A method, apparatus and medium for online handwritten signature authentication based on path development.

Abstract

This invention discloses an online handwritten signature authentication method, apparatus, and medium based on path development, belonging to the technical fields of artificial intelligence and computer vision. The method includes: acquiring online signature data and preprocessing the online signature data; extracting manual features from the preprocessed online signature data; constructing and training a deep feature extraction model based on path development according to the extracted manual features; and constructing an online signature recognition and authentication system based on the trained deep feature extraction model to predict the authenticity of the input signature. This invention employs path development technology, which uses Lie algebras to map temporal paths to Lie group space and uses matrix multiplication to compress path information, enabling a more robust representation of sequences. Simultaneously, a windowed averaging method is used to balance the global and local representation capabilities of the model, which is more beneficial to the operation of the path development layer.

Description

Technical Field

[0001] This invention relates to the technical fields of artificial intelligence and computer vision, and in particular to an online handwritten signature authentication method, apparatus and medium based on path imaging. Background Technology

[0002] Biometric identification technology refers to the automatic identification of individuals based on their physiological or behavioral characteristics, and it has been widely used in various sectors of society as a security technology. Biometric identification can be divided into two categories: physiological biometrics and behavioral biometrics. Physiological biometrics is based on measuring a user's biological characteristics, such as fingerprints, facial features, and iris scans, while behavioral biometrics considers a user's behavioral characteristics, such as handwritten signatures and voice recognition. Among these, handwritten signatures are simple to collect, non-invasive, and have been widely recognized as the most important means of verifying and ensuring someone's endorsement of a document's content, and are accepted by governments, laws, and commercial transactions as an identity authentication method. With the development of computer technology, the medium for signing has gradually shifted from traditional paper and pen to electronic devices. Compared to traditional signatures, it provides traceable dynamic information; this type of signature is called online signature.

[0003] Given a signature to be queried, the authentication task aims to determine whether the signature is the genuine signature of the user claiming to be queried. Unlike traditional binary classification tasks, signature authentication tasks can retrieve a sample of the user's genuine signature and match its similarity to the signature to be queried, thus enabling more efficient authentication. Early methods used manually designed features to represent the signature, but in recent years, with the development of deep learning technology, deep learning-based methods have gradually replaced manual features due to their robustness and versatility, becoming the mainstream in the field of signature authentication.

[0004] In recent years, many deep learning-based methods have been proposed in the field of online signature authentication. However, these methods perform poorly when faced with problems such as highly skilled signature forgery and cross-era signatures. Furthermore, some models have high computational costs and hardware requirements, hindering their deployment in practical applications. Therefore, how to construct a lightweight, efficient, and high-quality online signature authentication model has become a significant unsolved problem in this field. Summary of the Invention

[0005] In order to at least partially solve one of the technical problems existing in the prior art, the present invention aims to provide an online handwritten signature authentication method, device and medium based on path development.

[0006] The technical solution adopted in this invention is:

[0007] An online handwritten signature authentication method based on path rendering includes the following steps:

[0008] Obtain online signature data and preprocess the online signature data;

[0009] Manual feature extraction is performed on the preprocessed online signature data;

[0010] Based on the extracted artificial features, a deep feature extraction model based on path development is constructed and trained;

[0011] Based on the trained deep feature extraction model, an online signature recognition and authentication system is constructed to predict the authenticity of input signatures.

[0012] Furthermore, the online signature data includes multiple sampling points, each sampling point including position coordinates (x, y), pen pressure value p, and timestamp t;

[0013] The preprocessing of the online signature data includes:

[0014] The position coordinates (x, y) and pen pressure value p in the online signature data are normalized; the normalized position coordinates are... Normalized pen pressure value

[0015] Normalized position coordinates Filtering is performed to remove high-frequency noise from the location data.

[0016] Furthermore, the manual feature extraction of the preprocessed online signature data includes:

[0017] Multiple time functions are extracted from the location coordinates, pen pressure values, and timestamps in the online signature data as artificial features;

[0018] Perform random pruning, resampling, and standardization operations on multiple time functions.

