponding segmented strokes and calculates the stroke similarity. The above inventions all use the DTW algorithm, but when calculating the stroke shape features and similarity using the DTW algorithm, they still do not consider that the beginning and end of the signature are not aligned, do not consider the omitted or redundant strokes in the signature, and reverse strokes. Summary of the Invention

[0005] In view of the above problems existing in electronic signatures, in the trajectory alignment task of signature authentication, the present invention adopts the traditional dynamic time programming algorithm to add problems such as boundary, continuity, and monotonicity restrictions, resulting in poor stroke alignment effects in signature authentication. The present invention proposes an unconstrained dynamic time programming algorithm. Based on the lognormal distribution human motion speed model, the discretized signature trajectory points are fitted into a continuous dynamic trajectory function, and the trust region algorithm is used to iteratively solve the optimal continuous alignment path, which can achieve high-precision trajectory alignment in multi-style complex signatures. Solve a series of restrictive problems of the time dynamic programming algorithm (DTW) in online signature comparison.

[0006] The technical solution of the present invention to solve the above technical problems is to propose an online signature identification method based on unconstrained dynamic time planning, including: preprocessing to obtain discrete trajectory points of the retained sample signature and discrete trajectory points of the signature to be identified, fitting the retained sample signature continuous trajectory function S according to the discrete trajectory points of the retained sample signature with a human muscle movement model, performing feature trajectory mapping, and obtaining the retained sample signature feature trajectory function F, fitting the signature continuous trajectory function T to be identified according to the discrete trajectory points of the signature to be identified, performing feature trajectory mapping, and obtaining the signature feature trajectory function G to be identified, constructing a signature alignment path mapping function according to the feature trajectory functions of the retained sample signature and the continuous trajectory of the signature to be identified, initializing the alignment path as a linear function, and aligning the retained sample signature head to tail, solving the retained sample signature loss function, obtaining the difference between the signatures according to the retained sample signature loss function and the signature duration for normalization, and online identifying the signature to be identified according to the difference.

[0007] Further preferably, the fitting signature continuous trajectory function further includes: obtaining the time t0 when each muscle module sends a motion signal, the angle when the arc is started, the angle when the arc is stopped, the length of the arc, the standard deviation of the lognormal distribution, the mean of the lognormal distribution, estimating the motion parameters of each muscle module according to the signature trajectory points, establishing a muscle module signature angle function, superimposing the motion trajectory of each muscle module, and reconstructing a continuous signature trajectory function. Specifically, it can be: obtaining the time t0 when each muscle module sends a motion signal, the angle when the arc is started, the angle when the arc is stopped, the length of the arc, the standard deviation of the lognormal distribution, the mean of the lognormal distribution, estimating the motion parameters of each muscle module according to the signature trajectory points, according to the formula: v j (t)=Λ(tt 0j ;μ j ,σ j ) Calculate the velocity function of the jth muscle module at time t, where Λ is the log-normal distribution probability density function, t 0j , μ j , σ j The time, lognormal distribution mean, and standard deviation of the motion signal emitted by the j-th muscle module are used to establish the signature angle function of the j-th muscle module: Calling formula:

[0008]

[0009]

[0010] Get the coordinates (x(t), y(t)) of the signature trajectory at time t, and obtain the (x, y) coordinates of the signature trajectory, where θ sj ,θ ej , Dj The angle θ at which the jth muscle module starts to draw the arc s , the angle when the arc is stopped, and the length of the arc.

[0011] More preferably, the feature trajectory mapping further includes: using the (x, y) coordinates of the signature trajectory, the x and y axis components of the velocity and acceleration as 6-dimensional features to generate a continuous feature trajectory function: F(t) = (x(t), y(t), x′(t), y′(t), x″(t), y″(t)) T , establish a mapping from the signature trajectory function to its characteristic trajectory function as Φ:S→F.

[0012] Further preferably, the trust region algorithm is used to solve the optimal alignment path according to the signature feature trajectory functions F and G, specifically: regularize and adjust the constraint conditions, and call the formula:

[0013] Calculate the target loss function L(W; F, G). According to the target loss function, call the formula: Get the optimal alignment path W * If the difference between the corresponding trajectory points of the retained signature and the signature to be authenticated is greater than d, it means that there are omitted or redundant strokes in the alignment path of the trajectory point. If the trajectory point is at the beginning or end of the signature handwriting, it means that the beginning and end of the signature cannot be completely aligned. Among them, d represents the maximum difference allowed between the corresponding trajectory points of the retained signature and the signature to be authenticated, and λ represents the penalty for reverse alignment.

