3D Dimension Measurement Method for Curved Surface Structures

Abstract

This invention relates to a 3D dimensional measurement method applicable to curved surface structures. The method involves capturing the target curved surface using a camera and laser scanner; generating point cloud data using structured light; registering point clouds across multiple views using the SIFT feature matching algorithm to generate a unified point cloud model; training a feature recognition model using a deep learning algorithm to extract key geometric features of the surface; identifying surface features with different edges, angles, and curvatures through labeling and classification, and converting these features into mathematical representations using a parametric modeling method based on Bezier curves; establishing a comprehensive error model to evaluate multiple error sources, and fitting an error propagation function using experimental data; adjusting the dimensional measurement using the least squares method; and introducing a real-time data acquisition and feedback system, using temperature and humidity sensors to monitor environmental changes, and adjusting scanning parameters including scanning speed and light source brightness using a PID controller.

Description

Technical Field

[0001] This invention relates to the field of 3D dimension measurement of curved structures, and more specifically to a 3D dimension measurement method applicable to curved structures. Background Technology

[0002] Current 3D dimension measurement methods applied to curved surfaces still have many shortcomings and drawbacks in practical applications, mainly in terms of measurement accuracy, adaptability, efficiency, and stability. First, traditional 3D dimension measurement methods rely primarily on fixed geometric rules or preset feature extraction parameters, which are often unable to adapt to the complex and varied geometric characteristics of curved surfaces. For example, high curvature and sharp-edge regions commonly found in curved surfaces often cannot be effectively identified and fitted using traditional methods. This is because traditional methods typically rely on manually preset thresholds and rules to extract surface features, such as edges, angles, or curvature variations, making it difficult to handle highly irregular and multi-scale surface features, thus severely limiting measurement accuracy on complex curved surfaces. Second, regarding error correction, traditional measurement methods often ignore the diversity and complexity of error sources. Typically, existing technologies correct for single error sources, such as compensating for equipment errors through simple scanner calibration or environmental errors through environmental monitoring. However, in practical applications, the error sources for 3D dimension measurement are often diverse, with various error sources such as equipment errors, changes in material properties, and environmental influences all working together to affect the measurement results. Traditional methods lack a systematic error model to comprehensively consider the synergistic effects of different error sources. In particular, the deformation of material properties under varying external conditions such as temperature and humidity often cannot be effectively compensated, leading to decreased stability and measurement accuracy in diverse measurement environments. Furthermore, existing error correction methods are usually static and cannot be dynamically adjusted according to different measurement conditions, resulting in insufficient flexibility and adaptability of error compensation.

[0003] Another common problem is the inefficiency of traditional methods in data processing. 3D dimensional measurement of curved surfaces requires processing massive amounts of point cloud data, especially in complex, high-curvature regions where the data volume grows exponentially. Existing methods are generally inefficient, particularly when dealing with large amounts of data or complex surfaces, and are easily limited by computational resources. To reduce computational complexity, traditional methods often employ low-order geometric fitting methods, such as low-order Bezier curves or polynomial fitting, to simplify the model. However, this simplification usually sacrifices fitting accuracy, leading to increased errors between the measured results and the actual dimensions. Even when using high-order curves for fitting, traditional methods lack a dynamic adjustment mechanism to control point density, making it impossible to flexibly allocate computational resources based on the geometric characteristics of different regions of the surface. Therefore, in practical applications, traditional methods face a trade-off between high accuracy and high efficiency, particularly in applications requiring real-time measurement and feedback. Furthermore, existing 3D dimensional measurement methods also exhibit significant limitations in adaptability to complex curved surface structures. Traditional methods rely on single feature extraction strategies or fixed error compensation models, which cannot effectively adapt to surface features of different types and scales, especially in complex structures with significant variations in curvature and angles. For example, the surfaces of certain special materials may deform under specific temperatures or humidity levels due to their inherent properties (such as elastic modulus and coefficient of thermal expansion), leading to inaccurate measurement results. Existing methods lack dynamic adjustment and flexibility in response to different measurement environments. Especially under conditions of drastic environmental changes, measurement accuracy is easily affected, resulting in poor stability and a lack of repeatability and reliability in the measurement results. Summary of the Invention

[0004] The purpose of this invention is to provide a 3D dimension measurement method suitable for curved surface structures, thereby addressing some of the drawbacks and shortcomings pointed out in the background art.

