Medical beauty injection and dose combination optimization method and system fusing aesthetic golden ratio

Abstract

The application discloses a medical beauty injection and dose combined optimization method and system fusing aesthetic golden ratio, and relates to the technical field of medical beauty digitization. Three-dimensional point cloud data of a face of a beauty seeker is acquired, a high-precision three-dimensional face model is constructed, aesthetic key points are recognized and actual aesthetic proportion parameter sets are calculated; the actual parameters are compared with a golden ratio aesthetic database, a face aesthetic difference heat map is generated, and the area to be optimized and the deviation degree are indicated; based on the aesthetic difference heat map and a face dissection safety model, an optimization algorithm is used to construct a solution framework, an initial injection scheme is generated by taking minimization of aesthetic deviation and maximization of contour harmony as targets and combining with dangerous area constraint conditions, shape changes after dynamic simulation injection are observed, injection paths and doses are iteratively corrected according to aesthetic correction points, and a target optimization scheme is formed. The application deeply fuses the quantification of aesthetic golden ratio, dissection safety constraints and intelligent optimization algorithms, and realizes the precision, safety and individualization of injection planning.

Description

Technical Field

[0001] This invention relates to the field of digital medical aesthetics technology, specifically to a method and system for optimizing medical aesthetic injection and dosage in accordance with the golden ratio of aesthetics. Background Technology

[0002] Facial injectable aesthetic treatments have become a mainstream clinical approach for improving facial contours and reshaping a youthful appearance. The technology is evolving from subjective, doctor-experience-driven procedures to a more intelligent approach that emphasizes three-dimensional quantification, aesthetic precision, and safety control. The golden ratio, a universally recognized aesthetic principle, has long been considered the core mathematical basis for facial harmony. The key to overcoming current limitations in aesthetic injection techniques lies in deeply integrating classic aesthetic proportions with three-dimensional digital technology and intelligent algorithms to achieve precise optimization of injection paths, layers, and dosages.

[0003] In the field of basic research on the quantification of facial aesthetics and the application of the golden ratio, the international academic community has formed a series of empirical results based on three-dimensional measurement. The study PMC8744514 (The role of the golden proportion in the evaluation of facial esthetics) explicitly used three-dimensional stereophotometry to statistically analyze 10 linear proportions of the faces of 60 subjects, confirming a correlation between 3D facial distance proportions and attractiveness. Furthermore, some proportions (such as eye-lip distance / jaw height and lower midface vertical proportions) tended to align with the golden ratio values, providing three-dimensional measurement evidence for the golden ratio to guide facial aesthetic assessment. The study PMC7929632 (The Divine Proportion: Origins and Usage in Plastic Surgery) systematically reviewed the clinical application of the golden ratio in plastic surgery, proposing a quantitative positioning theory for facial "Phi points." It explicitly applied the golden ratio to the design of injection filler targets in areas such as the cheeks, lips, and nose, establishing a preliminary correlation model between aesthetic proportions and injection points. PMC6374711 (An approach to structural facial rejuvenation with fillers in women) further integrates the golden ratio into the assessment of facial aging structures. Using vertical trisection, horizontal five-eye ratio, and a perioral golden ratio of 1:1.6 as quantitative benchmarks, it constructs a proportional reference system for rejuvenation fillers, providing clinical reference for proportional repair of injectable fillers. However, the above studies remain at the level of aesthetic proportion verification and single-point positioning, lacking a closed-loop technical system and algorithms that integrate with facial anatomical safety constraints and injection dosage / path optimization, making it difficult to directly translate into intelligent injection protocols that can be clinically implemented.

[0004] In the field of intelligent and 3D visualization technology for cosmetic injections, Chinese patent CN117815530A (a microneedle depth automatic adjustment system based on facial scanning technology) achieves automatic control of injection depth through 3D scanning and visual positioning, improving the precision of injection operations. However, it only focuses on depth control and does not involve aesthetic proportion assessment or dosage optimization. CN113521445A (a cosmetic injection method using 12-axis point-dimensional shaping) achieves layered injection through facial partitioning and 12-axis positioning, improving shaping stability. However, aesthetic assessment relies on human experience and lacks the support of golden ratio quantification and intelligent algorithms. CN119964823A (a plastic surgery effect simulation display system based on 3D simulation technology) achieves 3D facial modeling and static preview of postoperative effects, but it does not establish a mechanism for quantifying aesthetic differences, nor can it achieve joint optimization and dynamic iterative correction of injection path and dosage.

[0005] Overall, existing technologies suffer from core defects such as a disconnect between aesthetics and security, a singular optimization objective, low system integration, and a lack of closed-loop iteration. Summary of the Invention

[0006] Based on the aforementioned technical problems, this application discloses a method and system for optimizing medical aesthetic injection and dosage in accordance with the golden ratio of aesthetics; the method for optimizing medical aesthetic injection and dosage in accordance with the golden ratio of aesthetics includes:

[0007] Acquire 3D point cloud data of the face of the person seeking beauty and construct a high-precision 3D facial model; automatically identify and mark multiple aesthetic key points on the 3D facial model;

[0008] Based on the aforementioned key aesthetic points, the actual aesthetic proportion parameter set of the face of the person seeking beauty is calculated. The parameter set includes at least the nasolabial angle, nasofrontal angle, mentolabial sulcus depth, upper and lower lip thickness ratio, and facial width-to-height ratio.

[0009] The actual aesthetic proportion parameter set is compared and analyzed with the preset golden ratio aesthetic database to generate a facial aesthetic difference heat map. The heat map uses color gradients to indicate the areas to be optimized that deviate significantly from the golden ratio and their deviation values.

[0010] Based on the facial aesthetic difference heatmap and combined with a preset facial anatomical safety model, at least one initial injection plan is generated through an optimization algorithm. The initial injection plan includes the injection path, injection layer, injection dosage, and injection material type. The optimization algorithm takes minimizing the deviation value and maximizing the harmony of the facial contour as the objective function, and uses the facial danger area as a constraint condition.

[0011] The facial morphology changes after the initial injection plan are dynamically simulated on the three-dimensional facial model. Aesthetic correction points for the postoperative effect preview are received, and the injection path and / or dosage in the initial injection plan are iteratively corrected according to the aesthetic correction points to form a target optimized injection plan.

[0012] Preferably, the step of acquiring the three-dimensional point cloud data of the patient's face and constructing a high-precision three-dimensional facial model includes:

[0013] Multi-angle image data of the patient's face is acquired using a structured light scanner or a stereo vision camera.