[0014] Further preferably, the alignment path is initialized to the simplest linear function, and the signatures are aligned head to tail, according to the formula:

[0015] Calculate the alignment path W at time t after the signature is aligned 0 (t), iteratively solve the nonlinear optimization problem, according to the formula: W * =argmin W∈k阶幂函数 L(W; F, G) obtains the optimal alignment path between the retained signature and the signature to be authenticated.

[0016] Further preferably, according to the loss function L(W * ; Φ(S), Φ(T)), and normalized by signature duration to obtain the difference D(S, T) between the above signatures:

[0017] According to the formula THR = 1.2 × max i≠j D(S i ,S j) Calculate the maximum signature difference threshold THR, compare the verification signature with all the retained signatures one by one, and obtain the difference between the verification signature and all the retained signatures. If the average value of the difference is less than or equal to the difference threshold THR, the signature to be authenticated is a genuine signature.

[0018] The present invention also proposes an online signature authentication system based on unconstrained dynamic time planning, comprising: a preprocessing module, a human muscle motion model, a path alignment module, and a signature recognition module. The preprocessing module obtains discrete trajectory points of a retained sample signature and discrete trajectory points of a signature to be authenticated. The human muscle motion model fits a continuous trajectory function S of the retained sample signature according to the discrete trajectory points of the retained sample signature, performs feature trajectory mapping, and obtains a feature trajectory function F of the retained sample signature. The continuous trajectory function T of the signature to be authenticated is fitted according to the discrete trajectory points of the signature to be authenticated, performs feature trajectory mapping, and obtains a feature trajectory function G of the signature to be authenticated. The path alignment module constructs a signature alignment path mapping function according to the continuous trajectory function of the retained sample signature and the signature to be authenticated. The signature recognition module initializes the alignment path as a linear function and aligns the head and tail of the retained sample signature. The retained sample signature loss function is solved according to the signature alignment path mapping function. The difference between the signatures is obtained according to the retained sample signature loss function and normalized by the signature duration, and the signature to be authenticated is identified online according to the difference. Further preferably, fitting the signature continuous trajectory function further includes: obtaining the time t0 when each muscle module emits a motion signal, the angle when starting to draw an arc, the angle when stopping to draw an arc, the length of the arc, the standard deviation of the log-normal distribution, the mean of the log-normal distribution, estimating the motion parameters of each muscle module according to the signature trajectory points, establishing a muscle module signature angle function, superimposing the motion trajectory of each muscle module, and reconstructing a continuous signature trajectory function.

[0019] More preferably, the feature trajectory mapping further includes: using the (x, y) coordinates of the signature trajectory, the x and y axis components of the velocity and acceleration as 6-dimensional features to generate a continuous feature trajectory function:

[0020] F(t)=(x(t),y(t),x′(t),y′(t),x″(t),y″(t)) T , establish the mapping from the signature trajectory function to its feature trajectory function as Φ; according to the signature feature trajectory functions F and G, the trust region algorithm is used to solve the optimal alignment path. Specifically, regularize the constraints and call the formula:

[0021] Calculate the loss function L(W; F, G) and call the formula according to the loss function: Get the optimal alignment path W of the signature trajectory points *, where d represents the maximum difference allowed between the corresponding trajectory points of the retained signature and the signature to be authenticated, and λ represents the penalty for reverse alignment.

[0022] Further preferably, the alignment path is initialized to the simplest linear function, and the signatures are aligned head to tail, according to the formula: Calculate the alignment path W at time t after the signature is aligned 0 (t), iteratively solve the nonlinear optimization problem, according to the formula: W * =argmin W∈k阶幂函数 L(W; F, G) obtains the optimal alignment path of the sample signature and the signature to be identified; according to the loss function L(W * ; Φ(S), Φ(T)), and normalized by signature duration to obtain the difference D(S, T) between the above signatures:

[0023] According to the formula THR = 1.2 × max i≠j D(S i ,S j ) Calculate the maximum signature difference threshold THR, compare the verification signature with all the retained signatures one by one, and obtain the difference between the verification signature and all the retained signatures. If the average value of the difference is less than or equal to the difference threshold THR, the signature to be authenticated is a genuine signature.

