A smiley face recognition clock-in method and system based on a child face

Abstract

The application is particularly a smile face recognition clock-in method and system based on children's faces, relating to the technical fields of biological feature recognition, three-dimensional machine vision and intelligent attendance, comprising: extracting the physical Euclidean straight line distance between the outer canthi of both eyes to obtain the outer canthus bone scale parameters of both eyes, combining the average curvature basic value to construct the heterogeneous homology tension mapping partial differential equation containing the outer canthus bone scale parameters of both eyes. In the application, the three-dimensional reconstruction mechanism combining the homology topological partition and the heterogeneous homology tension mapping is helpful to improve the reconstruction accuracy and recognition robustness of children's faces in the occlusion scene; relying on the depth gradient and normal divergence related geometric features to complete the division of the exposed area and the occlusion area, constructing the curvature field and the topological homology emission anchor point based on the real geometric data of the exposed area, combining the physiological constraints of the outer canthus bone scale to establish the partial differential mapping equation, and realizing the elastic baseline fitting of the occlusion area through the Poisson surface reconstruction.

Description

Technical Field

[0001] This invention relates to the fields of biometric recognition, three-dimensional machine vision and intelligent attendance technology, and in particular to a method and system for attendance tracking based on smile recognition of children's faces. Background Technology

[0002] With the advancement of digital construction in smart campuses and childcare settings, facial recognition attendance systems have become an important technological means for managing children's attendance and verifying pick-up and drop-off. Leveraging the uniqueness and contactless data collection characteristics of facial biometrics, such systems can achieve rapid identity verification, effectively improving the efficiency of campus management and ensuring the safety of children during pick-up and drop-off. Currently, most mainstream facial recognition solutions are based on two-dimensional visible light imaging technology, using facial texture feature extraction and comparison to complete identity recognition. Combined with conventional liveness detection mechanisms to resist basic spoofing attacks, they have already demonstrated mature application results in typical scenarios with suitable lighting and unobstructed faces.

[0003] To address challenges such as facial occlusion and complex lighting conditions, 3D face recognition technology has been gradually applied and developed. Existing 3D face recognition solutions primarily acquire facial point cloud data using depth sensing technologies such as structured light and time-of-flight, relying on algorithms like point cloud registration and surface reconstruction to complete 3D feature extraction and identity matching. For occluded scenarios, some solutions employ region segmentation and feature completion techniques, combining prior facial models to fit and repair missing regions, thus mitigating the impact of occlusion on recognition accuracy and expanding the applicable scenarios for face recognition technology.

[0004] In specific application scenarios of children's facial recognition check-in, young children often have missing facial areas due to wearing masks, bangs covering their faces, or wearing headwear. In addition, children's faces are in the growth and development stage, and there are differences in individual geometric shapes, which puts forward higher requirements for the reconstruction accuracy of the occluded areas and the adaptability of expression anti-spoofing judgment. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for checking in based on children's facial smile recognition in order to solve the above problems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for checking in using smile recognition based on children's faces, including: The initial 3D spatial point cloud is obtained, and the absolute value of the depth gradient and the normal divergence are calculated. The facial point cloud is divided into the homogeneous topological exposure area and the occlusion stripping area. In the topologically exposed region of the same origin, construct the three-dimensional surface analytical equation, calculate the Gaussian curvature scalar field and the mean curvature scalar field, extract the curvature gradient vector field through global spatial differentiation operation, and determine the topological same origin emission anchor point with the mean curvature fundamental value and the tangent plane tension vector. The physical Euclidean linear distance between the outer canthi of both eyes is extracted to obtain the skeletal scale parameters of the outer canthi of both eyes. Combined with the basic value of the average curvature, a partial differential equation for heterogeneous tension mapping containing the skeletal scale parameters of the outer canthi of both eyes is constructed. Within the shading stripping zone, starting from the topological homogeneous emission anchor point, the virtual normal vector field of the whole domain is generated by using the partial differential equation of tension mapping of different regions homogeneous tensions along the tangential plane tension vector direction and the curvature gradient vector direction. The three-dimensional Poisson core partial differential reconstruction equation is solved to extract the zero isovalue surface and reconstruct the static elastic baseline of the shading stripping zone. The transient 3D dynamic point cloud is acquired and aligned with the static elastic baseline of the occlusion stripping area. The resting Gaussian curvature on the baseline and the skeletal scale parameter of the outer canthus of both eyes are combined to calculate the adaptive elastic modulus space matrix. The local 3D stress tensor matrix is ​​obtained, the stress evolution time gradient field is extracted, the natural smile anti-counterfeiting judgment is performed, and an encrypted digital attendance certificate is generated.

[0007] Preferably, the operation of obtaining the initial three-dimensional spatial point cloud includes: Drive a heterogeneously integrated vertical cavity surface-emitting laser array to radiate a sinusoidal continuous wave with high-frequency amplitude modulation onto the child's face within the field of view. Using a near-infrared single-photon avalanche diode phase-sensitive detector, the received photon energy is sampled at high speed at multiple phase nodes, and the absolute physical space straight-line distance is calculated based on the optical time-of-flight continuous wave phase mapping equation to generate an initial point cloud. In three-dimensional space, a spherical neighborhood is constructed with discrete data points as the center, and the three-dimensional geometric covariance matrix of the point cloud spatial coordinates within the spherical neighborhood is calculated. Eigenvalue decomposition is performed on the three-dimensional geometric covariance matrix. If the smallest eigenvalue among the three eigenvalues ​​is significantly larger than the other two eigenvalues, the discrete data points are determined to belong to environmental flypoint noise and are removed to obtain the basic facial depth point cloud set.

[0008] Preferably, the step of calculating the absolute value of the depth gradient and the normal divergence to divide the facial point cloud into a homogeneous topological exposure region and an occlusion stripping region includes: Calculate the absolute values ​​of the depth gradient along the horizontal and vertical spatial axes, and define the boundary of the region where the absolute value of the depth gradient exceeds the limit of the natural physiological bulge as the edge of the physical fault. The spatial divergence of the three-dimensional normal vector array across the edge of a physical fault is used to quantify the normal random oscillations caused by the micro-level undulations and wrinkles of the fabric. Connected regions are generated using a region growing algorithm. Smooth regions with spatial divergence below the physical blocking threshold of normal divergence and without deep faults are designated as homogeneous topological exposure regions. Connected regions with deep faults and a surge in spatial divergence are marked as occlusion stripping regions.

[0009] Preferably, the step of constructing a three-dimensional surface analytical equation in the topologically exposed region, calculating the Gaussian curvature scalar field and the mean curvature scalar field, extracting the curvature gradient vector field through global spatial differentiation, and determining the topologically related emission anchor points with the mean curvature fundamental value and the tangent plane tension vector specifically includes: Using a thin plate spline interpolation algorithm, the natural bending state of a metal thin plate with ideal isotropic elasticity under the forced constraint of normal stress at discrete control points is simulated. The analytical equation of a continuous three-dimensional surface is constructed by minimizing the global bending strain energy integral. The Gaussian curvature scalar field and the mean curvature scalar field are obtained by using the differential curvature algorithm, and the curvature gradient vector field is solved by combining the three-dimensional Hamiltonian operator. Spatial orientation clustering analysis is performed on the gradient vectors in the curvature gradient vector field to extract the geometric coordinate points corresponding to the main gradient convergence streamlines pointing towards the shading stripping region. These points are defined as topological homogeneous emission anchor points, and the three-dimensional spatial orientation angles of the Gaussian curvature, mean curvature, and tangential tension vector of the topological homogeneous emission anchor points are recorded.

[0010] Preferably, before constructing the partial differential equation for heterogeneous homogeneous tension mapping, a heterogeneous spatial mapping tensor constrained by the skeletal scale parameters of the outer canthi of both eyes needs to be established. The expression of the heterogeneous spatial mapping tensor is as follows: ;in, Represents a heterogeneous space mapping tensor; Indicates the horizontal tension conductivity; Indicates vertical tension conductivity; The specific expansion of the partial differential equation for the tension mapping between different regions with the same origin is as follows: ; in, Represents the divergence operator; Represents the gradient operator; Represents the scalar function of the local surface tension to be solved; Represents a heterogeneous space mapping tensor; Indicates the tissue spatial distance attenuation factor; This represents the equivalent constant of hydrostatic pressure; Indicates the local mean curvature; When solving the partial differential equation of tension mapping between different regions, the known curvature scalar of the topological homogeneous emission anchor point is forcibly and equivalently assigned to the integral starting boundary profile of the equation, and a physical geometric energy conservation penalty constraint term is embedded to limit the sum of the elastic potential energy integrals of the derived internal voxel units to tend to a local minimum in the global space.

[0011] Preferably, the step of generating a global virtual normal vector field by deriving the partial differential equation of tension mapping from different regions along the tangential plane tension vector direction and the curvature gradient vector direction within the occlusion stripping region includes: The variable step size fourth-order Runge-Kutta method is used to iterate along the virtual three-dimensional space integral physical streamline to the unknown space, and to solve in real time the geometric normal vector deflection space angle, the local Gaussian curvature prediction value and the average curvature prediction value under the current small step distance. A virtual spring repulsive force model is established between adjacent integral physical streamline motion nodes, and adaptive node relaxation is performed by coupling the attractive and repulsive potential fields: When the streamline distance is lower than the physical limit of the minimum thickness of the preset biological tissue, the repulsive potential energy generates lateral thrust to adjust the yaw angle of the next integral step; when the streamline spacing is too far and there is a risk of mesh gaps, the gravitational potential energy plays a pulling and contracting role, and finally generates a global virtual normal vector field.