[0014] The image data is subjected to point cloud registration and denoising to generate a dense point cloud;

[0015] Based on the dense point cloud, a three-dimensional mesh model with topological consistency is constructed using the Poisson surface reconstruction algorithm, and texture mapping is performed on the three-dimensional mesh model to obtain the high-precision three-dimensional facial model containing skin texture information.

[0016] Preferably, the step of calculating the actual aesthetic proportion parameter set of the patient's face based on the aesthetic key points includes:

[0017] Define the set of aesthetic key points ,in Indicates the first 3D coordinates of key points ;

[0018] Calculating the nasolabial angle using vector operations The calculation formula is as follows: ,in, Let be the vector pointing from the columella to the subnasal point. The vector pointing from the subnasal point to the philtrum point;

[0019] Calculate the thickness ratio of the upper and lower lips using Euclidean distance The calculation formula is as follows: ,in, Point on the upper lip margin Point on the lower lip margin This is the inner edge of the lower lip. This is the inner edge of the upper lip.

[0020] Preferably, the step of comparing and analyzing the actual aesthetic proportion parameter set with a preset golden ratio aesthetic database to generate a facial aesthetic difference heatmap includes:

[0021] Obtain the standard parameter set for the corresponding region from the Golden Ratio Aesthetics Database. ;

[0022] Calculate the actual aesthetic proportion parameter set Normalized deviation value between the standard parameter set and the standard parameter set : ,in, For the first The weighting coefficients of each parameter;

[0023] The normalized deviation value Mapped to the corresponding region of the 3D facial model, and according to The size of the color gradient is assigned to generate the facial aesthetic difference heatmap.

[0024] Preferably, the objective function of the optimization algorithm is... The structure is as follows: ,in, and For balance coefficient, For the first The target golden ratio position of each aesthetic key point Predict the location of key points under the current injection protocol. Let be the curvature function of the facial surface. The first item refers to the facial surface area, and the second item is used to constrain the smoothness of the facial surface to avoid unnatural bulges after injection.

[0025] Preferably, the constraints of the optimization algorithm include facial danger zone constraints, expressed as: ,in, Let the coordinates be any point on the injection path. This is a pre-defined set of facial vascular and nerve danger zones. The preset safe avoidance radius;

[0026] If the injection path passes through the danger zone, then the objective function... Imposing penalties : ,in, The penalty coefficient is... is the width of the Gaussian kernel.

[0027] Preferably, the step of dynamically simulating facial morphological changes after executing the initial injection protocol on the three-dimensional facial model includes:

[0028] A biomechanical model of facial soft tissue based on the finite element method was established, which divides the facial tissue into the epidermis, dermis, subcutaneous fat layer and muscle layer.

[0029] The injection dose in the initial injection protocol Transformed into volume expansion force applied at the injection layer nodes : ,in, The coefficient of thermal expansion of the material. The organization's normal vector;

[0030] Solve the biomechanical equilibrium equations ,in For the overall stiffness matrix, The node displacement vector is used to obtain the facial mesh deformation result after injection.

[0031] Preferably, the step of receiving aesthetic correction points for the postoperative effect preview and iteratively correcting the injection path and / or dosage in the initial injection plan based on the aesthetic correction points includes:

[0032] The correction point displacement vector is received on the three-dimensional facial model by the user input. ;

[0033] The sensitivity matrix of the correction point displacement vector to the injection dose was calculated using the adjoint method. ;

[0034] Based on the sensitivity matrix and the displacement vector of the correction point Calculate the dose correction amount : ,in, For regularization parameters, It is the identity matrix;

[0035] Using the dose correction amount Update the injection dose in the initial injection protocol and re-execute the dynamic simulation until the preset convergence condition is met.

[0036] Preferably, the method further includes:

[0037] Optimize the injection plan according to the target and generate injection guidance data, which includes augmented reality projection instructions;

[0038] Augmented reality devices are used to project the injection path, injection depth indicator lines, and injection dosage scale onto the patient's facial skin surface to assist doctors in performing visual injection procedures.

[0039] Its medical aesthetic injection and dosage optimization system, which integrates the golden ratio of aesthetics, is used to achieve the methods described above, including:

[0040] The 3D modeling module acquires 3D point cloud data of the patient's face and constructs a 3D facial mesh model containing skin texture information based on the Poisson surface reconstruction algorithm.

[0041] The key point recognition module automatically locates and marks multiple aesthetic key points, including the glabella, nasal apex, subnasal apex, philtrum, and chin point, on a 3D facial mesh model using a cascaded regression tree algorithm.

[0042] The parameter calculation module constructs a spatial vector based on the three-dimensional coordinates of key aesthetic points, and calculates the actual aesthetic proportion parameter set including the nasolabial angle, nasofrontal angle, and mentolabial sulcus depth.

[0043] The difference analysis module compares the actual set of aesthetic proportion parameters with the preset golden ratio aesthetic database using Euclidean distance, and generates a facial aesthetic difference heatmap with color gradients indicating deviation values.

[0044] The scheme generation module constructs an anatomical safety constraint space containing a mask of the facial danger area, and uses a sequential minimum optimization algorithm within the constraint space to solve the initial distribution matrix of the injection path, injection layer and injection dose to generate an initial injection scheme.

[0045] The simulation correction module simulates the soft tissue deformation after the initial injection plan is executed on the three-dimensional facial mesh model, updates the initial distribution matrix according to the received aesthetic correction points, and outputs the target optimized injection plan.

[0046] Compared with the prior art, the technical solution of this application has the following technical effects:

[0047] Based on facial aesthetic difference heatmaps and anatomical safety models, this invention rapidly generates an initial injection plan that adapts to individual facial features. By optimizing algorithms, a complete solution framework is constructed, allowing the injection-related planning process to form a systematic operational logic. This avoids the fragmented and disordered state in the plan generation process, ensuring that the overall planning process remains stable and coherent.

[0048] This invention achieves precise control and reasonable arrangement of injection-related parameters by optimizing the core algorithm. It can fully integrate aesthetic features and anatomical safety conditions into the scheme generation process, so that the initial injection scheme conforms to the actual facial structure and aesthetic needs. It ensures that the injection points, dosage and layers are all within a reasonable planning range, reducing the adaptation deviation between the scheme and the actual application scenario.

[0049] This invention achieves comprehensive constraints and standardization of the injection scheme generation process by optimizing the solution framework. It can simultaneously take into account the safety boundary of the anatomical structure during the scheme formation stage, automatically avoid potential unreasonable planning directions, maintain the safety of the plan without the need for additional complex auxiliary verification processes, and improve the overall planning efficiency.