[0024] The present invention adopts an unconstrained dynamic time planning algorithm to identify and recognize online signatures, which can adapt to more complex and changeable Chinese signatures, and solve the signature comparison and identification problems such as misalignment between the beginning and the end, omitted or redundant strokes, and inconsistent stroke order. In addition, since the alignment path is a continuous path, the alignment accuracy is higher, and it is also more robust to devices with different sampling rates, and it does not encounter the one-to-many or many-to-one problems caused by discrete point alignment in traditional algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Flowchart of online signature alignment path based on unconstrained dynamic time planning;

[0026] Figure 2 Linear relationship diagram of the time alignment path between the retained signature and the verification signature;

[0027] Figure 3 Schematic diagram of the online signature verification and comparison process according to an embodiment of the present invention. DETAILED DESCRIPTION

[0028] In order to facilitate a clear understanding of the present invention and make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. In the following description, specific details such as specific configurations and components are provided only to help fully understand the embodiments of the present invention. Therefore, it should be clear to those skilled in the art that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. In addition, for clarity and brevity, the description of known functions and configurations has been omitted, and it should be understood that the embodiments are only for the purpose of illustrating the present invention, and are not intended to limit the scope of protection of the present invention.

[0029] like Figure 1 The figure shows a flow chart of the online signature identification method based on unconstrained dynamic time planning of the present invention. It includes the following main steps: pre-processing the original signature data to obtain discrete trajectory points of the sample signature and discrete trajectory points of the verification signature; the human muscle movement model fits the sample signature continuous trajectory function S according to the discrete trajectory points of the sample signature, performs feature trajectory mapping, and obtains the sample signature feature trajectory function F; the human muscle movement model fits the test signature continuous trajectory function T according to the discrete trajectory points of the test signature, performs feature trajectory mapping, and obtains the verification signature feature trajectory function G; the trust region algorithm is used to solve the optimal alignment path based on the sample signature feature trajectory function F and the verification signature feature trajectory function; the signature difference D is calculated based on the sample signature feature trajectory function F, the verification signature feature trajectory function, and the optimal alignment path. It further specifically includes:

[0030] The original signature data is preprocessed to obtain signature discrete trajectory points, which can be obtained using the following method, or other methods well known to those skilled in the art can be used to obtain signature discrete trajectory points.

[0031] First, the discrete signature trajectory points of the original data are interpolated using linear interpolation and resampled at a fixed sampling rate (e.g., 100 Hz). If the original data contains suspended strokes or broken touch sections, the B-spline interpolation method is used to repair the signature trajectory of that section. Other interpolation methods (such as the simplest linear interpolation method) can also be used to repair suspended strokes or broken touch sections of the signature trajectory. The entire signature trajectory is then filtered using a Butterworth low-pass filter to make it smoother.

[0032] Fitting the continuous trajectory function of the signature. The signature trajectory is caused by the combined action of multiple different muscle modules of the writer, and each muscle module is performing circular motion, and the change of its motion speed over time follows a lognormal distribution. Therefore, the present invention can estimate muscle motion parameters such as the time of human hand muscle movement during signature, the angle during writing, the distribution state, etc. to construct a characteristic trajectory function. Specifically, the following method can be used, or other similar methods can be used to fit the characteristic trajectory function. The following takes a preferred embodiment as an example to specifically illustrate the method of fitting the characteristic trajectory function.

[0033] The human muscle motion model obtains the time t0 when the muscle emits a motion signal, the angle θ when starting to draw an arc s and the angle θ when stopping to draw an arc e , the length D of the arc, the standard deviation σ of the lognormal distribution, the mean μ of the lognormal distribution, and estimate the motion parameters of each muscle module according to the signature trajectory points:

[0034] P = [t0, θ s , θ e , D, σ, μ]. According to the formula: v j (t) = Λ(t - t 0j ; μ j , σ j ) to calculate the velocity function of the jth muscle module at time t, where Λ is the probability density function of the lognormal distribution, t 0j , μ j , σ j are the time when the jth muscle module emits a motion signal, the mean of the lognormal distribution, and the standard deviation.

[0035] Furthermore, the angle function is established as: Superimpose the motion trajectories of each muscle module to reconstruct the continuous signature trajectory function S(t) = (x(t), y(t)) T , where the current coordinates (x(t), y(t)) in the signature trajectory function are obtained according to the following formula,

[0036]

[0037]

[0038] where θ sj , θ ej , D j are the angle θ when the jth muscle module starts to draw an arc s , the angle when stopping to draw an arc, and the length of the drawn arc. Obtain the coordinates of all signature stroke trajectories to fit the continuous signature trajectory function. Construct the characteristic trajectory function according to the biometric information of the signer's signature trajectory.