[0012] Preferably, the step of solving the three-dimensional Poisson core partial differential reconstruction equation to extract the zero isovalued surface and reconstruct the static elastic baseline of the occlusion stripping region includes: A divergence conservation balance mechanism is established between the continuous scalar potential field and the global virtual normal vector field. Smooth energy penalty constraints are added at the boundary between the exposed area and the occlusion stripping area to ensure that the potential function remains zero-order continuous and first-order differentiable when crossing the physical boundary line. Matrix operations are performed on the discrete three-dimensional octree voxel grid to solve for the high-precision continuous scalar potential field. Using a voxel interpolation-based moving cube algorithm, all isosurface polygon meshes with values ​​equal to zero are tracked, extracted, and connected in high resolution in a continuous scalar potential field array, and used as the static elastic baseline of the occlusion stripping region.

[0013] Preferably, the step of acquiring the transient three-dimensional dynamic point cloud and aligning it with the static elastic baseline of the occlusion stripping region, and calculating the adaptive elastic modulus space matrix by combining the resting Gaussian curvature on the baseline, includes: High-rigidity physiological and anatomical anchor points are extracted, and the homogeneous spatial transformation matrix is ​​solved by the weighted point-to-surface iterative nearest point algorithm. The macroscopic rigid body motion of the head is stripped away by the inverse spatial transformation multiplication, so that the transient three-dimensional dynamic point cloud and the static elastic baseline of the occluded stripping area are locked to the same absolute physical coordinate system. The resting Gaussian curvature value was extracted from the static elastic baseline of the reconstructed occlusion stripping area. The value was then combined with the skeletal scale parameters of the outer canthus of both eyes using a pre-defined biomechanical empirical correction equation to calculate the local Young's modulus estimate and construct an adaptive elastic modulus space matrix. The directed Euclidean physical distance from the discrete spatial coordinates to the static elastic baseline of the shading stripping area in the corresponding normal direction is calculated point by point to generate a three-dimensional spatial displacement vector field.

[0014] Preferably, the extraction of the stress evolution time gradient field for natural smile anti-counterfeiting determination includes the following dimensions of judgment: Extract the absolute amplitude of the local maximum principal stress and verify whether the absolute amplitude exceeds the preset reference resting physical threshold. The stress scalar's first derivative with time is calculated to generate the stress evolution time gradient field. The peak connectivity region is dynamically located and the phase velocity is calculated to verify whether the spatial propagation direction vector follows the biological anatomical muscle contraction path extending from the middle of the mandibular ramus to the outer canthus and zygomatic arch. The sum of the main diagonal elements generated during the calculation of the three-dimensional local strain tensor matrix is ​​extracted as the total volumetric strain rate of the local micro-element; if obvious volume expansion is detected in a local area, it is determined that the material of the tested surface violates the basic physical laws of biomaterials, and the check-in request is forcibly blocked.

[0015] A smile recognition check-in system based on children's faces includes: Deep point cloud acquisition and occlusion determination module: acquires the initial 3D spatial point cloud, performs depth gradient absolute value and normal divergence calculation, and divides the facial point cloud into the homogeneous topological exposure area and the occlusion stripping area. The module for extracting the curvature gradient of the same origin in the exposed region: constructs a three-dimensional surface analytical equation in the exposed region of the same origin topology, calculates the Gaussian curvature scalar field and the mean curvature scalar field, extracts the curvature gradient vector field through global spatial differentiation operation, and determines the topological same origin emission anchor point with the mean curvature basic value and the tangent plane tension vector. The module for constructing the heterogeneous tension mapping equation extracts the physical Euclidean straight-line distance between the outer canthi of both eyes to obtain the skeletal scale parameters of the outer canthi of both eyes. Combined with the basic value of the average curvature, a heterogeneous tension mapping partial differential equation containing the skeletal scale parameters of the outer canthi of both eyes is constructed. The occlusion zone elastic baseline integral reconstruction module: In the occlusion stripping zone, starting from the topological homogeneous emission anchor point, the module uses the tension vector direction of the tangential plane and the curvature gradient vector direction to derive the global virtual normal vector field using the tension mapping partial differential equation of different regions homogeneous tension. The module solves the three-dimensional Poisson core partial differential reconstruction equation to extract the zero isovalue surface and reconstruct the static elastic baseline of the occlusion stripping zone. The adaptive modulus calculation and stress evolution smiley face determination module acquires transient 3D dynamic point clouds and aligns them with the static elastic baseline of the occlusion stripping area. It combines the resting Gaussian curvature on the baseline with the skeletal scale parameters of the outer canthi of both eyes to calculate the adaptive elastic modulus space matrix. It then obtains the local 3D stress tensor matrix through the Cauchy micro-strain geometric equation and the generalized Hooke's law. Finally, it extracts the stress evolution time gradient field to perform natural smiley face anti-counterfeiting determination and generates encrypted digital attendance vouchers.

[0016] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. This invention uses a three-dimensional reconstruction mechanism that combines homologous topological partitioning with heterologous homologous tension mapping, which helps to improve the reconstruction accuracy and recognition robustness of children's faces in occluded scenarios. It completes the division of exposed and occluded areas based on the geometric features related to depth gradient and normal divergence, constructs curvature field and topological homologous emission anchor points based on the real geometric data of exposed areas, establishes partial differential mapping equations in combination with the physiological constraints of the skeletal scale of the outer canthus of both eyes, and achieves elastic baseline fitting of the occluded area through Poisson surface reconstruction.

[0017] 2. This invention aligns the resting elastic baseline with the transient dynamic point cloud and solves the three-dimensional stress tensor by combining the adaptive elastic modulus space matrix. It completes a comprehensive judgment of natural smiles from multiple dimensions such as stress amplitude, spatial propagation path, and volumetric strain rate. It verifies the naturalness of the expression based on the biological anatomical laws of facial muscle contraction and can form an effective defense against various types of prosthetic attacks. Attached Figure Description

[0018] Further details, features, and advantages of this application are disclosed in the following description of exemplary embodiments in conjunction with the accompanying drawings, in which: Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0019] Several embodiments of this application will now be described in more detail with reference to the accompanying drawings to enable those skilled in the art to implement this application. This application may be embodied in many different forms and for various purposes and should not be limited to the embodiments set forth herein. These embodiments are provided to make this application thorough and complete, and to fully convey the scope of this application to those skilled in the art. The embodiments described do not limit this application.

[0020] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It will be further understood that terms such as those defined in commonly used dictionaries shall be interpreted as having a meaning consistent with their meaning in the relevant field and / or the context of this specification, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein. Example

[0021] Its specific implementation method is combined with the appendix Figure 1 Please provide a detailed explanation.

[0022] In this embodiment, it includes: Step 1: Depth Point Cloud Acquisition and Occlusion Determination This step uses high-frequency physical optics to acquire raw data containing three-dimensional geometric topological information of the face. By utilizing the mutation characteristics of pure physical geometric gradients, it accurately removes the failure areas obscured by non-rigid attachments (such as thick scarves, improperly worn masks, high collars of clothing, and loose hair) without relying on any prior samples or machine learning classifiers. This provides a highly pure spatial basis free of physical artifacts for subsequent homeomorphic topological mapping.

[0023] The optical acquisition hardware matrix deployed at the attendance terminal is activated. This hardware matrix adopts a heterogeneous integrated architecture, including a vertical-cavity surface-emitting laser array and a high dynamic range near-infrared single-photon avalanche diode phase-sensitive detector.

[0024] To penetrate the very superficial stratum corneum of a child's face, avoid strong interference from the external visible light spectrum, and precisely reach the dermal interface with epidermal deformation tension, the system sets the emission center wavelength of the vertical-cavity surface-emitting laser to a specific physical near-infrared band (such as the 940 nm or 850 nm band). This band has good superficial penetration capability into biological tissues and can effectively resist the photon submersion effect of the visible light band in background sunlight.

[0025] At the transmitting end, the driving circuit modulates the emitted photons with a high-frequency continuous wave amplitude at the megahertz level (typically tens to hundreds of megahertz), using a high-fidelity sine wave as the modulation waveform. The modulated light wave then radiates into the space around the child's face within the field of view, in the form of a spherical wave with a specific divergence angle.

[0026] When emitted high-frequency modulated infrared photons touch a child's facial skin, hair, or external obstructions, the photons undergo complex diffuse reflection and backscattering at the interface of different physical media. These echo photons carry phase delay information due to spatial distance differences and are ultimately captured by the focal plane array of a near-infrared phase-sensitive detector.

[0027] The system's internal high-speed field-programmable gate array (FPGA) uses a phase-locked loop (PLL) and a multi-step phase-shift detector circuit to perform high-speed integration sampling of the received photon energy at multiple phase nodes, thereby measuring the microscopic phase shift between the emitted and received light waves. To ensure the physical reproducibility and engineering accuracy of the depth dimension (Z-axis) calculation in the three-dimensional coordinate system, the system uses the vacuum speed of light constant and modulation frequency, and the time-of-flight continuous-wave phase mapping equation to calculate the absolute physical spatial straight-line distance from the detector focal plane to every point on the target surface.

[0028] The specific time-of-flight continuous-wave phase mapping equation for light is as follows: ; in, : Represents the absolute physical straight-line distance from a point on the target surface to the focal plane of the near-infrared phase-sensitive detector, which serves as the core parameter for constructing the Z-axis coordinates of the 3D point cloud; : Represents the constant speed of light waves in the current space medium; : Represents the phase delay in radians of the received optical wave extracted by the field-programmable gate array; : Indicates the amplitude modulation center frequency of the continuous wave emitted by a vertical cavity surface-emitting laser.