[0019] Furthermore, the multiplexing time function includes:

[0020] 1) Original coordinates Original pressure value Original timestamp t;

[0021] 2) Lateral velocity and longitudinal velocity: v x v y ;

[0022] 3) Velocity amplitude:

[0023] 4) Velocity tangent angle: θ = arctan(v) y / v x );

[0024] 5) cos(θ), sin(θ);

[0025] 6) First derivatives of velocity and tangent angle:

[0026] 7) Logarithmic radius of curvature:

[0027] 8) Centripetal acceleration:

[0028] 9) Total acceleration:

[0029] The multi-channel time function is then subjected to random pruning and resampling to obtain the artificial feature tensor;

[0030] By standardizing the artificial feature tensors, we obtain standard feature tensors that are beneficial for deep model training and inference.

[0031] Furthermore, the deep feature extraction model includes an embedding module, a mask self-attention module, a path development module, and a classification head;

[0032] The embedding module is a fully connected layer used to map artificial features to a specific number of channels;

[0033] The masked self-attention module includes a masked multi-head self-attention layer and a multilayer perceptron. The masked multi-head self-attention layer uses a self-attention mechanism to interact with sequence information and avoids receiving information from subsequent data through masking. The multilayer perceptron independently processes the features of a single point in the sequence and adds non-linear properties to the masked self-attention module.

[0034] The path development module includes windowing operation, path development layer, and average layer.

[0035] The classification head is a fully connected layer used to map the feature vector output by the path imaging module to a vector with the same dimension as the number of users, in order to calculate the cross-entropy loss.

[0036] Furthermore, the path development layer employs path development technology:

[0037] If the input sequence contains N feature vectors Path development techniques utilize Lie algebras to construct learnable mapping layers M. θ The difference values ​​of the input temporal features (considered as paths) are mapped to the Lie group space, the matrix exponents of the mapping results are calculated, and these matrix exponents are then fused together sequentially through matrix multiplication to obtain the feature vector z containing all the information of the sequence. N-1 The analytical expression for path development is:

[0038]

[0039] Here, exp represents the matrix exponentiation operation.

[0040] Furthermore, the windowing operation is used to divide the feature sequence into n equal parts with 50% overlap according to a predefined parameter n, to obtain n' = 2 × n-1 windowed sequences;

[0041] The path development layer compresses n' windowed sequences into n' feature vectors, and then concatenates these n' feature vectors with the global average value of their corresponding window sequences to compensate for the path development layer's lack of absolute position perception.

[0042] The averaging layer performs an averaging operation on the n' feature vectors to obtain a single feature vector.

[0043] Furthermore, the construction of the online signature recognition and authentication system includes a registration phase and a recognition and authentication phase;

[0044] During the registration phase, the user's real signature is obtained, preprocessed and its features are extracted, and used as the user's template signature features, which are then stored in the database.

[0045] In the identification and authentication phase, the signature to be authenticated is obtained, and a deep feature extraction model is used to extract features from the signature to be authenticated. The extracted features are compared with the template signature features stored in the database. When the L2 Euclidean distance between the signature to be authenticated and the template signature is lower than a preset threshold, the signature to be authenticated is determined to be a genuine signature; otherwise, the signature to be authenticated is determined to be a forged signature.

[0046] Another technical solution adopted in this invention is:

[0047] An online handwritten signature authentication device based on path imaging includes:

[0048] At least one processor;

[0049] At least one memory for storing at least one program;

[0050] When the at least one program is executed by the at least one processor, the at least one processor performs the method as described above.

[0051] Another technical solution adopted in this invention is:

[0052] A computer-readable storage medium storing a processor-executable program, which, when executed by a processor, performs the method described above.

[0053] The beneficial effects of this invention are as follows: This invention employs path development technology, which uses Lie algebra to map temporal paths to Lie group space and uses matrix multiplication to compress path information, enabling a more robust representation of sequences. Simultaneously, the use of a windowed averaging method balances the global and local representation capabilities of the model, further benefiting the operation of the path development layer. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following description is provided with accompanying drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the accompanying drawings described below are only for the purpose of clearly illustrating some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a flowchart of an online handwritten signature authentication method based on path rendering, according to an embodiment of the present invention.

[0056] Figure 2 This is a schematic diagram of the deep feature extraction model according to an embodiment of the present invention.

[0057] Figure 3 This is a schematic diagram of the path development technology used in an embodiment of the present invention.