[0039] If the signature trajectory point (x, y) coordinates, the x- and y-axis components of velocity and acceleration are considered as 6D features, and a continuous feature trajectory function is generated:

[0040] F(t) = (x(t), y(t), x′(t), y′(t), x″(t), y″(t)) T , a mapping Φ from the signature trajectory function S to its feature trajectory function F is established as: S(t) → F(t). Among them, the first-order derivatives x′(t), y′(t) in the feature trajectory function F(t) correspond to the velocity of the signature trajectory point (x, y), and the second-order derivatives x″(t), y″(t) correspond to the acceleration.

[0041] According to the feature trajectory functions of the continuous trajectories of the retained signature and the verification signature, a signature alignment path mapping function is constructed to find the optimal alignment path, so that the signature feature difference after alignment is minimized. Suppose the continuous trajectories of the retained signature and the signature to be authenticated are S and T respectively, and the writing durations of the retained signature and the verification signature are t m , t n , and their feature trajectory functions are F and G respectively:

[0042] F = Φ(S)

[0043] G = Φ(T)

[0044] The goal of dynamic time warping is to find an optimal alignment path W * : [0, t m → [0, t n , so that the signature feature difference after alignment is minimized. Among them, the original alignment path is determined according to the following formula:

[0045]

[0046] Among them, F(t) is the feature trajectory function of the retained signature, and G(W(t)) is the feature trajectory function of the verification signature after alignment with it.

[0047] If the constraint conditions in the traditional dynamic time warping algorithm are adopted, there are the following constraint conditions,

[0048]

[0049] However, in a complex Chinese signature environment, it is difficult to meet the above constraint conditions. Therefore, considering regularizing the constraint conditions, a target loss function L(W; F, G) is constructed:

[0050]

[0051] Its goal is to minimize the difference degree between signatures based on the current alignment path. According to the target loss function, the formula is called: Get the optimal alignment path W after regularizing the constraints * . Among them, W′(t) is the first-order derivative of the alignment path with respect to time, W(t) is the time alignment path, which represents the time corresponding to the corresponding points of the retained signature and the verification signature in their respective signatures, and d and λ are both regularization parameters. d represents the maximum difference allowed between two points in the signature. If the difference between the corresponding trajectory points of the retained signature and the signature to be verified is greater than d, it means that there are omitted strokes or redundant strokes in the alignment path at that location. If the location is at the beginning or end of the signature handwriting, it means that the beginning and end of the signature cannot be completely aligned. Among them, the larger d is, the stronger the constraint on boundary and continuity. λ represents the penalty for reverse alignment. The larger λ is, the stronger the constraint on monotonicity.

[0052] Initialize the alignment path as a linear function and align the signatures head to tail, and find the optimal alignment path for the retained signature and the verification signature. To facilitate calculation, consider the alignment path W(t) at time t as a k-order power function, that is, use the general form of the k-order power function:

[0053]

[0054] Here, k is an empirical value, which can be set according to the number of strokes in the signature. A larger k can be considered for more complex signatures.

[0055] like Figure 2 The linear relationship diagram of the alignment path is shown. The alignment path W can be initialized 0 It is the simplest linear function, and the signature is aligned at the beginning and end. According to the writing time t of the signature sample m and the writing time t of the verification signature n , calling the formula: As the initialization parameter of the iterative algorithm.

[0056] The trust region algorithm (such as Levenberg-Marquardt algorithm) can be used to iteratively solve the nonlinear optimization problem. According to the formula: W * =argmin W∈k阶幂函数 L(W; F, G) obtains the optimal alignment path between the retained signature and the verification signature.

[0057] like Figure 3The figure shows a schematic diagram of the online signature verification and comparison process described in an embodiment of the present invention. A sample signature set and a signature to be tested are collected and subjected to a time-dependent dynamic time warping (DTW) algorithm. The normalized distances between the sample signatures and the normalized distances between the sample signatures and the signature to be tested are obtained. A sample signature difference threshold is determined based on the maximum normalized distance between multiple sample signatures. The difference between the signature to be tested is determined based on the average normalized distance between the sample signatures and the signature to be tested. The difference between the signature to be tested is then compared with the difference threshold to determine whether the signature to be tested is the signatory's authentic signature. The signature difference between the sample signature and the verification signature can be determined based on the aforementioned loss function.