[0029] By applying the aforementioned spatial mapping equation to each valid pixel within the field of view of the phase-sensitive detector array, the system generates an initial 3D spatial point cloud at the current check-in transient moment. Since real-world check-in environments, such as school campuses or kindergartens, typically exhibit strong light multipath interference effects, the initial point cloud inevitably contains shot noise and "flying points" caused by volume scattering of photons on airborne particles. To eliminate the interference of these environmental noises on subsequent geometric differential calculations, the system implements anisotropic diffusion filtering based on the physical space covariance matrix on the initial 3D spatial point cloud.

[0030] The specific filtering mechanism is as follows: In a 3D point cloud coordinate system, a spherical neighborhood with a predetermined physical radius is constructed centered on each discrete data point. The 3D geometric covariance matrix of all point cloud spatial coordinates within this spherical neighborhood is calculated. By performing rigorous eigenvalue decomposition on this covariance matrix, three orthogonal eigenvalues ​​and their corresponding eigenvectors characterizing the local spatial point distribution are obtained.

[0031] If the smallest of the three eigenvalues ​​is significantly larger than the other two, this indicates that the local point cloud exhibits a disordered, spherical, divergent shape rather than a smooth biological surface. The system will determine that this point belongs to environmental flying point noise and forcibly remove it from the original matrix. After the above filtering and reconstruction of the pure geometric distribution, the system obtains a high-precision set of basic facial depth point clouds.

[0032] The system implements a heterogeneous occlusion determination mechanism based on physical topological continuity. From the interdisciplinary perspective of biological anatomy and continuum mechanics, the facial skin of children and the soft tissue network attached beneath it are a continuous manifold with highly homeomorphic properties in physical space. The derivative of the absolute depth of its surface along each spatial direction should be smooth and continuous. In contrast, when there are fabric coverings such as masks and scarves on the face, the hanging and stacking of the fabric, the weaving gaps, and the physical space thickness between the fabric edge and the skin will inevitably produce steep jumps and high-frequency roughness spikes in the point cloud normal vector field and depth scalar field.

[0033] Leveraging this significant physical difference, the system employs a dual physical constraint mechanism of first-order depth gradient magnitude and second-order local normal roughness to region-divide the facial point cloud. In a unified Cartesian three-dimensional coordinate system, the system performs partial derivative operations on any point in the basic facial depth point cloud set, calculating the absolute values ​​of the depth gradient along both the horizontal and vertical spatial axes. When the absolute value of the depth gradient within a certain local continuous region exceeds the maximum natural physiological elevation limit of a child's epidermis, the boundary of that region is defined as the edge of a physical fault.

[0034] By crossing the edge of this physical fault, the spatial divergence of the three-dimensional normal vector array on both sides of the edge is further calculated. Due to the uniform distribution of elastic potential energy and dense collagen support in children's skin, the normal vectors of the uncovered facial area will exhibit a gradually converging or diverging state that conforms to biological geometry, with minimal divergence. In areas obscured by fabric, the microscopic undulations and wrinkles of the fiber structure cause the local normal vector to exhibit violent random oscillations within a very small spatial neighborhood, leading to a surge in divergence. The system sets a physical blocking threshold for normal divergence and uses a region growing algorithm to scan and generate connected components across the entire point cloud space.

[0035] Smooth regions with normal divergence below the physical blocking threshold and without deep faults are designated as "homogeneous topological exposure regions"; connected regions with obvious deep faults and a surge in normal divergence are blocked and marked as occlusion stripping regions.

[0036] Step 2: Extraction of homologous curvature gradient in the exposed region After clarifying the physical spatial boundaries between the topologically exposed area and the occlusion stripping area, this step delves into the intrinsic geometric features of the exposed area (such as the center of the forehead, the lower edge of the brow ridge, the upper edge of the cheekbone, and the lateral region of the orbicularis oculi muscle, which are not covered by masks or scarves).

[0037] We will extract homologous curvature gradients that reflect the unique skeletal physiological development and static soft tissue fat distribution patterns of children. These gradients, acting as sources of biomechanical information, will serve as the core boundary parameters and initial energy values ​​for subsequent reconstruction of the occluded cheek baseline.

[0038] Because directly calculating higher-order derivatives from scattered discrete point clouds is highly susceptible to amplification and interference from localized minute sampling noise, the system first transforms the three-dimensional scattered point cloud of the homologous topological exposed area into a regular parameterized surface capable of performing higher-order continuous partial differentials. The system then lays out a uniform two-dimensional parameterized derivation mesh in the three-dimensional space of the exposed area and utilizes a thin-plate spline interpolation algorithm based on the principle of minimizing physical elastic energy to construct continuous analytical basis functions for the surface deformation of the exposed area.

[0039] In a physical sense, this thin-plate spline interpolation process simulates the natural bending state of a metal sheet with ideal isotropic elasticity under the forced constraint of normal stress at various discrete control points (i.e., the actual collected point cloud coordinates). By minimizing the global bending strain energy integral of this virtual thin plate in all directions of space, the system obtains a continuous, globally quadratically differentiable three-dimensional surface analytical equation.

[0040] This equation accurately reproduces the true physical undulations and stretching of the skin in the exposed area of ​​a child with extremely high geometric approximation, eliminating the discrete step effect caused by insufficient sensor grid resolution.

[0041] After obtaining the analytical equations for continuous three-dimensional surfaces, the system introduces the first and second fundamental forms from classical differential geometry to perform mathematical quantification and curvature measurement of children's skin surfaces.

[0042] At any valid spatial coordinate point on the parametric grid, the system sets the parametric equation of the continuous surface as follows: ,in These are mutually orthogonal two-dimensional parameterized coordinate variables on a continuous surface. The system assigns parameters... Find the first-order partial derivatives to obtain two local tangent vectors that characterize the local surface tangential trend. These two orthogonal tangent vectors form the mathematical basis of the local tangent plane.

[0043] The system constructs the first fundamental formal equation for quantifying the local micro-area elements and surface arc length of biological epidermis using this set of substrates: ; in, : A metric parameter representing the square of the length of a tiny line segment on a curved surface, reflecting the inherent two-dimensional stretching characteristics of the skin surface when normal deformation is not considered; : Represents the first coefficient of the first basic form, whose calculated value is the tangent vector. The inner product with itself, that is ; : represents the second coefficient of the first basic form, whose calculated value is the inner product of two orthogonal tangent vectors, i.e. This characterizes the degree of angular distortion of the parametric curves on the biological surface; : Represents the third coefficient of the first basic form, whose calculated value is the tangent vector. The inner product with itself, that is ; : Represents the differential component in the newly calibrated surface parametric coordinate system.

[0044] Based on this, the system calculates the unit normal vector perpendicular to the tangent plane at that point on the biological surface by performing a cross product operation on the two first-order tangent vectors and then performing vector normalization. .

[0045] To quantify the curvature of a surface in three-dimensional space, the system calculates the second-order partial derivatives of the surface along the normal direction of the local tangent plane, i.e. Using these second-order partial derivatives, the system constructs a second fundamental equation describing how the skin surface physically bends and deforms away from the tangent plane in space: ; in, : This is a second-order approximate metric parameter representing the normal distance of a local deviation of a curved surface from its tangent plane. It is a core mathematical indicator for measuring local protrusions or depressions in tissues. : Represents the first coefficient of the second fundamental form, calculated as a second-order partial derivative. At the unit normal vector Spatial projection on, i.e. ; : Represents the second coefficient of the second fundamental form, calculated as a mixed second-order partial derivative. At the unit normal vector Spatial projection on, i.e. ; : Represents the third coefficient of the second fundamental form, calculated as a second-order partial derivative. At the unit normal vector Spatial projection on, i.e. .

[0046] Combining the physical quantization values ​​of the coefficients extracted from the first and second fundamental forms, the system precisely calculates, within the same topological exposure region, for each effective parameter coordinate point, two core scalar fields characterizing the local biogeometry of the child: the Gaussian curvature scalar field and the mean curvature scalar field, using a specific differential curvature algorithm. The specific curvature calculation equations are as follows: ; The Gaussian curvature obtained from this set of calculation equations This represents the intrinsic geometric characteristics of a biological surface. The sign of its value directly reflects whether the skin surface at that location is an elliptical protrusion (e.g., the high point of a child's full cheekbone, with a positive Gaussian curvature), a hyperboloid saddle point (e.g., the concave area where the root of the nose transitions to the eye sockets, with a negative Gaussian curvature), or a flattenable cylindrical shape. The calculated average curvature... It is the arithmetic mean of the two principal curvatures, which profoundly reflects the average degree of expansion or contraction of the skin surface in the normal direction. It is a key physical parameter for measuring the volume change of facial soft tissue caused by subcutaneous tissue fluid filling or static fat accumulation.

[0047] Because children are in a period of rapid growth and development, their faces not only have an overall physiological curvature, but more importantly, the distribution of their curvature in three-dimensional space is not uniform. Instead, it exhibits a specific gradient decay or surge as the original resting tension distribution of the superficial musculoaponeurotic system (SMAS) changes.

[0048] Simply obtaining the absolute curvature values ​​of isolated coordinate points is insufficient to support physical deductions across occluded regions. Therefore, after obtaining the global scalar fields of Gaussian curvature and mean curvature, the system further introduces a three-dimensional Hamiltonian operator to perform global spatial differentiation on the two scalar fields, thereby solving for the high-dimensional Gaussian curvature gradient vector field and the mean curvature gradient vector field.