[0058] Figure 4 This is a flowchart illustrating the online signature recognition and authentication system according to an embodiment of the present invention. Detailed Implementation

[0059] The embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0060] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0061] In the description of this invention, "several" means one or more, "more than" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0062] Furthermore, in the description of this invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0063] In the description of this invention, unless otherwise explicitly defined, terms such as "setting," "installing," and "connecting" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0064] like Figure 1 As shown, this embodiment proposes an online handwritten signature authentication method based on path development. This method improves authentication performance and speed while reducing hardware requirements, achieving efficient and lightweight online handwritten signature authentication. The method specifically includes the following steps:

[0065] S1. Obtain online signature data and preprocess the online signature data.

[0066] Each online signature data contains several sampling points. Each sampling point specifically includes location coordinates (x, y), pen pressure value p, and timestamp t. The sampling rate is 100Hz.

[0067] Specifically, step S1 includes steps S11-S12:

[0068] S11, Normalization process.

[0069] Specifically, the following four equations are used to normalize the position coordinates (x, y) and pen pressure value p of the time series data:

[0070]

[0071]

[0072]

[0073]

[0074] The normalized position coordinates are Normalized pen pressure value

[0075] S12, noise reduction processing.

[0076] This step uses a Butterworth low-pass filter with a cutoff frequency of 15Hz to process the position coordinates. Filter out high-frequency noise in location data.

[0077] S2. Perform manual feature extraction on the preprocessed online signature data.

[0078] In this embodiment, the location coordinates of the normalized online signature data are used. Pen pressure value The timestamp t is used to calculate the following 15 time functions:

[0079] 1) Original coordinates Original pressure value Original timestamp t;

[0080] 2) Lateral velocity and longitudinal velocity: v x v y ;

[0081] 3) Velocity amplitude:

[0082] 4) Velocity tangent angle: θ = arctan(v) y / v x );

[0083] 5) cos(θ), sin(θ);

[0084] 6) First derivatives of velocity and tangent angle:

[0085] 7) Logarithmic radius of curvature:

[0086] 8) Centripetal acceleration:

[0087] 9) Total acceleration:

[0088] The 15-channel time function requires random pruning and resampling. Specifically, a random probability p is sampled from a uniform distribution U(0.6,1.0). If the time series length of the time function is l, the pruning length is specified as l×p, ensuring that this pruning length is within the range [100,l]. Otherwise, the nearest boundary value is taken as the pruning length. Next, the time series with the pruned length is sampled from a random starting point and resampled to 480. This results in an artificial feature tensor with a length of 480 and 15 feature channels.

[0089] This tensor also needs to be standardized to obtain a standard feature tensor that is beneficial for deep model training and inference.

[0090] S3. Based on the extracted artificial features, construct and train a path development-based depth feature extraction model.

[0091] Construct and train a deep feature extraction model based on path development. This model receives the artificial features obtained in the previous steps and outputs a more discriminative signature representation. Specific steps include S31-S32:

[0092] S31, such as Figure 2 As shown, the path development-based deep feature extraction model includes an embedding module, a mask self-attention module, a path development module, and a classification head.

[0093] The embedding module is a fully connected layer that maps the aforementioned artificial features to a specific number of channels.

[0094] The masked self-attention module comprises a masked multi-head self-attention layer and a multilayer perceptron, both with residual connections. The masked multi-head self-attention module uses a self-attention mechanism to interact with sequence information and uses masking to prevent preceding data from receiving information from subsequent data. The multilayer perceptron independently processes the features of individual points in the sequence and adds non-linear properties to the masked self-attention module.

[0095] The path development module includes windowing operations, path development layers, and an averaging layer.

[0096] The windowing operation divides the feature sequence into n equal parts with 50% overlap according to a predefined parameter n, resulting in n' = 2 × n-1 windowed sequences.

[0097] The path development layer employs path development technology, as illustrated in the diagram below. Figure 3 As shown. If the input sequence contains N feature vectors Path development techniques utilize Lie algebras to construct learnable mapping layers M. θThe difference values ​​of the input temporal features (considered as paths) are mapped to the Lie group space, the matrix exponents of the mapping results are calculated, and these matrix exponents are then fused together sequentially through matrix multiplication to obtain the feature vector z containing all the information of the sequence. N-1 The analytical expression for path development can be written as:

[0098]

[0099] Where exp is the matrix exponentiation operation.