[0058] According to the loss function L(W * ; Φ(S), Φ(T)), and use the signature duration to normalize and obtain the difference D(S, T) between the retained signature and the signature to be authenticated:

[0059]

[0060] This difference can be used as a basis for identifying electronic signatures.

[0061] Assume that the signature set is {S i |i=1,2,3…} can compare all the sample signatures of the user one by one, and use the maximum signature difference as the difference threshold THR of the user.

[0062]

[0063] Then compare the verification signature with all the sample signatures one by one to get the difference between the verification signature and all the sample signatures. According to the formula: Dist = mean i D(S i ,T) calculates the average value Dist of the signature difference, where D(S i ,T) is the i-th retained signature. If Dist≤THR, the verification signature is the real signature of the signer; otherwise it is a fake signature.

Claims

1. An online signature authentication method based on unconstrained dynamic time programming, characterized in that, Obtain discrete trajectory points of the sample signature and discrete trajectory points of the verification signature. The human muscle motion model uses the time, angle, and distribution state of the human hand muscle movement during signing to estimate the muscle motion parameters to obtain discrete trajectory points of the sample signature. Fit the sample signature continuous trajectory function S according to the discrete trajectory points of the sample signature, perform feature trajectory mapping, and obtain the sample signature feature trajectory function F. Fit the continuous trajectory function T of the signature to be identified according to the discrete trajectory points of the verification signature, perform feature trajectory mapping, and obtain the feature trajectory function G of the signature to be identified. According to the feature trajectory functions of the continuous trajectories of the sample signature and the verification signature, construct a signature alignment path mapping function, initialize the alignment path as a linear function, and align the signatures head to tail, solve the loss function under the optimal alignment path, and use the signature duration for normalization to obtain the difference between the signatures, and use this difference as the basis for identifying and verifying the authenticity of the signatures. Among them, the trust region algorithm is used to solve the optimal alignment path according to the signature feature trajectory functions F and G, and the constraints are regularized to construct the target loss function: According to the target loss function, call the formula: Calculate the optimal alignment path W after regularizing the constraint conditions * , where W represents the alignment function of the retained sample signature and the verification signature in time series, and t m represents the total time consumption of the retained sample signature, W′(t) is the first-order derivative of the alignment path with respect to time, W(t) represents the time alignment path, d represents the maximum allowable difference between the corresponding trajectory points of the signatures, and λ represents the penalty degree for reverse alignment.

2. The online signature authentication method according to claim 1, wherein Fitting the signature continuous trajectory function further includes: obtaining the time t0 when each muscle module sends a motion signal, the angle when starting to draw an arc, the angle when stopping to draw an arc, the length of the arc, the standard deviation of the log-normal distribution, the mean of the log-normal distribution, estimating the motion parameters of each muscle module based on the signature trajectory points, establishing a muscle module signature angle function, superimposing the motion trajectory of each muscle module, and reconstructing a continuous signature trajectory function.

3. The online signature authentication method according to claim 1, wherein The feature trajectory mapping further includes: using the (x, y) coordinates of the signature trajectory, the x and y axis components of the velocity and acceleration as 6-dimensional features to generate a continuous feature trajectory function: F(t) = (x(t), y(t), x'(t), y'(t), x''(t), y''(t)) T , establish a mapping relationship Φ: S → F from the signature trajectory function to its characteristic trajectory function.

4. The online signature authentication method according to any one of claims 1-3, characterized in that Initialize the alignment path as the simplest linear function and align the beginning and end of the signature. According to the formula: Obtain the time W 0 (t) corresponding to the corresponding points of the retained signature and the verification signature at the initialization in their respective signatures, respectively, as the initialization parameters of the iterative algorithm, and iteratively solve the non-linear optimization problem. According to the formula: W * = argmin W∈k阶幂函数 L(W; F, G) obtains the optimal alignment path between the retained sample signature and the signature to be authenticated, where t n represents the total time consumed for verifying the signature.