[0049] The curvature gradient vector field not only contains the direction vectors of the most dramatic changes in curvature numerical space, but also, at a biomechanical level, indicates the mechanical transmission path of facial surface tension in this local area. In the resting state without facial expression intervention, the curvature gradient direction of the upper exposed area of ​​a child's facial skin (such as the outer edge of the canthus and above the zygomatic arch) is constrained by the static traction force at the intersection of the zygomaticus major muscle origin and the orbicularis oculi muscle fibers. By performing spatial orientation clustering analysis on all generated curvature gradient vectors within the exposed area, the main gradient convergence streamlines that geometrically point towards the occluded and stripped area (such as the mandibular ramus or the lower half of the cheek) are extracted.

[0050] These curvature gradient streamlines extending into the depths of the occlusion space, much like electric field lines in electromagnetism, contain topological homogeneous information that crosses the physical occlusion boundary. The system rigorously defines these sets of three-dimensional geometric coordinate points, which are precisely located at the edge of the boundary zone between the exposed area and the occlusion stripping area and have a high degree of consistency in gradient direction, as "topological homogeneous emission anchor points".

[0051] The system records in detail the basic Gaussian curvature value, the basic mean curvature value, the rate of change of spatial partial derivatives, and the three-dimensional spatial orientation angle of the tangential tension vector at each topological homogeneous emission anchor point.

[0052] Step 3: Construction of the Heterogeneous-Origin Tension Mapping Equation In this step, the core technology aims to solve the computational challenge of scientifically transferring and rigorously extrapolating physical parameters from the exposed area to the severely data-deficient occluded and stripped area. Due to physical obstruction by winter fabrics, masks, or other non-rigid attachments, the initial morphological optical data of the lower half of the child's face often presents large areas of deep blanks. To reconstruct the physiological state of this area in high-fidelity in computer 3D space, the "topological homogeneous emission anchor points" extracted in step two are used as initial boundary conditions to construct a spatial mapping model that conforms to the biomechanical rheological characteristics of the child's facial soft tissue.

[0053] From the perspective of continuum mechanics, the facial skin of children and the superficial musculoaponeurotic system (SMAS) and fat pads attached beneath it are, in terms of physical structure, a biocomposite material with anisotropic and nonlinear hyperelastic characteristics. Compared to adults, the facial fibrous tissue of developing children is highly hydrated, and the collagen network structure is denser and richer in water. This results in a highly consistent distribution of static surface tension and hydrostatic pressure characteristics across the entire face when there are no significant facial expressions (i.e., at rest). In other words, the minute tension state in the upper exposed areas (such as the junction of the orbicularis oculi muscle and the zygomatic bone) is mechanically transmitted through the facial subcutaneous fascia network, and necessarily has a spatial mapping ratio with the internal hydrostatic pressure and outward supporting tension of the lower buccal fat pads.

[0054] This microscopic biological tension-mechanical transmission mechanism is transformed into a macroscopic mathematical-physical model that can be analyzed by a computer processor. The system introduces a hyperelastic constitutive equation based on the strain energy density function. In a three-dimensional continuous medium space, assuming that the child's cheek tissue is approximately a mixture of incompressible fluid and elastic solid, the system uses a biomechanically modified two-parameter Mooney-Rivlin physical model to characterize the initial mechanical properties of this biological tissue. Within this model framework, the local strain energy density of the biological tissue is defined as a nonlinear scalar function of the first and second principal invariants of the deformation tensor.

[0055] Obtain the topological homogeneous emission anchor points located at the physical boundary between the homogeneous topological exposure area and the shading stripping area in step two, and read the basic values ​​of the average curvature, the basic values ​​of the Gaussian curvature, and the three-dimensional direction angle of the tangential tension vector at these anchor points from the memory register. According to the generalized Laplace-Young equation variant principle in the intersection of fluid mechanics and thin film mechanics, on the surface of a biofilm in static equilibrium, the local surface tension scalar has a direct linear physical proportionality to the local principal curvature at that location, and this proportionality coefficient is subject to multiple constraints such as local tissue thickness, the downward component of the gravitational field, and the ambient air pressure difference.

[0056] After extracting the initial values ​​of the local tension parameters at the boundary anchor points of the exposed area, the system needs to construct a second-order partial differential equation to extrapolate the spatial evolution of this tension into the depth of the shading and stripping area. The construction of this equation needs to fully consider the underlying physical support provided by the child's skull to the facial soft tissue, as well as the natural physical attenuation and damping of surface tension as it extends through the soft tissue network with spatial transmission distance.

[0057] The system establishes a tension conduction coefficient matrix to control spatial conduction characteristics. Considering that the tissue thickness in the cheek region gradually increases from below the eye socket to the edge of the mandible (i.e., increased accumulation of buccal fat pads), tension conduction is not an isotropic linear process. Therefore, the system introduces a tissue spatial attenuation factor that varies non-linearly with the three-dimensional spatial depth coordinates.

[0058] Meanwhile, considering the significant differences in facial width and lateral bone development among individual children during growth and development, the system accurately extracts the physical Euclidean distance between two points (outer canthus) on the left and right outer canthi (lateral corners of the eyes) in the three-dimensional point cloud coordinate system of the exposed area, and defines this value as the skeletal scale parameter of the outer canthi of both eyes. Using this scale parameter, the system dynamically calibrates a second-order symmetric tensor to control the tension diffusion rate of each coordinate axis.

[0059] The control tensor is defined as a two-dimensional heterogeneous space diagonal tensor, and an explicit analytic function is established between its internal elements and the binocular lateral canthus skeletal scale parameters.

[0060] This heterogeneous space mapping tensor The specific mathematical expansion is as follows: ; In the tensor expansion above, the main diagonal elements represent the tension in the local tangent plane along two mutually perpendicular orthogonal directions (horizontal width direction). with vertical depth direction The diffusion conductivity of ).

[0061] To match the lateral stretching effect of children's bones on soft tissues with the downward traction effect of gravity, these two diagonal elements are measured from the skeletal scale parameters of the outer canthi of both eyes. Apply nonlinear constraints: Horizontal tension conductivity The wider a child's face, the greater the space for the natural release of lateral tension, and the diffusion derivative within a unit space decreases inversely proportionally. Vertical tension conductivity The vertical overhang lipid damping, which is affected by the skeletal span, exhibits an exponential natural decay law. in All of these are system-preset physical constants determined by the baseline density of biological tissues.

[0062] By integrating the complex underlying physical parameters and functional relationships described above, the system formally constructs a core model that dominates the global derivation. This model belongs to the typical second-order elliptic spatial evolution equations in the classification of partial differential equations. Based on the steady-state diffusion principle and the static equilibrium theory of non-uniform thin films, a continuous mechanical equation is constructed to deduce the dynamic coupling relationship between tension scalar and geometric curvature in unknown space.

[0063] The full name of this core model is the partial differential equation of tension mapping between different regions with the same origin, and its specific mathematical form is as follows: ; in, : Represents the divergence operator, used to describe the hydrodynamic distribution properties of the tension vector field converging or diverging towards small voxels in three-dimensional space; : Represents the gradient operator, used to find the maximum spatial rate of change vector of the tension scalar field in each orthogonal direction in three-dimensional space; : Represents the local surface tension scalar function to be solved, whose value exhibits a continuous surface distribution as the three-dimensional spatial coordinate system within the shading and peeling area changes; : This refers to the two-dimensional heterogeneous space diagonal tensor that is dynamically calibrated and expanded based on the skeletal scale parameters of the outer canthus of both eyes, used in the equation to precisely control the anisotropic spatial diffusion physical rate when tension is transmitted in the soft tissue of the cheek. : Represents the tissue spatial distance attenuation factor, characterizing the loss of tension transmission kinetic energy in the non-rigid soft tissue network of the face due to the viscosity damping effect of collagen fibers; : Represents the hydrostatic pressure equivalent constant of the buccal fat pad in children, reflecting the volumetric physical pressure exerted by the internal soft tissue on the outer epidermis; : Represents the local average curvature at any infinitesimal element in the target space to be derived.

[0064] In the partial differential equation, the position vector of the three-dimensional spatial coordinate point is used as the independent variable; the local surface tension scalar and the spatial geometric curvature scalar to be determined are used as mutually coupled dependent variables. In order to start the numerical calculation, the initial boundary conditions of the equation adopt the first type of boundary conditions, that is, the known curvature scalars and tension directions of all topological homogeneous emission anchor points extracted in step two are directly and equivalently assigned to the integral starting boundary profile of the equation.

[0065] To ensure that the higher-order partial differential equation has a mathematically unique and physically consistent solution that fully conforms to biological characteristics in the subsequent numerical integration process, the system embeds a physical geometric energy conservation penalty constraint term into the solver algorithm.

[0066] This constraint requires: In a completely resting state without external muscle contraction (i.e., without the pulling of facial expressions such as smiling or crying), the sum of the elastic potential energy of all tiny voxel units within the deduced occlusion-stripping zone system must tend towards a local minimum in the global space. This, from the first principles of physics, dictates that the deduced facial curvature of a child must be naturally relaxed, conforming to gravity and the logic of skeletal attachment, excluding any geometric singularities that violate the laws of biological tissue growth, such as suspension, self-folding, or abrupt spikes.

[0067] Step 4: Elastic baseline integral reconstruction in the occluded area After constructing the partial differential equation for the tension mapping of different regions with the same origin, this step transforms the highly abstract mathematical and physical equation into a concrete and visible three-dimensional spatial geometric coordinate sequence and dense normal vector field in computer memory.

[0068] That is, it gradually evolves and grows from the boundary of the same source anchor point to the unknown space inside, and finally reconstructs the static basic surface of the cheek area covered by the fabric in the point cloud world, which is the key geometric reference base used for subsequent physical stress verification of the smiling face state.