[0050] This invention can accurately match the aesthetic differences in an individual's face, making the injection-related planning more in line with personalized needs. At the same time, it relies on the anatomical safety model to ensure the reliability of the plan in terms of safety, so that aesthetic enhancement and structural safety form a unified planning whole.

[0051] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the preferred embodiments of this application are described in detail below with reference to the accompanying drawings.

[0052] The above and other objects, advantages and features of this application will become more apparent to those skilled in the art from the following detailed description of specific embodiments in conjunction with the accompanying drawings. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In all drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0054] Based on the description of the figures and their corresponding technical content in the document, the titles of the figures are as follows:

[0055] Figure 1 A schematic diagram of the overall process of the combined optimization method of medical aesthetic injection path and dosage;

[0056] Figure 2 A framework diagram for solving injection schemes based on aesthetic heatmaps and anatomical safety models;

[0057] Figure 3 A heat map illustration of the distribution of facial aesthetic differences and deviations from the golden ratio;

[0058] Figure 4 Optimize the curve of the iterative convergence process of the objective function of the algorithm;

[0059] Figure 5 A comparative diagram of changes in facial shape and curvature before and after injection optimization;

[0060] Figure 6 Aesthetic score and curvature error trends with iteration number;

[0061] Figure 7A modular architecture diagram of a medical aesthetic injection optimization system that integrates aesthetic golden ratio. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. In the following description, specific details such as specific configurations and components are provided merely to help fully understand the embodiments of this application. Therefore, those skilled in the art should understand that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. In addition, for clarity and brevity, descriptions of known functions and structures are omitted in the embodiments.

[0063] It should be understood that the phrase "an embodiment" or "this embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "an embodiment" or "this embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0064] Furthermore, reference numerals and / or letters may be repeated in different examples within this application. Such repetition is for the purpose of simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or settings discussed.

[0065] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, and A and B exist simultaneously. The term " / and" in this article describes another type of relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone, and A and B exist alone. In addition, the character " / " in this article generally indicates that the related objects before and after it are in an "or" relationship.

[0066] In this article, the term "at least one" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, "at least one of A and B" can mean: A exists alone, A and B exist simultaneously, or B exists alone.

[0067] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion.

[0068] Example 1

[0069] This embodiment mainly describes a method for optimizing medical aesthetic injection and dosage in accordance with the golden ratio of aesthetics, such as... Figure 1 As shown, it specifically includes:

[0070] Acquire 3D point cloud data of the face of the person seeking beauty and construct a high-precision 3D facial model; automatically identify and mark multiple aesthetic key points on the 3D facial model;

[0071] Based on the aforementioned key aesthetic points, the actual aesthetic proportion parameter set of the face of the person seeking beauty is calculated. The parameter set includes at least the nasolabial angle, nasofrontal angle, mentolabial sulcus depth, upper and lower lip thickness ratio, and facial width-to-height ratio.

[0072] The actual aesthetic proportion parameter set is compared and analyzed with the preset golden ratio aesthetic database to generate a facial aesthetic difference heat map. The heat map uses color gradients to indicate the areas to be optimized that deviate significantly from the golden ratio and their deviation values.

[0073] Based on the facial aesthetic difference heatmap and combined with a preset facial anatomical safety model, at least one initial injection plan is generated through an optimization algorithm. The initial injection plan includes the injection path, injection layer, injection dosage, and injection material type. The optimization algorithm takes minimizing the deviation value and maximizing the harmony of the facial contour as the objective function, and uses the facial danger area as a constraint condition.

[0074] The facial morphology changes after the initial injection plan are dynamically simulated on the three-dimensional facial model. Aesthetic correction points for the postoperative effect preview are received, and the injection path and / or dosage in the initial injection plan are iteratively corrected according to the aesthetic correction points to form a target optimized injection plan.

[0075] Furthermore, in the process of acquiring the three-dimensional point cloud data of the patient's face and constructing a high-precision three-dimensional facial model, a structured light scanner or stereo vision camera is used to collect multi-angle image data of the face. The acquisition viewpoints cover seven directions: frontal, left 30°, left 60°, right 30°, right 60°, upward, and downward. The resolution of a single image is no less than 4096×3072 pixels, and the original density of the acquired point cloud is no less than 2000 points per square centimeter. After completing the acquisition of the original images and point cloud, image distortion is performed. The process includes distortion correction, feature matching, initial point cloud registration, fine point cloud registration, outlier filtering, and point cloud smoothing and densification. Distortion correction employs Zhang Zhengyou's planar calibration method to solve for camera intrinsic and extrinsic parameters, radial and tangential distortion coefficients. The reprojection error of the corrected image is controlled within 0.005 pixels. Feature matching uses SIFT combined with FLANN matching strategies to establish the correspondence between stable facial feature points. Point cloud registration first uses the SAC-IA algorithm for coarse registration, and then uses the ICP iterative nearest-point algorithm for fine registration. The current fine-grained registration is performed, with the registration convergence condition set at no less than 80 iterations and a root mean square error of less than 0.008 mm. Outlier filtering adopts a combination of radius filtering and statistical filtering. The radius filtering is set with a neighborhood radius of 0.3 mm and a minimum number of neighborhood points of 6, while the statistical filtering is set with a neighborhood number of 15 and a standard deviation factor of 1.2. After processing, a dense facial point cloud without noise, redundancy, or missing data is obtained. Based on this, a three-dimensional mesh model is constructed using the Poisson surface reconstruction algorithm. The octree depth is set to 11 levels, the surface fitting number is set to 8 levels, and the normal vector consistency constraint error is less than 0.04 rad to ensure that the model has a closed topology and a continuous surface. Texture mapping is performed on the three-dimensional mesh model. Through automatic UV unwrapping and per-vertex texture coordinate optimization, the high-resolution facial color texture is accurately fitted to the mesh surface, and the mapping error is controlled within 0.015 mm. A high-precision three-dimensional facial model with a geometric accuracy better than 0.05 mm, a vertex count of no less than 800,000, a triangular facet count of no less than 1.5 million, and complete preservation of skin texture and skin color information is obtained.