[0100] The path development layer compresses n' windowed sequences into n' feature vectors, and then concatenates these n' feature vectors with the global average of their corresponding window sequences to compensate for the path development layer's lack of perception of absolute position.

[0101] The averaging layer performs an averaging operation on the n' feature vectors to obtain a single feature vector.

[0102] The feature vector processed by the path development module is regarded as the depth feature of the online signature. The authenticity can be determined by calculating the L2 Euclidean distance between the signature depth features.

[0103] The classification head is a fully connected layer that maps the feature vectors output by the path imaging module to a vector with the same dimension as the number of users, which is used to calculate the cross-entropy loss.

[0104] S32. Supervise the model using triplet loss and cross-entropy loss, and optimize it using the Adam optimizer. The initial learning rate is 0.001. After training for 100 generations using an exponentially decreasing learning rate, adjust the learning rate to a constant 0.0001 and continue training for another 100 generations.

[0105] S4. Based on the trained deep feature extraction model, construct an online signature recognition and authentication system to predict the authenticity of the input signature.

[0106] In step S3, the trained deep feature extraction model extracts the output vector of its path rendering layer as the deep features of the input signature. This operation is called deep feature extraction for online signatures.

[0107] Building an online signature recognition and authentication system, such as Figure 4 As shown, it is specifically divided into a registration phase and an identification and authentication phase.

[0108] During the registration phase, new users need to enter their real signature. After preprocessing (such as the preprocessing in step S1) and feature extraction (i.e. manual feature extraction and deep feature extraction), the signature will be stored in the database as the user's template signature feature vector.

[0109] During the identification and authentication phase, for a signature to be queried with a declared user, it needs to be preprocessed and feature extracted to obtain its features, and then compared with the similarity features of the template signature of the corresponding user in the database: when the L2 Euclidean distance between the signature to be queried and the template signature is lower than a certain threshold, the signature to be queried is accepted as a genuine signature, otherwise it is a forged signature.

[0110] For a signature to be queried without a declared user, after preprocessing and feature extraction, the feature needs to be compared with the similarity features of all template signature features in the database. The signature with the highest similarity is selected, and the user corresponding to it is the predicted user. The prediction result is used as the declared user of the signature to be queried, so that the authenticity of the signature can be verified.

[0111] In summary, the method of this application has at least the following advantages and beneficial effects compared with the prior art:

[0112] (1) This application uses a masked self-attention module to perceive the time sequence, which can better focus on the time sequence information and extract high-quality global features.

[0113] (2) This application employs path development technology, which uses Lie algebra to map temporal paths to Lie group space and uses matrix multiplication to compress path information, enabling more robust representation of sequences. Simultaneously, the proposed windowed averaging method balances the model's global and local representation capabilities, efficiently authenticating online handwritten signatures while ensuring robustness against skilled forgery attacks. It also boasts faster inference speed and lower hardware requirements, making it highly valuable for practical applications and widely applicable in the fields of artificial intelligence and computer vision.

[0114] (3) The model constructed in this application is more lightweight, has a faster inference speed, requires less hardware, and has good robustness in the face of skilled forgery attacks, and has good practical application value.

[0115] The present invention also provides an online handwritten signature authentication device based on path development, comprising:

[0116] At least one processor;

[0117] At least one memory for storing at least one program;

[0118] When the at least one program is executed by the at least one processor, the at least one processor performs the following: Figure 1 The method shown.

[0119] This embodiment of the online handwritten signature authentication device based on path development can execute the online handwritten signature authentication method based on path development provided in the method embodiment of the present invention. It can execute any combination of implementation steps of the method embodiment and has the corresponding functions and beneficial effects of the method.

[0120] This application also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform... Figure 1 The method shown.

[0121] This embodiment also provides a storage medium storing instructions or programs that can execute the online handwritten signature authentication method based on path development provided in the method embodiment of the present invention. When the instructions or programs are run, any combination of implementation steps of the method embodiment can be executed, and the method has the corresponding functions and beneficial effects.

[0122] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is altered and sub-operations described as part of a larger operation are executed independently.