[0069] In essence, the entire reconstruction process involves solving the second-order elliptic partial differential equation established in step three with high-precision discrete numerical integration within a specific irregular spatial region.

[0070] Since the three-dimensional space of the occlusion stripping area is initially a void voxel space that completely lacks effective absolute depth coordinates, the system first needs to pre-deploy an initial virtual simulation mesh framework in this unknown space using an algorithm.

[0071] The system uses all topologically homogeneous emission anchor points as the starting endpoints for computation. Along the pre-calculated curvature gradient vectors and tangential tension directions at these anchor points, multiple virtual three-dimensional spatial integral physical streamlines extend into the depth of the occlusion stripping region. Considering the significant nonlinear easing phenomenon in the transition phase of facial curvature changes from below the cheekbone to the mandibular ramus, to balance computational accuracy with the limited computing power bottleneck of edge devices (such as embedded microcontrollers or neural processing units), the system employs a variable-step-size fourth-order Runge-Kutta method with an automatic error control mechanism to perform layer-by-layer spatial iterative derivation of ordinary differential equations along these virtual integral streamlines.

[0072] In each Runge-Kutta spatial step iteration, the system, based on the three-dimensional spatial coordinates of the current streamline location and the curvature state of the previous adjacent node, substitutes all relevant parameters into the heterogeneous homogeneous tension mapping partial differential equation to solve in real time for the geometric normal deflection space angle, the predicted value of local Gaussian curvature, and the predicted value of average curvature at the current small step distance. As the depth of integral derivation increases, the aforementioned heterogeneous spatial mapping tensor and its associated spatial distance damping attenuation factor begin to play a dominant role.

[0073] This physically simulates the natural shock absorption and smoothing effect of the abundant fat pads in the lower part of a child's cheeks, so that the curvature changes derived from the streamline no longer fluctuate drastically, but gradually become smooth and rounded, thus closely matching the real chubby geometric shape of a child's jawline.

[0074] Meanwhile, to prevent numerous integral streamlines from spatially diverging (leading to mesh tearing) or colliding with each other during the inward extrapolation process (physically implying that the soft tissue has undergone illogical self-intersection and penetrating rupture), an adaptive node relaxation mechanism based on the coupling of gravitational and repulsive potential fields is introduced. A virtual spring repulsive force model obeying Hooke's law is established between adjacent integral streamline motion nodes.

[0075] When any two streamlines get too close during the simulation, even below the physical limit of the minimum thickness of biological tissue, the repulsive potential energy between the two nodes increases sharply, forcibly generating a lateral thrust to adjust the yaw angle of the next integral step. Conversely, when the streamlines are too far apart, posing a risk of mesh gaps, the gravitational potential energy exerts a pulling effect, forcibly bringing the streamlines together, thus always maintaining the topological homeomorphism and compactness of the simulation mesh.

[0076] Through thousands of iterative integrations from top to bottom and from the edges towards the center, the system successfully generated a high-density three-dimensional lattice field containing extremely rich physical property parameters within a three-dimensional space where optical data was severely lacking due to occlusion by fabrics such as scarves. Each discrete node in this lattice field possesses a predicted three-dimensional spatial normal vector and a hypercurvature scalar value obtained through complex mechanical deductions, which together constitute a high-precision global virtual normal vector field.

[0077] Spatial gradient information alone (normal vector field and curvature scalar field) cannot be directly used for comparing small displacements in the final absolute coordinate system. The system must inversely reconstruct this pure gradient information into three-dimensional spatial coordinates with absolute Cartesian coordinates. The system aims to reconstruct continuous, realistic surfaces. Therefore, it employs a computationally modified 3D Poisson surface reconstruction algorithm.

[0078] The core mathematical philosophy of Poisson reconstruction is to transform the problem of extracting surface meshes into solving a scalar field of characteristic functions in a three-dimensional continuous space. The system treats the global virtual normal vector field obtained from the previous integral derivation as the geometric gradient of an unknown spatial scalar potential field. According to the fundamental theorem of vector calculus, if this normal vector field is indeed derived from a physically existing biological surface, then the divergence of this vector field must be equivalent to the Laplace operator of the potential function of that surface space.

[0079] Based on this mathematical principle, the system constructs a three-dimensional Poisson core partial differential equation for the occlusion stripping region. Using the integral normal vector components derived from all reconstruction nodes within this region as known inputs, a divergence conservation balance mechanism is established between the continuous scalar potential field and the normal vector field. The complete expansion of the three-dimensional Poisson reconstruction equation is as follows: ; in, : Represents the three orthogonal physical position coordinate variables of any discrete voxel within the target occlusion stripping area in the three-dimensional Cartesian coordinate system; : Represents the scalar potential function (i.e., spatial characteristic function) inside the entire three-dimensional space to be solved. The positive and negative polarities of its function range are used to distinguish whether the spatial coordinate point is located inside biological soft tissue, in external free space, or exactly on the skin surface interface. : represent scalar potential functions respectively exist The second-order continuous partial derivatives along the three physical spatial axes, when superimposed and summed in space, constitute the Laplace operator. ; : These represent the global virtual normal vector fields obtained through front-end integral derivation. Known scalar components on three orthogonal coordinate axes; : These represent the first-order partial derivatives of the scalar components of the virtual normal vector on the corresponding coordinate axes. The sum of these three values ​​is the normal vector field. The divergence field.

[0080] When solving the Poisson equation, the system incorporates a smooth energy penalty constraint at the physical boundary between the exposed and shading stripping regions to ensure that the calculated potential function remains zero-order continuous and first-order differentiable when crossing the boundary line.

[0081] The partial differential equation is subjected to large-scale matrix operations on a discrete three-dimensional octree voxel grid using Gauss-Seidel iteration or preprocessing conjugate gradient method, and finally a high-precision continuous scalar potential field covering the entire target space is obtained.

[0082] In the resulting scalar potential field, each voxel in the spatial matrix is ​​assigned a specific real value. A pre-defined positive physical value represents that the point floats in the air medium outside the biological epidermis, while a negative value represents that the point is deeply embedded in the cheek fat pad or muscle soft tissue. The system then employs a moving cube algorithm based on voxel interpolation to track, extract, and connect all isosurface polygon meshes with values ​​equal to zero in the scalar potential field array at high resolution.

[0083] The zero-equivalence surface extracted by the algorithm is a high-fidelity reverse reconstruction performed in a computer system after extremely complex heterogeneous mechanical mapping, Runge-Kutta geometric integral derivation, and Poisson space divergence solution. The virtual physical base of the occlusion stripping area is the static elastic baseline of the child's face when it is relaxed and naturally stretched by gravity under the influence of gravity in a resting state without any facial expressions or movements.

[0084] The successful reconstruction of the static elastic baseline in the occlusion stripping area has decisive engineering anti-counterfeiting and identification significance. Through mathematical and mechanical deduction, it filters out optical shot noise and false depth faults introduced by environmental obstructions such as winter clothing collars and non-standard mask wearing from the source. This provides an absolutely pure initial comparison anchoring reference surface, free from external optical contamination, for capturing, extracting, and calculating the true nonlinear compression strain field of subcutaneous fat when a child smiles in the subsequent step five.

[0085] Step 5: Adaptive Modulus Calculation and Stress Evolution Smile Determination In step four, the system has overcome the challenge of obstructed optical vision and reconstructed the static elastic baseline of the occlusion stripping area with high fidelity. After obtaining the initial reference physical surface of the child's face in a neutral, expressionless resting state, this step accurately captures the dynamic 3D point cloud of the child's face at the moment of a smile in a continuous, high-frequency dynamic check-in video stream.

[0086] Using non-rigid solid mechanics theory and tensor calculus, the dynamic physical strain field and force tensor field are solved. By extracting the geometric distribution of this physical field in three-dimensional space and the mechanical wave propagation characteristics on the time axis, it is possible to accurately determine whether the facial expression is a genuine spontaneous smile, and then execute the final liveness check-in status verification.

[0087] The system continuously drives the front-end high-frequency optical acquisition hardware matrix to acquire transient 3D dynamic point cloud sequences of children at the moment of check-in (i.e., the brief spatiotemporal window during which a smiling expression may occur). Because active children inevitably undergo rapid head movements, lateral translations, and pitch and rotations during the check-in process, directly comparing point clouds from two frames would result in the massive coordinate displacements caused by these rigid body movements instantly obscuring the minute facial muscle deformation data. Therefore, a high-precision spatial registration and rigid body motion stripping algorithm must be executed.

[0088] The system extracts a set of highly rigid physiological and anatomical anchor points within the "homogeneous topological exposure area" defined in step one (e.g., the central region of the frontal bone, the junction of hard and bony structures at the root of the nose, and other rigid regions that hardly undergo relative physical displacement with any facial expression). Using the coordinates of the rigid anchor points in the currently captured transient dynamic point cloud as the reference source point set, and the three-dimensional physical coordinate system where the static elastic baseline of the occlusion stripping area established in step four is located as the target space, a six-degree-of-freedom homogeneous spatial transformation matrix characterizing the macroscopic rigid body motion of the head is solved using a weighted point-to-surface iterative nearest point spatial registration algorithm.

[0089] The registration process establishes a residual objective function and uses singular value decomposition to continuously minimize the projected geometric residual from the reference source point set to the normal direction of the target reference surface in multiple iterations.