[0076] In the process of automatically identifying and marking aesthetic key points on a high-precision 3D facial model, using the 3D mesh vertex coordinates, vertex normals, mesh curvature, and local geometric features as inputs, a cascaded regression tree algorithm is employed to achieve synchronous and accurate localization of multiple key points, thus defining a set of aesthetic key points. ,in Representing the 3D coordinates of key points The key points covered include the glabella, nasofrontal point, nasal apex, columella, subnasal point, nasal ala point, philtrum point, upper lip edge point, lower lip edge point, upper lip inner edge point, lower lip inner edge point, corner of mouth point, mentolabial sulcus point, prementum point, submentum point, left and right inner canthi, left and right outer canthi, left and right zygomatic prominence points, and left and right mandibular angle points, totaling 36 points. The cascaded regression tree is set to 12 levels, with 60 regression trees in each level. The maximum depth of a single tree is 7 levels. Each regression level performs residual correction on the key point position, gradually reducing the positioning deviation. The overall positioning error of the key points is less than 0.08mm. All key point coordinates are stored in double-precision floating-point format, providing a stable and reliable geometric benchmark for subsequent spatial vector operations and distance calculations of aesthetic proportion parameters.

[0077] When calculating the actual aesthetic proportion parameters of a patient's face based on key aesthetic points, all parameters are accurately solved using three-dimensional coordinates through spatial vector operations, Euclidean distance operations, point-to-line distance operations, and curvature integral operations, including the calculation of the nasolabial angle. The calculation formula is: ,in Let be the spatial vector pointing from the columella to the subnasal point. Let be the spatial vector pointing from the subnasal point to the philtrum. The formula for calculating the vector magnitude is: The formula for calculating the vector dot product is: The calculation results are expressed in radians and rounded to 6 decimal places; next, the nasofrontal angle is calculated. The formula is ,in Let be the vector pointing from the glabella point to the nasofrontal point. Let the vector from the nasofrontal point to the nasal apex be denoted; then calculate the depth of the mentolabial sulcus. The formula is This is used to characterize the standard degree of the recessed structure between the chin and lips; then the thickness ratio of the upper and lower lips is calculated. The formula is The formula for calculating the Euclidean distance between two points is: Finally, calculate the facial width-to-height ratio. The formula is At the same time, the facial proportions in the face are calculated. Proportion of the lower part The formulas are respectively , This results in a complete set of actual aesthetic proportion parameters, including the nasolabial angle, nasofrontal angle, mentolabial sulcus depth, upper and lower lip thickness ratio, facial width-to-height ratio, mid-face proportion, and lower face proportion. All parameter calculations are performed using double-precision floating-point operations to ensure numerical stability and high precision.

[0078] When comparing the actual aesthetic proportion parameter set with the preset golden ratio aesthetic database and generating a facial aesthetic difference heatmap, the corresponding standard parameter set is extracted from the golden ratio aesthetic database. The standard values ​​for the nasolabial angle, nasofrontal angle, and mentolabial sulcus depth were 1.309 rad, 1.222 rad, 4.5 mm, 0.618, 0.618, 0.618, 0.618, and 0.618 for the midface and lower face proportions, respectively. The normalized deviation was then calculated. The formula is The weighting coefficient satisfy Specifically, the weights are allocated as follows: nasolabial angle 0.22, nasofrontal angle 0.18, mentolabial sulcus depth 0.14, upper and lower lip thickness ratio 0.22, facial width-to-height ratio 0.12, mid-face proportion 0.06, and lower face proportion 0.06. To improve the continuity and spatial consistency of the deviation distribution, the deviation values ​​are subjected to two-dimensional Gaussian smoothing. The smoothing formula is as follows: Where σ is taken as 1.2mm, the smoothed deviation values ​​are mapped to the corresponding colors according to the gradient interval. Mapped to dark blue, Mapped to light blue, Mapped to yellow, Mapped to orange, Mapped to deep red, the color attribute is assigned to each vertex of the 3D facial model and globally smoothed to obtain a facial aesthetic difference heatmap that can intuitively display the deviation area, deviation level and precise deviation value. The heatmap value resolution reaches 0.001, which can accurately guide the determination of injection optimization area and optimization intensity allocation.

[0079] like Figure 2 As shown, when generating the initial injection plan based on the facial aesthetic difference heatmap and the facial anatomical safety model, a complete solution framework is constructed with the optimization algorithm as the core, and the objective function of the optimization algorithm is established. The formula is: To further ensure the safety of the facial anatomical model, combined with Single-point dose, To further constrain the upper limit of safe dosage, the formula is as follows: Where α is 0.68, β is 0.22, γ is 0.10, and K represents 36 aesthetic key points. The key point is the golden ratio target coordinate. Predict coordinates for the current scheme. Let Ω be the curvature function of the facial mesh, ∇ be the gradient operator, Ω be the effective area of ​​the face, and L be the number of injection points. Single-point dose, To determine the upper limit of safe dosage, the objective function simultaneously constrains aesthetic deviation, surface smoothness, and dosage rationality, avoiding localized overdose and abrupt contours. It also sets facial anatomical safety constraints. The core constraint formula is as follows: ,in Let the coordinates be any point on the injection path. This is a collection of dangerous areas including the facial artery, facial vein, infraorbital nerve, trochlear nerve, and nasal alar plexus. The constraint is set to 2.0 mm, and then further transformed into a penalty term added to the objective function. The formula for the penalty term is: Where γ is 1200 and σ is 1.0 mm, the penalty term increases exponentially as the injection point gets closer to the danger zone, forcing the optimization path to actively avoid the danger zone. Under the combined effect of the objective function and the constraints, the sequential minimum optimization algorithm combined with the gradient descent method is used for iterative solution. The maximum number of iterations is set to 150, and the convergence threshold is set to the objective function change being less than 1e-7. The final output includes the three-dimensional injection path coordinate sequence, injection level, single-point injection dose, total injection dose, and injection material type of the initial injection plan. The spacing between injection path points is controlled within 0.4 mm. The level division is accurate to six levels: epidermis, superficial dermis, deep dermis, superficial subcutaneous fat, deep subcutaneous fat, and superficial muscle. The dose accuracy reaches 0.005 ml, and the material matching strictly corresponds to the level and mechanical properties.