[0005] The present invention solves the above-mentioned technical problems by adopting the following technical solution: a 3D dimension measurement method applicable to curved surface structures, including: S1, multi-view curved surface reconstruction:

[0006] S1.1. The target surface is captured using a camera and laser scanner; point cloud data is generated using structured light.

[0007] S1.2 Using the SIFT feature matching algorithm, point cloud registration is performed between multiple views to generate a unified point cloud model;

[0008] S2, Intelligent Feature Recognition and Parametric Modeling:

[0009] S2.1 Utilize deep learning algorithms to train a feature recognition model and extract key geometric features of the surface;

[0010] S2.2. Identify surface features with different edges, angles, and curvatures through labeling and classification, and transform the features into mathematical representations using the parametric modeling method of Bezier curves;

[0011] S3. Size measurement based on error model:

[0012] S3.1 Establish a comprehensive error model to evaluate multiple error sources, including the geometric error of the scanner itself, deformation caused by material properties, and the influence of environmental factors; fit the error propagation function using experimental data;

[0013] S3.2. Adjust the dimensional measurements using the least squares method;

[0014] S4. Dynamic Adjustment and Feedback Control:

[0015] S4.1 Introduce a real-time data acquisition and feedback system, using temperature and humidity sensors to monitor environmental changes, and adjust scanning parameters including scanning speed and light source brightness through a PID controller.

[0016] Furthermore, the intelligent feature recognition and parameterized modeling include:

[0017] A multi-scale analysis strategy is introduced to enable the neural network to extract local feature information at different scales. This strategy extracts features at different levels by introducing convolutional layers, allowing the identification of edges, angles, and curvature information in the surface at a fine scale. For local curvature regions of the surface, the second derivative is calculated and adaptively adjusted to identify local surface features. The local curvature is calculated using the following formula:

[0018]

[0019] Among them, C local (x,y) represents the local curvature of the surface at position (x,y); It represents the second derivative of the surface height function Z(x,y) in the x-direction, and is used to calculate the curvature change of the surface; This represents the second derivative of the surface height function Z(x,y) in the y-direction; w i The weights of local features represent the degree of influence of a feature within a specific region, and are typically dynamically adjusted based on the geometric properties of the surface; A i The area of ​​region i is used to weigh the spatial factors in the calculation of local curvature.

[0020] Furthermore, the intelligent feature recognition and parameterized modeling include:

[0021] Local surface fitting is performed by selecting Bezier curves; the density of control points is dynamically adjusted according to different surface characteristics; high-order Bezier curves are used to fit surface changes; while in flat or low-curvature regions, low-order Bezier curves are used to simplify modeling; a parametric modeling method using Bezier curves is employed, and control points are interpolated and surface fitted in each local region using the following formula:

[0022]

[0023] Among them, S Bezier (u,v) represents the values ​​of the Bezier surface with respect to the parameters u and v, i.e., the geometry of the local surface;

[0024] P ij These represent control points on a Bezier surface, whose positions and numbers are adaptively adjusted according to the surface characteristics; the density of control points is greater in high curvature regions and sparser in flat regions. Let m denote the Bezier basis function, the i-th basis function on parameter u, with order m; Let m represent the Bezier basis function, the j-th basis function on parameter v, with order n; m and n represent the order of the surface in the u and v directions, respectively, which are adjusted according to the changes in surface characteristics.