[0090] The solved homogeneous spatial transformation matrix contains a three-dimensional orthogonal rotation tensor (representing Euler angle deflection) and a three-dimensional translation vector. Subsequently, the system uses this transformation matrix to perform an inverse spatial transformation multiplication operation on the global three-dimensional dynamic point cloud of the current transient frame, forcibly aligning the displaced dynamic point cloud with the static elastic baseline of the occlusion stripping area and locking it into the same absolute physical coordinate system.

[0091] Through this reverse transformation, the system successfully removed the spatial displacement artifacts caused by the external environment and body posture, retaining only the pure geometric deformation data of non-rigid soft tissue of the face within a unified coordinate system.

[0092] After spatial alignment is completed, an adaptive calculation mechanism for the local elastic modulus is initiated, taking into account the unique physiological development differences of each child. Traditional anti-spoofing methods for facial recognition usually pre-set a uniform fixed elastic constant, but this is very likely to lead to recognition failures such as "overweight children being misjudged as excessively deformed, and underweight children being missed as insufficiently deformed" when facing children of different body types and bone ages.

[0093] In this scheme, the system is based on the microscopic force balance theory of continuous media and establishes an elastic modulus inversion function based on physiological resting curvature.

[0094] Within the area of ​​the cheek where the static elastic baseline of the occlusion and dissection zone has been reconstructed, for any spatial coordinate micro-point on this baseline, the system extracts its inherent resting Gaussian curvature value and retrieves the binocular lateral canthus skeletal scale parameters extracted in step three. Using a pre-defined biomechanical empirical correction equation, the system combines the curvature scalar with the bone width characteristics to calculate the actual Young's modulus estimate at that local coordinate point.

[0095] The system divides the cheek analysis area into tens of thousands of tiny finite element voxels and assigns each voxel an adaptively calculated Young's modulus parameter, thereby constructing a three-dimensional non-uniform scalar field, namely the adaptive elastic modulus space matrix, that perfectly matches the child's current actual nutritional development status within the computer.

[0096] Differential calculations of the physical fields of fat accumulation and muscle compression are performed. In a unified three-dimensional Cartesian coordinate system, the spatially aligned transient dynamic point cloud is extracted, and the directed Euclidean physical distance from the discrete coordinates on each point to the static elastic baseline of the continuous occlusion and stripping area in the corresponding normal direction is calculated. This directed distance field characterizes the pure physical displacement of soft tissue caused by the contraction of the zygomaticus major muscle and the pushing and accumulation of the buccal fat pad, and is defined as a three-dimensional spatial displacement vector field (containing...). Displacement components in three orthogonal directions wait).

[0097] In order to transform the apparent three-dimensional spatial displacement vector field into a tensor matrix that can reflect the relative proportion of the actual deformation inside biological tissue, the Cauchy small strain geometric equation from the solid mechanics of continuum is introduced.

[0098] The partial derivative matrix of each component in the spatial displacement vector field with respect to the three-dimensional spatial coordinate axes is obtained, and the symmetric part of the partial derivative matrix is ​​extracted to generate a three-dimensional local strain tensor matrix that characterizes the local spatial deformation rate.

[0099] The specific expansion of Cauchy's geometric equation for small strain is as follows: ; in, : represents the th element in the derived three-dimensional local strain tensor matrix. Line number The dimensionless strain components of the column describe the relative tensile or shear deformation rates of the infinitesimal element in different dimensions. : Represents the spatial fundamental orthogonal coordinate axis variables (i.e., macroscopic physical location) in a three-dimensional Cartesian coordinate system; : Represents the absolute physical displacement component of the spatial displacement vector field calculated above in the corresponding coordinate axis direction; : These represent the first-order spatial partial derivatives of the physical displacement components with respect to the spatial fundamental coordinate axis variables, reflecting the gradient of displacement in space.

[0100] After obtaining the local three-dimensional local strain tensor matrix, in order to further quantify the internal biomechanical potential energy accumulated by these tiny deformations, the system combines the aforementioned adaptive elastic modulus space matrix with the fixed Poisson's ratio of biological soft tissue and substitutes them into the generalized Hooke's law formula (i.e., the derivation of Cauchy stress tensor) for isotropic linear elastic bodies.

[0101] By using the elastic resistance coefficient of local tissues, the dimensionless geometric strain is transformed into an internal stress state with real physical units. The core stress tensor calculation equation is as follows: ; in, : Represents the th element in the final obtained local three-dimensional stress tensor matrix. Line number The stress components of the column (its physical unit is Pascal, which truly reflects the physical stress compression or tension state inside the soft tissue). : Represents the estimated dynamic Young's modulus value corresponding to this local coordinate point in the adaptive elastic modulus space matrix (characterizing the ability of skin and fat at a specific location to resist external elastic deformation); : Represents the Poisson's ratio of human soft tissue (since human facial tissue is rich in water and lipids, its hydrodynamic properties are approximately incompressible, so the system sets it to a high constant value close to 0.49). : represents the Kronecker function, whose mathematical properties are: under the subscript Its value is 1 when Its value is 0 at that time; : represents the individual deformation components in the three-dimensional local strain tensor matrix obtained by the Cauchy small strain geometric equations above; : Represents the sum of the main diagonal elements of the three-dimensional local strain tensor matrix (i.e., the trace of the tensor), and its physical meaning is the total volumetric strain rate of the local infinitesimal volume during the expansion or contraction process.

[0102] Through the aforementioned continuous chain of first-principles partial differential equations, the system substantially transforms the superficial, easily forged image pixel displacements into a rigorous three-dimensional spatial stress tensor field. This tensor field depicts the physical gradient of the internal stress distribution of facial fat and subcutaneous superficial fascia when stretched by a smile.

[0103] Based on this solid physical foundation, the system officially enters the stage of extracting the spatiotemporal features of smiles and determining high-strength anti-counterfeiting measures. From a biological perspective, children's genuine spontaneous smiles (i.e., Duchenne smiles driven by emotions) and artificially forged smiles or deliberate muscle twitches (such as instantaneous cheek puffing and blowing air) exhibit significant heterogeneity in the spatiotemporal evolution trajectory of the stress field in a physical dimension.

[0104] A genuine smile stress field does not suddenly surge and erupt across the entire face. Instead, it is a physical mechanical waveform that originates at the junction of the outer periphery of the orbicularis oris muscle and the corner of the mouth muscle, and then spreads outward toward the outer side of the zygomatic arch and below the earlobe in a specific fan shape at a certain mechanical speed.

[0105] The system extracts stress tensor field data from dozens of consecutive frames of dynamic point clouds along the time axis, calculates the first derivative of the stress scalar with time at each three-dimensional spatial micro-element point, and generates a stress evolution time gradient field. It dynamically locates the core peak connected region where the stress scalar reaches a local maximum in the three-dimensional spatial coordinate system. By tracking the spatial coordinate trajectory of this main peak region at different millisecond-level timestamps, the system calculates the spatial propagation direction vector and propagation phase velocity of the stress wave.

[0106] The system internally executes comprehensive judgment rules based on multi-dimensional physical parameters: The first-dimensional logic judgment involves the system checking whether the absolute amplitude of the maximum principal stress extracted locally exceeds the baseline resting physical threshold set based on the child's adaptive modulus matrix. If it does not exceed the threshold, it indicates that the facial twitching is merely a minor neurological movement or a slight twitching during speech. The system determines that the energy generated is insufficient to constitute a valid "check-in" expression and ignores it.

[0107] The second dimension of logical judgment involves the system verifying the three-dimensional spatial propagation trajectory vector of the stress wave peak. If the trajectory vector follows a specific path of biological anatomical muscle contraction extending from the middle of the mandibular ramus towards the outer corner of the eye and the zygomatic arch, it satisfies the spatial mechanical wave transmission constraint of a real facial expression. If the captured image is an instantaneous surge in stress across the entire face (such as a child taking a deep breath, puffing out their cheeks, or sticking out their tongue in front of a camera), and the stress field trajectory exhibits characteristics of disorder, multiple concurrent points, or zero propagation distance, the system will determine it as an invalid action and intercept it.

[0108] The third-dimensional logical analysis executes high-strength liveness detection based on the physical properties of the material medium. Because counterfeiters commonly use materials such as silicone human skin headgear, 3D-printed flexible masks, or high-resolution distorted photographs, the elastic modulus and fluid Poisson's ratio of these materials differ significantly from those of real biological tissue. The system extracts the Cauchy stress tensor to calculate the total volumetric strain rate during the intermediate process. .

[0109] Based on the near-incompressible physical property of real human soft tissue due to its high water content, when a real smiley face deforms, the soft tissue mainly undergoes spatial slippage and shape distortion, with its local volumetric strain rate being extremely small (approaching zero); if the system captures significant volume expansion in a local area (i.e., If the value is significantly non-zero (e.g., a rubber mask with obvious porosity and elasticity will substantially expand in volume when stretched by an external force), the system will immediately determine that the material of the tested face violates the basic physical principles of biomaterials and forcibly block the corresponding check-in request. This anti-counterfeiting mechanism based on pure physical materials science significantly improves the interception accuracy and anti-spoofing capability.

[0110] When the physical parameters of multiple dimensions, such as the absolute amplitude of stress, the spatiotemporal transmission vector of stress wave, and the volumetric strain rate of biomaterials, all fall completely within the strictly preset real physiological verification range, the system clearly determines that the currently collected action is not only a sign of living life, but also belongs to a natural smiling emotional state.