[0080] Furthermore, when dynamically simulating post-injection morphological changes on a 3D facial model and iteratively refining the injection plan to form a target optimization scheme, a facial soft tissue biomechanical model based on the finite element method was established. The face was divided into five layers according to anatomical structure: epidermis, dermis, subcutaneous fat, muscle, and fascia. Mechanical parameters such as elastic modulus, Poisson's ratio, density, and shear modulus were assigned to each layer. The elastic modulus of the epidermis was 1.2 MPa, the dermis 5.5 MPa, the subcutaneous fat 0.6 MPa, the muscle 11 MPa, and the fascia 8 MPa. The model used a tetrahedral unstructured mesh with a minimum of 300,000 elements and 550,000 nodes. Boundary conditions were fixed in the skull and temporal bone regions to ensure that the deformation conformed to the real tissue mechanical response. The injection dose was converted into volumetric expansion force, using the formula: Where κ is the coefficient of thermal expansion of the material, κ=1.22 for hyaluronic acid and κ=1.13 for collagen, Q is the injection dose, and n is the tissue normal vector at the injection point. The formula for calculating the normal vector is... Where n1, n2, and n3 are the normal vectors of the neighborhood surface of the injection point, the biomechanical equilibrium equation is then solved. Where K is the overall stiffness matrix, obtained by integrating the mechanical parameters of each layer with the stiffness of the mesh elements, and u is the nodal displacement vector. To determine the self-weight load, a preconditional conjugate gradient method is used, with a convergence error of less than 1e-9, yielding a high-precision facial deformation field and rendering the postoperative effect in real time. After previewing the effect, the system receives the displacement vector of the aesthetic correction points input by the user. The sensitivity matrix S of displacement to injection dose is calculated using the adjoint variable method. The calculation formula is as follows: Then, the dose correction is calculated using regularized least squares. The formula is Where λ is 1e-6 and I is the identity matrix, the injection path and injection dose are updated according to the correction amount, the biomechanical deformation simulation is re-executed, and the iterative process is repeated until the convergence condition is met. The displacement error of the correction point is less than 0.03mm and the number of iterations does not exceed 12. Finally, the target optimized injection scheme that takes into account the golden aesthetic ratio, smooth and natural surface, absolute anatomical safety, and accurate and reasonable dosage is obtained.

[0081] After optimizing the injection plan, augmented reality injection guidance data is generated, converting the injection path, depth of layer, dosage scale, and danger zone boundaries in the 3D model space into real-world spatial coordinates. The coordinate transformation formula is as follows: Where R is the rotation matrix and T is the translation matrix, precise registration is achieved through camera calibration and hand-eye calibration, with a registration error of less than 0.08mm, and the injection guidance information is projected onto the facial skin surface of the patient in real time.

[0082] This detailed description of the implementation uses 3D facial modeling, golden ratio parameter calculation, and heat map deviation analysis to accurately locate areas of aesthetic defects. Combined with anatomical safety constraints and multi-objective optimization algorithms, it automatically generates an injection plan that balances aesthetics and safety. With the addition of biomechanical simulation and iterative correction, the results can be previewed and the parameters can be precisely controlled, effectively improving the accuracy and safety of injection planning, reducing operational risks, and making the facial contours more in line with the golden ratio.

[0083] To verify the reproducibility and clinical feasibility of the medical aesthetic injection and dosage optimization method that integrates the aesthetic golden ratio of this application, feasibility verification was achieved by collecting data with objective instruments and conducting repeated tests, specifically including Examples 2 and 3.

[0084] Example 2: In this example, a patient with a moderate deviation in facial aesthetic proportions is selected as the verification object to verify the modeling accuracy, key point localization stability, parameter calculation accuracy, algorithm convergence, and effectiveness of anatomical safety constraints of this application. The simulation hardware uses an Intel i9-13900K processor, an NVIDIA RTX 4090 24GB graphics card, and 64GB DDR5 memory. The software platform is built based on VTK, OpenCV, and ANSYS.

[0085] In the 3D facial model construction and aesthetic key point localization stage, a structured light scanner was used to complete high-density image acquisition from seven directions: frontal, left 30°, left 60°, right 30°, right 60°, upward, and downward. Each image had a resolution of 4096×3072 pixels, and the original point cloud acquisition density reached 2100 points / cm². After distortion correction using Zhang Zhengyou calibration method, SIFT-FLANN feature matching, SAC-IA coarse registration, ICP fine registration, and combined radius filtering and statistical filtering for noise reduction, a geometrically complete and noise-free image was generated. The remaining dense point cloud of the face was used to construct a 3D mesh model using a Poisson surface reconstruction algorithm with an octree depth of 11 levels and a surface fitting order of 8 levels. The final model achieved a geometric accuracy of 0.048 mm, 824,000 vertices, 1,563,000 triangular faces, and a texture mapping error of 0.012 mm. Based on this model, a 12-level cascaded regression tree algorithm was used to automatically locate 36 aesthetic key points. The average positioning error of all key points was only 0.077 mm. All indicators met the geometric requirements for subsequent high-precision aesthetic calculations and injection scheme optimization.

[0086] The facial aesthetic difference heatmap generated in this embodiment, such as Figure 3 As shown, the model's geometric accuracy is maintained at 0.048 mm. The figure uses five consecutive color gradients—dark blue, light blue, yellow, orange, and red—to correspond to different normalized deviation values. Specifically, the dark blue area corresponds to a deviation value of 0–0.15, the light blue area to 0.15–0.35, the yellow area to 0.35–0.6, the orange area to 0.6–0.85, and the dark red area to 0.85–1.0. Figure 3 The deviation values ​​for the nasolabial angle region (0.82), the upper and lower lip thickness ratio region (0.88), and the mentolabial sulcus depth region (0.35) can be clearly observed. These regions are highlighted in dark red and orange, directly identifying the core facial areas that need optimization.

[0087] Example 2 quantitatively tested core indicators such as modeling accuracy, key point localization error, parameter calculation time, and algorithm convergence count. The test results are uniformly integrated in Table 1. In Table 1, MD represents modeling accuracy, KPE represents key point localization error, CCT represents parameter calculation time, and AC represents algorithm convergence count. Five sets of independent test data show that the average MD is 0.048 mm, the average KPE is 0.077 mm, the average CCT is 1.17 s, and the average AC is 91.4 times. The final convergence value of the objective function stabilizes at 1.26 × 10⁻⁶. -5 All indicators meet the technical requirements of high precision, high efficiency, and high stability, fully demonstrating that each technical aspect of the method in this application has reliable feasibility for implementation.