[0123] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0124] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0125] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0126] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0127] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0128] In the foregoing description of this specification, references to terms such as "one embodiment," "another embodiment," or "some embodiments" indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0129] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0130] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for online handwritten signature authentication based on path rendering, characterized in that, Includes the following steps: Obtain online signature data and preprocess the online signature data; Manual feature extraction is performed on the preprocessed online signature data; Based on the extracted artificial features, a deep feature extraction model based on path development is constructed and trained; Based on the trained deep feature extraction model, an online signature recognition and authentication system is constructed to predict the authenticity of input signatures. The manual feature extraction of the preprocessed online signature data includes: Multiple time functions are extracted from the location coordinates, pen pressure values, and timestamps in the online signature data as artificial features; Perform random pruning, resampling, and standardization operations on multiple time functions; The deep feature extraction model includes an embedding module, a mask self-attention module, a path development module, and a classification head; The embedding module is a fully connected layer used to map artificial features to a specific number of channels; The masked self-attention module includes a masked multi-head self-attention layer and a multilayer perceptron. The masked multi-head self-attention layer uses a self-attention mechanism to interact with sequence information and avoids receiving information from subsequent data through masking. The multilayer perceptron independently processes the features of a single point in the sequence and adds non-linear properties to the masked self-attention module. The path development module includes windowing operation, path development layer, and average layer. The classification head is a fully connected layer used to map the feature vector output by the path imaging module to a vector with the same dimension as the number of users, so as to calculate the cross-entropy loss. The path development layer employs path development technology: If the input sequence contains eigenvectors Path rendering technology utilizes Lie algebras to construct learnable mapping layers. The difference values ​​of the input time-series features are mapped to a Lie group space, the matrix exponents of the mapping results are calculated, and these matrix exponents are then fused together sequentially through matrix multiplication to obtain a feature vector containing all the information of the sequence. The analytical expression for path development is: in, This is for matrix exponentiation operations.

2. The online handwritten signature authentication method based on path imaging according to claim 1, characterized in that, The online signature data contains multiple sampling points, each containing location coordinates. Pen pressure value and timestamp ; The preprocessing of the online signature data includes: Position coordinates in online signature data Pen pressure value Normalization is performed; the normalized position coordinates are Normalized pen pressure value ; Normalized position coordinates Filtering is performed to remove high-frequency noise from the location data.

3. The online handwritten signature authentication method based on path imaging according to claim 1, characterized in that, The multiplexed time function includes: 1) Original coordinates Original pressure value Original timestamp ; 2) Lateral and longitudinal velocities: , ; 3) Velocity amplitude: ; 4) Velocity tangent: ; 5） ， ； 6) First derivatives of velocity and tangent angle: , ; 7) Logarithmic radius of curvature: ; 8) Centripetal acceleration: ; 9) Total acceleration: ; The multi-channel time function is subjected to random pruning and resampling operations to obtain the artificial feature tensor; By standardizing the artificial feature tensors, we obtain standard feature tensors that are beneficial for deep model training and inference.

4. The online handwritten signature authentication method based on path imaging according to claim 1, characterized in that, The windowing operation is used to divide the feature sequence according to predefined parameters. Perform 50% overlap Divide into equal parts to obtain A windowed sequence; The path development layer will Each windowed sequence is compressed into These feature vectors, and then... Each feature vector is concatenated with the global average of its corresponding window sequence to compensate for the path imaging's lack of perception of absolute position. The averaging layer will A single feature vector is obtained by averaging the feature vectors.

5. The online handwritten signature authentication method based on path imaging according to claim 1, characterized in that, The construction of the online signature recognition and authentication system includes a registration phase and a recognition and authentication phase. During the registration phase, the user's real signature is obtained, preprocessed and its features are extracted, and used as the user's template signature features, which are then stored in the database. In the identification and authentication phase, the signature to be authenticated is obtained, a deep feature extraction model is used to extract features from the signature to be authenticated, and the extracted features are compared with the template signature features stored in the database. When the L2 Euclidean distance between the signature to be authenticated and the template signature is lower than a preset threshold, the signature to be authenticated is determined to be a genuine signature. Conversely, the signature to be authenticated is determined to be a forged signature.

6. An online handwritten signature authentication device based on path development, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method of any one of claims 1-5.

7. A computer-readable storage medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to perform the method as described in any one of claims 1-5.

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