5. The online signature authentication method according to any one of claims 1-3, characterized in that According to the loss function L(W * ; Φ(S), Φ(T)), and the difference between the signatures D(S, T) is obtained by normalizing the signature duration: According to the formula THR = 1.2 × max i≠j D(S i ,S j ) Calculate the maximum signature difference threshold THR, compare the verification signature with all retained signatures one by one, and obtain the difference between the verification signature and all retained signatures. If the average value of the difference is less than or equal to the difference threshold THR, the signature to be authenticated is a genuine signature; Among them, Φ(S) is the mapping from the continuous trajectory function S of the retained signature to its characteristic trajectory function, Φ(T) is the mapping from the continuous trajectory function T of the signature to be authenticated to its characteristic trajectory function; S i , S j respectively represent the i-th and j-th sample retention signatures in the sample retention signature group.

6. An online signature authentication system based on unconstrained dynamic time programming, characterized in that, include: A preprocessing module, a human muscle movement model, a path alignment module, and a signature recognition module are provided. The preprocessing module obtains discrete trajectory points of the sample signature and discrete trajectory points of the verification signature. The human muscle movement model uses the time of human hand muscle movement during signing, the angle during writing, and the distribution state to estimate muscle movement parameters to obtain discrete trajectory points of the sample signature. The sample signature continuous trajectory function S is fitted according to the discrete trajectory points of the sample signature to perform feature trajectory mapping to obtain the sample signature feature trajectory function F. The continuous trajectory function T of the signature to be identified is fitted according to the discrete trajectory points of the verification signature to perform feature trajectory mapping to obtain the verification signature feature trajectory function G. The path alignment module constructs a signature alignment path mapping function based on the continuous trajectory functions of the sample signature and the verification signature. The signature recognition module initializes the alignment path as a linear function and aligns the signatures from beginning to end. The loss function under the optimal alignment path is constructed according to the signature alignment path mapping function. The difference between the signatures is obtained by normalizing the signature loss function with the signature duration, and the verification signature is identified online according to the difference. The feature trajectory mapping further includes: using the (x, y) coordinates of the signature trajectory, the x and y axis components of the velocity and acceleration as 6-dimensional features to generate a continuous feature trajectory function: F(t)=(x(t),y(t),x′(t),y′(t),x″(t),y″(t)) T , establish a mapping Φ from the signature trajectory function to its feature trajectory function; use the trust region algorithm to solve the optimal alignment path based on the signature feature trajectory functions F and G, specifically: regularize and adjust the constraints to construct the loss function L(W; F, G): According to the loss function call formula: Get the optimal alignment path W of the signature trajectory points * , where W represents the alignment function of the retained signature and the verification signature in time series, t m represents the total time consumption of the retained signature, d represents the maximum difference allowed between the corresponding trajectory points of the retained signature and the signature to be authenticated, and λ represents the penalty for reverse alignment.

7. The online signature authentication system according to claim 6, wherein, The human muscle motion model obtains the time t0 when each muscle module sends a motion signal, the angle when the arc starts to draw, the angle when the arc stops to draw, the length of the arc, the standard deviation of the log-normal distribution, the mean of the log-normal distribution, and estimates the motion parameters of each muscle module based on the signature trajectory points. The muscle module signature angle function is established, the motion trajectory of each muscle module is superimposed, and a continuous signature trajectory function is reconstructed.

8. The online signature authentication system according to claim 6 or 7, characterized in that, Initialize the alignment path to the simplest linear function and align the signatures head to tail, according to the formula: Obtain the times \(W\) corresponding to the respective points in their respective signatures for the retained sample signature and the verification signature at initialization 0 \((t)\), as the initialization parameter of the iterative algorithm, iteratively solve the non-linear optimization problem according to the formula: \(W\) * =\(\arg\min\) W∈k阶幂函数 \(L(W; F, G)\) to obtain the best alignment of the retained sample signature and the signature to be authenticated The difference D(S,T) between the above signatures is obtained by standardization: According to the formula THR = 1.2 × max i≠j D(S i ,S j ), calculate the maximum signature difference threshold THR, compare the verification signature with all the retained sample signatures one by one to obtain the difference degree between the verification signature and all the retained sample signatures. If the average value of this difference degree is less than or equal to the difference degree threshold THR, the signature to be authenticated is a genuine signature; Where: t n represents the total time taken to verify the signature; Φ(S) is the mapping from the sample signature continuous trajectory function S to its characteristic trajectory function, Φ(T) is the mapping from the continuous trajectory function T of the signature to be authenticated to its characteristic trajectory function; S i ,S j respectively represent the i-th and j-th sample retention signatures in the sample retention signature group.

Images