[0088] Table 1. Verification Results of Accuracy and Efficiency of Core Technology Aspects

[0089]

[0090] In the initial injection protocol generation and anatomical safety constraint verification phase, a minimum safe avoidance distance of 2.0 mm for dangerous areas such as facial blood vessels and nerves was used as a hard constraint. A sequential minimum optimization algorithm combined with gradient descent was employed to iteratively solve the objective function, with a maximum of 150 iterations and a convergence threshold set at a change in the objective function of less than 1 × 10⁻⁶. -7 In the initial injection plan obtained by the solution, the shortest distance between all spatial points of the injection path and the danger zone is greater than 2.14 mm, which fully meets the safety constraints. The single-point injection dose is controlled in the range of 0.01 mL to 0.42 mL, the total dose error is less than 0.02 mL, and the injection layers are accurately divided into six anatomical layers: epidermis, superficial dermis, deep dermis, superficial subcutaneous fat, deep subcutaneous fat, and muscle layer. The plan parameters are complete, the spatial positioning is clear, and the dose distribution is reasonable.

[0091] like Figure 4 The high-precision two-dimensional coordinate test curve shown. Figure 4 The dataset contains five independent and smooth, continuous objective function descent curves, corresponding to the five independent test results in Table 1. The initial values ​​of all five curves are stable at 2.30 × 10⁻⁶. -3 Up to 2.42×10 -3 Within the interval, the number of iterations gradually stabilized between 89 and 94, and the final convergence value remained stable at 1.23 × 10⁻⁶. -5 Up to 1.31×10 -5 Within the range, the overall trend shows a highly consistent rapid decline to a stable convergence, without oscillation, divergence, or significant deviation. The objective function decreases rapidly in the interval from 0 to 30 iterations, and the rate of decline gradually slows down in the interval from 30 to 80 iterations. After 80 iterations, it maintains a stable convergence state. The overlap and consistency of the five curves are good, which intuitively reflects that the optimization algorithm adopted in this application has excellent stability, repeatability, and convergence reliability. It can stably output the optimal initial injection scheme that meets aesthetic and safety constraints within a limited number of iterations.

[0092] Example 3: Based on the feasibility verification of the core technology in Example 2, this example conducts facial soft tissue biomechanical deformation simulation and aesthetic correction point iterative correction. The verification objects cover three typical samples with mild, moderate and severe facial aesthetic deviations. Each group of samples undergoes complete scheme iterative optimization and AR projection registration test.

[0093] In the biomechanical dynamic simulation of facial soft tissue, the facial tissue was divided into five anatomical layers—epidermis, dermis, subcutaneous fat, muscle, and fascia—based on the finite element method. Mechanical parameters conforming to human physiological characteristics were assigned to each layer: 1.2 MPa for the epidermis, 5.5 MPa for the dermis, 0.6 MPa for the subcutaneous fat, 11 MPa for the muscle, and 8 MPa for the fascia. A tetrahedral unstructured mesh finite element model was constructed, with a total of 326,000 elements and 568,000 nodes. Boundary conditions were fixed for the skull and temporal bone regions, perfectly replicating the mechanical response characteristics of the real face. The injection dosage in the initial injection plan was converted into volumetric expansion force according to the material expansion coefficient. The biomechanical equilibrium equation was solved using the pre-conditional conjugate gradient method, with a convergence error of less than 1 × 10⁻⁶. -9 Ultimately, a three-dimensional deformation field of the face after injection was obtained, with a simulation deformation accuracy of 0.01mm, which truly restores the physical properties of tissue bulging, contour extension, and surface smoothing after hyaluronic acid and collagen injection.

[0094] In this embodiment, the morphology and curvature comparison of the entire facial optimization process is as follows: Figure 5 The complete presentation shown below, sub Figure 5-1 The image shows the original facial morphology, with curvature values ​​ranging from -0.8 to 0.8. Measured curvature values ​​were: nasolabial angle 0.52, upper and lower lip area 0.46, and mentolabial sulcus 0.41, indicating poor contour smoothness. Figure 5-2 The initial design was simulated with a deformation morphology diagram. After optimization, the curvature of the nasolabial angle was reduced to 0.31, the curvature of the upper and lower lip regions was reduced to 0.27, and the curvature of the mentolabial sulcus was reduced to 0.26, resulting in a significant improvement in smoothness. Figure 5-3 The resulting morphological diagram shows that the curvature across the entire region is stable between 0.10 and 0.20, with uniform and continuous contour lines without abrupt changes or unevenness. Figure 5-4 The attached figure is a standard golden ratio shape diagram with a curvature range of 0.12 to 0.18, which is highly consistent with the corrected shape. The attached figure uses quantitative data to intuitively demonstrate the aesthetic effect and smoothness improvement brought about by iterative correction.

[0095] Example 3 quantitatively tested key clinical indicators such as the number of iterations, correction point position error, deformation accuracy, AR projection error, and aesthetic score. The test results are summarized in Table 2. In Table 2, IC represents the number of iterations, CPE represents the correction point position error, DD represents the deformation accuracy, ARPE represents the AR projection error, and AS represents the 100-point professional aesthetic score. The test data shows that samples with mild deviations require an average of 2 iterations, samples with moderate deviations require an average of 4 iterations, and samples with severe deviations require an average of 6 iterations to reach the convergence condition. The average correction point position error for all samples was 0.029 mm, the average deformation accuracy was 0.010 mm, the average AR projection error was 0.076 mm, the average professional aesthetic score was 92.6 points, and the average optimized total dose was 1.23 mL. All data fully demonstrate that the iterative correction mechanism and AR visualization guidance of this application have excellent stability and accuracy in clinical application.

[0096] Table 2 Iterative optimization and AR-guided verification results

[0097]

[0098] Based on the iteration count, aesthetic score, and overall curvature error data in Table 2, such as Figure 6 As shown in the figure, the blue smooth curve represents the trend of the aesthetic score as the number of iterations increases, and the red smooth curve represents the trend of the comprehensive curvature error as the number of iterations increases. As the number of iterations increases from 0 to 6, the facial aesthetic score rises continuously from 78.3 to 90.9 and then quickly stabilizes, while the comprehensive curvature error decreases continuously from 0.52 to 0.02 and enters the convergence range. Neither smooth curve shows significant fluctuations or abrupt changes, fully demonstrating that the iterative correction mechanism of this application has excellent convergence speed, optimization stability, and clinical application reliability.

[0099] In the aesthetic correction point input and injection parameter iterative correction process, the system receives the three-dimensional displacement vector of the aesthetic correction point input by the user. The displacement vector accuracy is 0.01mm. The sensitivity matrix of the correction point displacement to the injection dose is calculated using the adjoint variable method. The single-point dose correction amount is calculated based on the regularized least squares method. After correction, the dose deviation is less than 0.01mL. Each dose correction restarts the biomechanical deformation simulation and updates the three-dimensional facial morphology in real time until the correction point displacement error is less than 0.03mm and the objective function value remains stable. The entire iterative correction process takes an average of 8.2s, which has efficient real-time interactive capabilities and can fully meet the actual needs of rapid adjustment of clinical face diagnosis.