[0111] The system extracts the precise millisecond-level timestamp of the current event, combines it with the physical network card MAC address of the optical acquisition device, and the child's unique Hamiltonian signature code bound to the system, and uses an asymmetric elliptic curve cryptography (ECC) algorithm to generate an unalterable encrypted digital attendance voucher. The system securely sends this encrypted voucher to a cloud database for archiving via the underlying TCP / IP communication protocol and simultaneously pushes it to the parental control application. Example

[0112] A smile recognition check-in system based on children's faces includes: Deep point cloud acquisition and occlusion determination module: acquires the initial 3D spatial point cloud, performs depth gradient absolute value and normal divergence calculation, and divides the facial point cloud into the homogeneous topological exposure area and the occlusion stripping area. The module for extracting the curvature gradient of the same origin in the exposed region: constructs a three-dimensional surface analytical equation in the exposed region of the same origin topology, calculates the Gaussian curvature scalar field and the mean curvature scalar field, extracts the curvature gradient vector field through global spatial differentiation operation, and determines the topological same origin emission anchor point with the mean curvature basic value and the tangent plane tension vector. The module for constructing the heterogeneous tension mapping equation extracts the physical Euclidean straight-line distance between the outer canthi of both eyes to obtain the skeletal scale parameters of the outer canthi of both eyes. Combined with the basic value of the average curvature, a heterogeneous tension mapping partial differential equation containing the skeletal scale parameters of the outer canthi of both eyes is constructed. The occlusion zone elastic baseline integral reconstruction module: In the occlusion stripping zone, starting from the topological homogeneous emission anchor point, the module uses the tension vector direction of the tangential plane and the curvature gradient vector direction to derive the global virtual normal vector field using the tension mapping partial differential equation of different regions homogeneous tension. The module solves the three-dimensional Poisson core partial differential reconstruction equation to extract the zero isovalue surface and reconstruct the static elastic baseline of the occlusion stripping zone. The adaptive modulus calculation and stress evolution smiley face determination module acquires transient 3D dynamic point clouds and aligns them with the static elastic baseline of the occlusion stripping area. It combines the resting Gaussian curvature on the baseline with the skeletal scale parameters of the outer canthi of both eyes to calculate the adaptive elastic modulus space matrix. It then obtains the local 3D stress tensor matrix through the Cauchy micro-strain geometric equation and the generalized Hooke's law. Finally, it extracts the stress evolution time gradient field to perform natural smiley face anti-counterfeiting determination and generates encrypted digital attendance vouchers. Example

[0113] Application Scenario Example: Winter Occlusion Smile Recognition Check-in Based on Tension Partial Differential Equation Setting: The attendance tracking device is deployed at the outdoor turnstile of a kindergarten in northern China. A 5-year-old child is walking towards the turnstile. The temperature is extremely low. The child is wearing a thick woolen scarf that covers his chin, mouth, and most of his cheeks, leaving only his eyes, forehead, and part of the upper edge of his cheekbones exposed.

[0114] Step 1: Depth Point Cloud Acquisition and Occlusion Determination When a child enters the gate's field of view, the optical acquisition matrix built into the card reader terminal is activated. A vertical-cavity surface-emitting laser array radiates a high-frequency amplitude-modulated sinusoidal continuous wave toward the child's face. The echo is captured by a near-infrared single-photon avalanche diode phase-sensitive detector, and the system's underlying field-programmable gate array extracts the phase delay radian value of the received light wave. The absolute physical distance is calculated by substituting it into the continuous wave phase mapping equation of light flight time. This generates an initial three-dimensional point cloud: , In the above formula, The speed of light is constant. The amplitude modulation center frequency of the continuous wave is used. Subsequently, the system calculates the absolute value of the depth gradient and the normal divergence. Due to the microscopic overhangs and wrinkles on the surface of the wool scarf, its normal divergence increases dramatically. The system uses a region growing algorithm to define the exposed forehead and eye area of ​​the child as the homologous topological exposure region, and marks the lower half of the face covered by the heavy scarf as the occlusion stripping region.

[0115] Step 2: Extraction of homologous curvature gradient in the exposed region Within the topologically exposed region, the system utilizes a thin-plate spline interpolation algorithm to construct analytical equations for a continuous three-dimensional surface, and then constructs the first and second fundamental equations on a two-dimensional parametric derivation mesh. ; The system uses the obtained metric coefficients. The Gaussian curvature scalar field is then calculated using the differential curvature algorithm. With mean curvature scalar field : ; ; The system extracts the coordinates of the main gradient convergence streamlines pointing deep into the occlusion at the junction of the outer periphery of the orbicularis oculi muscle and the scarf, defines them as topological homogeneous emission anchor points, and records their basic curvature and tangential tension vector.

[0116] Step 3: Construction of the Heterogeneous-Origin Tension Mapping Equation The system measures the Euclidean linear distance between the left and right outer canthi of the aforementioned child in the 3D point cloud of the exposed area, obtaining the skeletal scale parameters of both eyes' outer canthi. Combining the lateral release space and suspension damping characteristics of the biological skeleton, the system establishes a heterogeneous spatial mapping tensor. : ; Subsequently, the system will use the aforementioned tensor and the local average curvature of the topological homogeneous emission anchor points. Tissue spatial distance attenuation factor and hydrostatic pressure equivalent constant By combining these, a partial differential equation for the heterogeneous, homogeneous tension mapping, which dominates the mechanical derivation, is constructed: ; Step 4: Elastic baseline integral reconstruction in the occluded area Starting from the topologically homogeneous emission anchor point at the edge of the scarf, the system employs the fourth-order Runge-Kutta method, along the tangential tension vector direction and the curvature gradient vector direction, and uses the aforementioned tension mapping partial differential equation to extrapolate into the depth of occlusion, generating a global virtual normal vector field (containing components). To transform the vector field into a continuous surface in an absolute physical coordinate system, the system solves the three-dimensional Poisson core partial differential reconstruction equation on a three-dimensional octree voxel mesh, and obtains the scalar potential function. : ; By using the moving cube algorithm to extract the isosurface where the scalar potential function is equal to zero, the system successfully reconstructed the three-dimensional surface of the cheek hidden under the scarf in a resting state inside the computer, namely the static elastic baseline of the occlusion stripping area.

[0117] Step 5: Adaptive Modulus Calculation and Stress Evolution Smile Determination When the aforementioned child smiles, the system acquires a transient 3D dynamic point cloud, which, after rigid body stripping, is aligned with the static elastic baseline of the occluded stripping area. The system then calculates a dynamic Young's modulus estimate that matches the child's bone age. And calculate the displacement vector field from the spatial discrete coordinates to the baseline (components are ). ).

[0118] The system utilizes Cauchy's geometric equations for small strain to transform apparent displacement into dimensionless strain components. : ; Subsequently, Poisson's ratio of biological human soft tissue was introduced. Substituting the generalized Hooke's law formula (stress tensor calculation equation) for isotropic linear elastic bodies, the true internal stress components of the local soft tissue are obtained. : ; The system tracks the evolution trajectory of the principal stress peaks to verify whether it conforms to the anatomical path; simultaneously, it extracts the sum of the main diagonal elements of the strain tensor. (Total volumetric strain rate). Because the high water content of soft tissues in the human body results in near-incompressibility, Approaching zero.

[0119] After all physical assessments are passed, the system confirms that the check-in action is a genuine and valid natural smiley face, and generates an encrypted digital check-in voucher.

[0120] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for checking in using smile recognition based on children's faces, characterized in that, include: The initial 3D spatial point cloud is obtained, and the absolute value of the depth gradient and the normal divergence are calculated. The facial point cloud is divided into the homogeneous topological exposure area and the occlusion stripping area. In the topologically exposed region of the same origin, construct the three-dimensional surface analytical equation, calculate the Gaussian curvature scalar field and the mean curvature scalar field, extract the curvature gradient vector field through global spatial differentiation operation, and determine the topological same origin emission anchor point with the mean curvature fundamental value and the tangent plane tension vector. The physical Euclidean linear distance between the outer canthi of both eyes is extracted to obtain the skeletal scale parameters of the outer canthi of both eyes. Combined with the basic value of the average curvature, a partial differential equation for heterogeneous tension mapping containing the skeletal scale parameters of the outer canthi of both eyes is constructed. Within the shading stripping zone, starting from the topological homogeneous emission anchor point, the virtual normal vector field of the whole domain is generated by using the partial differential equation of tension mapping of different regions homogeneous tensions along the tangential plane tension vector direction and the curvature gradient vector direction. The three-dimensional Poisson core partial differential reconstruction equation is solved to extract the zero isovalue surface and reconstruct the static elastic baseline of the shading stripping zone. The transient 3D dynamic point cloud is acquired and aligned with the static elastic baseline of the occlusion stripping area. The resting Gaussian curvature on the baseline and the skeletal scale parameter of the outer canthus of both eyes are combined to calculate the adaptive elastic modulus space matrix. The local 3D stress tensor matrix is ​​obtained, the stress evolution time gradient field is extracted, the natural smile anti-counterfeiting judgment is performed, and an encrypted digital attendance certificate is generated.

2. The method for checking in based on a child's face using smile recognition according to claim 1, characterized in that, The operations for obtaining the initial 3D point cloud include: Drive a heterogeneously integrated vertical cavity surface-emitting laser array to radiate a sinusoidal continuous wave with high-frequency amplitude modulation onto the child's face within the field of view. Using a near-infrared single-photon avalanche diode phase-sensitive detector, the received photon energy is sampled at high speed at multiple phase nodes, and the absolute physical space straight-line distance is calculated based on the optical time-of-flight continuous wave phase mapping equation to generate an initial point cloud. In three-dimensional space, a spherical neighborhood is constructed with discrete data points as the center, and the three-dimensional geometric covariance matrix of the point cloud spatial coordinates within the spherical neighborhood is calculated. Eigenvalue decomposition is performed on the three-dimensional geometric covariance matrix. If the smallest eigenvalue among the three eigenvalues ​​is significantly larger than the other two eigenvalues, the discrete data points are determined to belong to environmental flypoint noise and are removed to obtain the basic facial depth point cloud set.