[0025] Furthermore, the intelligent feature recognition and parameterized modeling include:

[0026] By analyzing the changes in angle and curvature in different regions of the surface, the number and density of control points are dynamically adjusted; the mechanism of dynamic control point adjustment can be expressed by the following formula:

[0027]

[0028] Density controlpoints This indicates the density of control points, i.e., the spacing or density between control points; Z(x,y) represents the second derivative of the surface height function Z(x,y) in the x-direction, reflecting the degree of change of the surface in the x-direction; Z(x,y) represents the second derivative of the surface height function Z(x,y) in the y direction, reflecting the degree of change of the surface in the y direction; n represents the number of sample points in the surface calculation region, which is the total number of local feature points in the region.

[0029] Furthermore, the dimension measurement method based on the error model includes:

[0030] A comprehensive error model is established to integrate the combined effects of the scanner, materials, and environment on the measurement results; the model is expressed in the following form:

[0031] E total =f(E scanner E material E environment )

[0032] Among them, E total E represents the final overall error, indicating the deviation between the measured result and the true value. scanner Geometric errors caused by the scanner originate from hardware problems or improper calibration of the scanner; E material This indicates the error caused by material properties, including changes in thermal expansion and elastic modulus at different temperatures; E environment Errors caused by environmental factors include the impact of changes in environmental conditions such as temperature and humidity on the measurement; f(·) is the error propagation function, which describes the interaction between different error sources and their contribution to the final measurement error.

[0033] Furthermore, the dimension measurement method based on the error model includes:

[0034] Experimental data provides error performance under different conditions and with different materials, allowing the error propagation function to be dynamically adjusted according to actual measurement conditions. Through regression analysis, the form of the error propagation function is fitted, expressed as:

[0035] ΔD=α1·E scanner +α2·E material +α3·E environment +∈

[0036] Where ΔD represents the deviation in dimensional measurement, i.e., the difference between the corrected measurement result and the true value; α1, α2, and α3 are regression coefficients, representing the degree of influence of scanner, material, and environmental factors on the measurement deviation, respectively; the regression coefficients are obtained by fitting experimental data and quantify the contribution of each error source to the final error; E scanner E material E environment These represent errors caused by scanner, material, and environmental factors, respectively; ∈ represents the fitting error, indicating the deviation between the error propagation function and the actual experimental data.

[0037] Furthermore, the dimension measurement method based on the error model includes:

[0038] The error propagation function is obtained, and regression coefficients are fitted based on experimental data. Size correction is then performed using the data. Parameters are optimized by minimizing the sum of squared errors between model predictions and actual measurements. Size measurements are adjusted using the least squares method, achieving the following objective function:

[0039]

[0040] in, This represents the corrected dimensional measurement result; the dimensional value obtained through least squares optimization to minimize error; D i It is the i-th data point in the original experimental measurement data, representing the original measurement result without error correction; The predicted value is calculated by the error propagation function and is dynamically adjusted according to the influence of error sources such as scanner, materials and environment; n is the number of experimental data points, that is, the number of samples used for training and optimization.

[0041] This invention offers a significant advantage in 3D dimensional measurement of curved surfaces. Firstly, it effectively extracts and processes complex geometric features of curved surfaces through intelligent feature recognition and parametric modeling. Especially with the support of multi-scale analysis and dynamic adjustment of control point density, it enables adaptive fitting of different curvature regions, thereby improving the accuracy of surface modeling. Secondly, this invention introduces a comprehensive error model, systematically considering the influence of scanner, material properties, and environmental factors on measurement accuracy. By fitting the error propagation function with experimental data and dynamically adjusting the regression coefficients, the model can adapt to different measurement conditions. Thirdly, through optimization using the least squares method, the bias of error sources on dimensional measurement is further reduced, improving the accuracy and stability of the measurement results. This method exhibits high adaptability under various environmental and material conditions, and is particularly suitable for the precise measurement of complex curved surfaces in industrial environments. It meets the demand for high-precision and high-efficiency 3D dimensional measurement, significantly improving the reliability and applicability of the measurement system. Furthermore, its automated and intelligent processing greatly reduces human intervention, making it more advantageous in practical operation. Attached Figure Description

[0042] Figure 1 This is a flowchart of the 3D dimension measurement method for curved surface structures according to the present invention.