[0100] The implementation verification of this embodiment shows that the modeling accuracy is high, the key point positioning is accurate, and safe and compliant injection plans can be generated quickly. After iterative optimization, the aesthetic score is significantly improved, the curvature error is significantly reduced, the AR guidance error is small and the convergence is stable. The overall process is realistic and feasible, and it has excellent clinical applicability and reliability.

[0101] Example 4 describes in detail a medical aesthetic injection and dosage optimization system that integrates aesthetic golden ratio principles, such as... Figure 7 As shown, it includes:

[0102] The 3D modeling module is used to acquire 3D point cloud data of the face of the person seeking beauty, and to construct a 3D facial mesh model containing skin texture information based on the Poisson surface reconstruction algorithm.

[0103] The key point recognition module, connected to the 3D modeling module, is used to automatically locate and mark multiple aesthetic key points, including the glabella, nasal apex, subnasal apex, philtrum, and anterior chin point, on the 3D facial mesh model using a cascaded regression tree algorithm.

[0104] The parameter calculation module, connected to the key point recognition module, is used to construct a spatial vector based on the three-dimensional coordinates of the aesthetic key points and calculate the actual aesthetic proportion parameter set including the nasolabial angle, nasofrontal angle and mentolabial fold depth.

[0105] The difference analysis module, connected to the parameter calculation module, is used to compare the actual aesthetic proportion parameter set with the preset golden ratio aesthetic database using Euclidean distance, and generate a facial aesthetic difference heatmap with color gradient indicating the deviation value.

[0106] The scheme generation module, connected to the difference analysis module, is used to construct an anatomical safety constraint space containing a mask of the facial danger area, and to use a sequential minimum optimization algorithm within the constraint space to solve the initial distribution matrix of the injection path, injection layer and injection dose to generate an initial injection scheme.

[0107] The simulation correction module, connected to the scheme generation module, simulates the soft tissue deformation after the initial injection scheme is executed on the three-dimensional facial mesh model, updates the initial distribution matrix according to the received aesthetic correction points, and outputs the target optimized injection scheme.

[0108] Furthermore, the 3D modeling module is the basic unit for data input and model construction of the system. It is responsible for collecting original point cloud data of the face of the beauty seeker from multiple angles. After point cloud registration and filtering and noise reduction, the Poisson surface reconstruction algorithm is used to generate a 3D facial mesh model with complete topological structure and high geometric accuracy, and complete texture mapping so that the model carries real skin texture information.

[0109] Furthermore, the key point recognition module is directly connected to the 3D modeling module. Using the 3D facial mesh model as the processing object, the cascaded regression tree algorithm is used to achieve automatic, stable, and high-precision positioning of aesthetic key points. It can batch mark core aesthetic points such as the center of the eyebrows, the tip of the nose, the subnasal point, the philtrum, and the prechin point.

[0110] Furthermore, the parameter calculation module takes the three-dimensional coordinates output by the key point recognition module as input, and through spatial vector construction and geometric operations, quantitatively calculates the actual facial aesthetic proportion parameters, including key indicators such as nasolabial angle, nasofrontal angle, and mentolabial fold depth, forming a quantifiable set of aesthetic parameters, realizing the transformation from morphological observation to numerical expression, and providing a unified standard for the golden ratio comparison.

[0111] Furthermore, the difference analysis module compares the measured aesthetic parameters with the preset golden ratio aesthetic database using Euclidean distance quantification, calculates the parameter deviation values ​​for each region, and maps them onto the 3D facial model in the form of color gradients to generate an aesthetic difference heatmap. This heatmap visually highlights the areas with larger deviations that need optimization and the degree of deviation, providing clear optimization goals and priorities for solution generation.

[0112] Furthermore, the scheme generation module, guided by the heat map results, first constructs an anatomical safety constraint space containing masks of dangerous areas such as blood vessels and nerves. Then, with the goal of minimizing deviation and maximizing contour harmony, it uses a sequence minimum optimization algorithm to perform numerical solutions and outputs an initial distribution matrix containing the injection path, layer, and dosage, forming an initial injection scheme that takes into account both aesthetics and safety.

[0113] Furthermore, the simulation correction module serves as the system's dynamic optimization and closed-loop correction unit, simulating the soft tissue deformation effect after injection and providing a postoperative morphological preview. It also supports doctors to input aesthetic correction points, and iteratively updates injection parameters based on the displacement of the correction points, continuously optimizing the distribution matrix and outputting a safe, natural, and golden ratio-compliant target optimized injection plan.

[0114] This embodiment describes in detail how to quickly construct a high-precision 3D facial model, automatically identify key points and accurately calculate aesthetic parameters to generate an intuitive difference heatmap; under safety constraints, it intelligently generates an initial plan, and outputs an optimized injection plan after simulation iteration and correction. The overall efficiency is high, the positioning is accurate, and the safety is strong, significantly improving the aesthetic effect of medical aesthetic injections.

[0115] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any changes, modifications, substitutions, integrations, and parameter changes made to these embodiments within the spirit and principles of the present invention, without departing from the principles and spirit of the present invention, through conventional substitutions or to achieve the same function, fall within the scope of protection of the present invention.

Claims

1. A combined approach to optimizing medical aesthetic injections and dosages to achieve the golden ratio of aesthetics, including: Obtain 3D point cloud data of the face of the person seeking cosmetic enhancement and construct a high-precision 3D facial model; Multiple aesthetic key points are automatically identified and marked on the three-dimensional facial model; Based on the aforementioned key aesthetic points, the actual aesthetic proportion parameter set of the face of the person seeking beauty is calculated. The parameter set includes at least the nasolabial angle, nasofrontal angle, mentolabial sulcus depth, upper and lower lip thickness ratio, and facial width-to-height ratio. The actual aesthetic proportion parameter set is compared and analyzed with the preset golden ratio aesthetic database to generate a facial aesthetic difference heat map. The heat map uses color gradients to indicate the areas to be optimized that deviate significantly from the golden ratio and their deviation values. Based on the facial aesthetic difference heatmap and combined with a preset facial anatomical safety model, at least one initial injection plan is generated through an optimization algorithm. The initial injection plan includes the injection path, injection layer, injection dosage, and injection material type. The optimization algorithm takes minimizing the deviation value and maximizing the harmony of the facial contour as the objective function, and uses the facial danger area as a constraint condition. The facial morphology changes after the initial injection plan are dynamically simulated on the three-dimensional facial model. Aesthetic correction points for the postoperative effect preview are received, and the injection path and / or dosage in the initial injection plan are iteratively corrected according to the aesthetic correction points to form a target optimized injection plan.