3. The smile recognition check-in method based on children's faces according to claim 1, characterized in that, The absolute value of the depth gradient and the normal divergence are calculated, and the facial point cloud is divided into a homogeneous topological exposure region and an occlusion stripping region, including: Calculate the absolute values ​​of the depth gradient along the horizontal and vertical spatial axes, and define the boundary of the region where the absolute value of the depth gradient exceeds the limit of the natural physiological bulge as the edge of the physical fault. The spatial divergence of the three-dimensional normal vector array across the edge of a physical fault is used to quantify the normal random oscillations caused by the micro-level undulations and wrinkles of the fabric. Connected regions are generated using a region growing algorithm. Smooth regions with spatial divergence below the physical blocking threshold of normal divergence and without deep faults are designated as homogeneous topological exposure regions. Connected regions with deep faults and a surge in spatial divergence are marked as occlusion stripping regions.

4. The smile recognition check-in method based on children's faces according to claim 1, characterized in that, In the topologically exposed region of the same origin, a three-dimensional surface analytical equation is constructed, and the Gaussian curvature scalar field and the mean curvature scalar field are calculated. The curvature gradient vector field is extracted through global spatial differentiation operations. Topologically related emission anchor points with the fundamental value of the mean curvature and the tangential plane tension vector are determined, specifically including: Using a thin plate spline interpolation algorithm, the natural bending state of a metal thin plate with ideal isotropic elasticity under the forced constraint of normal stress at discrete control points is simulated. The analytical equation of a continuous three-dimensional surface is constructed by minimizing the global bending strain energy integral. The Gaussian curvature scalar field and the mean curvature scalar field are obtained by using the differential curvature algorithm, and the curvature gradient vector field is solved by combining the three-dimensional Hamiltonian operator. Spatial orientation clustering analysis is performed on the gradient vectors in the curvature gradient vector field to extract the geometric coordinate points corresponding to the main gradient convergence streamlines pointing towards the shading stripping region. These points are defined as topological homogeneous emission anchor points, and the three-dimensional spatial orientation angles of the Gaussian curvature, mean curvature, and tangential tension vector of the topological homogeneous emission anchor points are recorded.

5. The method for checking in based on a child's face using smile recognition according to claim 1, characterized in that, Before constructing the partial differential equations for heterogeneous homogeneous tension mapping, it is necessary to establish a heterogeneous spatial mapping tensor constrained by the skeletal scale parameters of the outer canthi of both eyes. The expression for the heterogeneous spatial mapping tensor is as follows: ;in, Represents a heterogeneous space mapping tensor; Indicates the horizontal tension conductivity; Indicates vertical tension conductivity; The specific expansion of the partial differential equation for the tension mapping between different regions with the same origin is as follows: ; in, Represents the divergence operator; Represents the gradient operator; Represents the scalar function of the local surface tension to be solved; Represents a heterogeneous space mapping tensor; Indicates the tissue spatial distance attenuation factor; This represents the equivalent constant of hydrostatic pressure; Indicates the local mean curvature; When solving the partial differential equation of tension mapping between different regions, the known curvature scalar of the topological homogeneous emission anchor point is forcibly and equivalently assigned to the integral starting boundary profile of the equation, and a physical geometric energy conservation penalty constraint term is embedded to limit the sum of the elastic potential energy integrals of the derived internal voxel units to tend to a local minimum in the global space.

6. The method for checking in based on a child's face using smile recognition according to claim 1, characterized in that, Within the occlusion stripping region, a global virtual normal vector field is generated by deriving the partial differential equation of tension mapping from different regions along the tangential plane tension vector direction and the curvature gradient vector direction, including: The variable step size fourth-order Runge-Kutta method is used to iterate along the virtual three-dimensional space integral physical streamline to the unknown space, and to solve in real time the geometric normal vector deflection space angle, the local Gaussian curvature prediction value and the average curvature prediction value under the current small step distance. A virtual spring repulsive force model is established between adjacent integral physical streamline motion nodes, and adaptive node relaxation is performed by coupling the attractive and repulsive potential fields: When the streamline distance is lower than the physical limit of the minimum thickness of the preset biological tissue, the repulsive potential energy generates lateral thrust to adjust the yaw angle of the next integral step; when the streamline spacing is too far and there is a risk of mesh gaps, the gravitational potential energy plays a pulling and contracting role, and finally generates a global virtual normal vector field.

7. The smile recognition check-in method based on children's faces according to claim 1, characterized in that, Solving the three-dimensional Poisson core partial differential equation to extract the zero-equivalence surface and reconstruct the static elastic baseline of the occlusion stripping region includes: A divergence conservation balance mechanism is established between the continuous scalar potential field and the global virtual normal vector field. Smooth energy penalty constraints are added at the boundary between the exposed area and the occlusion stripping area to ensure that the potential function remains zero-order continuous and first-order differentiable when crossing the physical boundary line. Matrix operations are performed on the discrete three-dimensional octree voxel grid to solve for the high-precision continuous scalar potential field. Using a voxel interpolation-based moving cube algorithm, all isosurface polygon meshes with values ​​equal to zero are tracked, extracted, and connected in high resolution in a continuous scalar potential field array, and used as the static elastic baseline of the occlusion stripping region.

8. The smile recognition check-in method based on children's faces according to claim 1, characterized in that, Obtain the transient 3D dynamic point cloud and align it with the static elastic baseline of the occlusion stripping region. Calculate the adaptive elastic modulus space matrix using the resting Gaussian curvature on the baseline, including: High-rigidity physiological and anatomical anchor points are extracted, and the homogeneous spatial transformation matrix is ​​solved by the weighted point-to-surface iterative nearest point algorithm. The macroscopic rigid body motion of the head is stripped away by the inverse spatial transformation multiplication, so that the transient three-dimensional dynamic point cloud and the static elastic baseline of the occluded stripping area are locked to the same absolute physical coordinate system. The resting Gaussian curvature value was extracted from the static elastic baseline of the reconstructed occlusion stripping area. The value was then combined with the skeletal scale parameters of the outer canthus of both eyes using a pre-defined biomechanical empirical correction equation to calculate the local Young's modulus estimate and construct an adaptive elastic modulus space matrix. The directed Euclidean physical distance from the discrete spatial coordinates to the static elastic baseline of the shading stripping area in the corresponding normal direction is calculated point by point to generate a three-dimensional spatial displacement vector field.

9. The smile recognition check-in method based on children's faces according to claim 1, characterized in that, Extracting the stress evolution time gradient field to perform natural smiley face anti-counterfeiting judgment includes the following dimensions of analysis: Extract the absolute amplitude of the local maximum principal stress and verify whether the absolute amplitude exceeds the preset reference resting physical threshold. The stress scalar's first derivative with time is calculated to generate the stress evolution time gradient field. The peak connectivity region is dynamically located and the phase velocity is calculated to verify whether the spatial propagation direction vector follows the biological anatomical muscle contraction path extending from the middle of the mandibular ramus to the outer canthus and zygomatic arch. The sum of the main diagonal elements generated during the calculation of the three-dimensional local strain tensor matrix is ​​extracted as the total volumetric strain rate of the local micro-element; if obvious volume expansion is detected in a local area, it is determined that the material of the tested surface violates the basic physical laws of biomaterials, and the check-in request is forcibly blocked.

10. A smile recognition check-in system based on children's faces, and a smile recognition check-in method based on children's faces according to any one of claims 1-9, characterized in that, include: Deep point cloud acquisition and occlusion determination module: acquires the initial 3D spatial point cloud, performs depth gradient absolute value and normal divergence calculation, and divides the facial point cloud into the homogeneous topological exposure area and the occlusion stripping area. The module for extracting the curvature gradient of the same origin in the exposed region: constructs a three-dimensional surface analytical equation in the exposed region of the same origin topology, calculates the Gaussian curvature scalar field and the mean curvature scalar field, extracts the curvature gradient vector field through global spatial differentiation operation, and determines the topological same origin emission anchor point with the mean curvature basic value and the tangent plane tension vector. The module for constructing the heterogeneous tension mapping equation extracts the physical Euclidean straight-line distance between the outer canthi of both eyes to obtain the skeletal scale parameters of the outer canthi of both eyes. Combined with the basic value of the average curvature, a heterogeneous tension mapping partial differential equation containing the skeletal scale parameters of the outer canthi of both eyes is constructed. The occlusion zone elastic baseline integral reconstruction module: In the occlusion stripping zone, starting from the topological homogeneous emission anchor point, the module uses the tension vector direction of the tangential plane and the curvature gradient vector direction to derive the global virtual normal vector field using the tension mapping partial differential equation of different regions homogeneous tension. The module solves the three-dimensional Poisson core partial differential reconstruction equation to extract the zero isovalue surface and reconstruct the static elastic baseline of the occlusion stripping zone. The adaptive modulus calculation and stress evolution smiley face determination module acquires transient 3D dynamic point clouds and aligns them with the static elastic baseline of the occlusion stripping area. It combines the resting Gaussian curvature on the baseline with the skeletal scale parameters of the outer canthi of both eyes to calculate the adaptive elastic modulus space matrix. It then obtains the local 3D stress tensor matrix through the Cauchy micro-strain geometric equation and the generalized Hooke's law. Finally, it extracts the stress evolution time gradient field to perform natural smiley face anti-counterfeiting determination and generates encrypted digital attendance vouchers.

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