2. The method for optimizing medical aesthetic injection and dosage based on the golden ratio of aesthetics according to claim 1, characterized in that, The process of acquiring 3D point cloud data of the patient's face and constructing a high-precision 3D facial model includes: Multi-angle image data of the patient's face is acquired using a structured light scanner or a stereo vision camera. The image data is subjected to point cloud registration and denoising to generate a dense point cloud; Based on the dense point cloud, a three-dimensional mesh model with topological consistency is constructed using the Poisson surface reconstruction algorithm, and texture mapping is performed on the three-dimensional mesh model to obtain the high-precision three-dimensional facial model containing skin texture information.

3. The method for optimizing medical aesthetic injection and dosage based on the golden ratio of aesthetics according to claim 1, characterized in that, The calculation of the actual aesthetic proportion parameter set of the patient's face based on the aforementioned aesthetic key points includes: Define the set of aesthetic key points ,in Indicates the first 3D coordinates of key points ; Calculating the nasolabial angle using vector operations The calculation formula is as follows: ,in, Let be the vector pointing from the columella to the subnasal point. The vector pointing from the subnasal point to the philtrum point; Calculate the thickness ratio of the upper and lower lips using Euclidean distance The calculation formula is as follows: ,in, Point on the upper lip margin Point on the lower lip margin This is the inner edge of the lower lip. This is the inner edge of the upper lip.

4. The method for optimizing medical aesthetic injection and dosage based on the golden ratio of aesthetics according to claim 1, characterized in that, The step of comparing and analyzing the actual aesthetic proportion parameter set with a preset golden ratio aesthetic database to generate a facial aesthetic difference heatmap includes: Obtain the standard parameter set for the corresponding region from the Golden Ratio Aesthetics Database. ; Calculate the actual aesthetic proportion parameter set Normalized deviation value between the standard parameter set and the standard parameter set : ,in, For the first The weighting coefficients of each parameter; The normalized deviation value Mapped to the corresponding region of the 3D facial model, and according to The size of the color gradient is assigned to generate the facial aesthetic difference heatmap.

5. The method for optimizing medical aesthetic injection and dosage based on the golden ratio of aesthetics according to claim 1, characterized in that, The objective function of the optimization algorithm The structure is as follows: ,in, and For balance coefficient, For the first The target golden ratio position of each aesthetic key point Predict the location of key points under the current injection protocol. Let be the curvature function of the facial surface. The first item refers to the facial surface area, and the second item is used to constrain the smoothness of the facial surface to avoid unnatural bulges after injection.

6. The method for optimizing medical aesthetic injection and dosage based on the golden ratio of aesthetics according to claim 5, characterized in that, The constraints of the optimization algorithm include facial danger zone constraints, expressed as: ,in, Let the coordinates be any point on the injection path. This is a pre-defined set of facial vascular and nerve danger zones. The preset safe avoidance radius; If the injection path passes through the danger zone, then the objective function... Imposing penalties : ,in, The penalty coefficient is... The width of the Gaussian kernel.

7. The method for optimizing medical aesthetic injection and dosage based on the golden ratio of aesthetics according to claim 1, characterized in that, The dynamic simulation of facial morphological changes after executing the initial injection protocol on the three-dimensional facial model includes: A biomechanical model of facial soft tissue based on the finite element method was established, which divides the facial tissue into the epidermis, dermis, subcutaneous fat layer and muscle layer. The injection dose in the initial injection protocol Transformed into volume expansion force applied at the injection layer nodes : ,in, The coefficient of thermal expansion of the material. The organization's normal vector; Solve the biomechanical equilibrium equations ,in For the overall stiffness matrix, The node displacement vector is used to obtain the facial mesh deformation result after injection.

8. The method for optimizing medical aesthetic injection and dosage based on the golden ratio of aesthetics according to claim 7, characterized in that, The step of receiving aesthetic correction points for the postoperative effect preview and iteratively correcting the injection path and / or dosage in the initial injection plan based on the aesthetic correction points includes: The correction point displacement vector is received on the three-dimensional facial model by the user input. ; The sensitivity matrix of the correction point displacement vector to the injection dose was calculated using the adjoint method. ; Based on the sensitivity matrix and the displacement vector of the correction point Calculate the dose correction amount : ,in, For regularization parameters, It is the identity matrix; Using the dose correction amount Update the injection dose in the initial injection protocol and re-execute the dynamic simulation until the preset convergence condition is met.

9. The method for optimizing medical aesthetic injection and dosage based on the golden ratio of aesthetics according to claim 1, characterized in that, The method further includes: Optimize the injection plan according to the target and generate injection guidance data, which includes augmented reality projection instructions; Augmented reality devices are used to project the injection path, injection depth indicator lines, and injection dosage scale onto the patient's facial skin surface to assist doctors in performing visual injection procedures.

10. A medical aesthetic injection and dosage optimization system integrating aesthetic golden ratio, used to implement the method as described in any one of claims 1 to 9, characterized in that, include: The 3D modeling module acquires 3D point cloud data of the patient's face and constructs a 3D facial mesh model containing skin texture information based on the Poisson surface reconstruction algorithm. The key point recognition module automatically locates and marks multiple aesthetic key points, including the glabella, nasal apex, subnasal apex, philtrum, and chin point, on a 3D facial mesh model using a cascaded regression tree algorithm. The parameter calculation module constructs a spatial vector based on the three-dimensional coordinates of key aesthetic points, and calculates the actual aesthetic proportion parameter set including the nasolabial angle, nasofrontal angle, and mentolabial sulcus depth. The difference analysis module compares the actual set of aesthetic proportion parameters with the preset golden ratio aesthetic database using Euclidean distance, and generates a facial aesthetic difference heatmap with color gradients indicating deviation values. The scheme generation module constructs an anatomical safety constraint space containing a mask of the facial danger area, and uses a sequential minimum optimization algorithm within the constraint space to solve the initial distribution matrix of the injection path, injection layer and injection dose to generate an initial injection scheme. The simulation correction module simulates the soft tissue deformation after the initial injection plan is executed on the three-dimensional facial mesh model, updates the initial distribution matrix according to the received aesthetic correction points, and outputs the target optimized injection plan.

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