[0043] Figure 2 This is a flowchart of the intelligent feature recognition and parametric modeling process of the present invention.

[0044] Figure 3 This is a flowchart of the dimension measurement method based on the error model of the present invention. Detailed Implementation

[0045] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0046] Combined with appendix Figure 1In this invention, the first step in a 3D dimension measurement method applicable to curved surfaces is multi-view surface reconstruction. This process mainly involves acquiring information about the target curved surface from different angles and integrating the data from different perspectives into a unified 3D point cloud model using an algorithm. Step S1.1 involves using a camera and laser scanner to capture the target curved surface and generating point cloud data using structured light. Structured light is a commonly used technique in 3D scanning. It projects light of a known pattern onto the surface of an object, then uses a camera to capture the reflected light, thereby calculating the 3D coordinates of the surface. Combining the use of a camera and laser scanner allows for efficient capture of every detail on the curved surface and generation of corresponding point cloud data. Point cloud data refers to a model composed of a set of discrete points in 3D space, each point having 3D coordinates (X, Y, Z). These points are obtained through the measurement process of a laser scanner or structured light, accurately reflecting the geometry of the object's surface, and the resolution can be adjusted as needed to ensure sufficient accuracy. Next, S1.2 achieves point cloud registration using the SIFT (Scale-Invariant Feature Transform) algorithm. SIFT is a feature matching algorithm widely used in computer vision, particularly adept at extracting and matching feature points from different viewpoints. During multi-view shooting, the target surface will produce different image data due to different viewpoints. The SIFT algorithm can find the same feature points from different viewpoints, thus achieving point cloud matching. The SIFT algorithm possesses scale invariance, rotation invariance, and partial illumination invariance, enabling it to effectively extract stable feature points when processing image data acquired from different angles and under different lighting conditions, thereby achieving accurate point cloud registration across multiple views. In this way, point cloud data captured from different viewpoints are stitched together to generate a unified and complete point cloud model. This point cloud model contains all the geometric information of the target surface and forms the basis for further 3D reconstruction and dimensional measurement. In this process, the accuracy of point cloud registration directly determines the accuracy of the final surface model. Therefore, it is necessary to use efficient and accurate algorithms to handle the matching problem, ensure that the registration error between point clouds is minimized, and thus improve the accuracy and reliability of the entire 3D reconstruction process.

[0047] The second step is intelligent feature recognition and parametric modeling. The core purpose of this process is to identify and extract key geometric features from the target surface using deep learning algorithms, and to transform these features into mathematical representations for further dimensional measurement and model analysis. S2.1 First, a feature recognition model is trained using deep learning algorithms to extract key geometric features of the surface from the acquired 3D point cloud data. These features include the surface's edges, angles, curvature, etc., which are important indicators of the surface's shape and determine its geometric properties and structural characteristics. To achieve this goal, deep learning models, especially convolutional neural networks (CNNs), are widely used in feature extraction tasks for images and 3D data. Through extensive training data, deep learning models can learn how to identify these key geometric features from surface point cloud data without human definition or manual extraction. This process effectively solves the problem of relying on human experience for feature recognition in traditional methods, improving the automation and accuracy of feature extraction. S2.2 Further, different surface features, including edges, angles, and curvature, are identified through labeling and classification, and these identified features are transformed into mathematical models. Specifically, edge regions typically exhibit significant curvature variations, while angular changes represent local shape changes on the surface, and curvature reflects the overall bending degree of the surface. Classifying these features helps to better understand the morphology of the surface and the geometric properties of its various parts. Subsequently, parametric modeling using Bezier curves is employed to transform these geometric features into mathematical representations. Bezier curves are a common type of parametric curve widely used in surface modeling, offering flexible curve fitting through control points and providing good accuracy and controllability. In this method, a suitable Bezier curve is selected for local fitting based on features identified on the surface, such as edges and curvature. By adjusting the control points and order of the Bezier curve, the local features of the surface can be accurately described; for example, increasing the density of control points in edge regions to accommodate curvature variations and reducing control points in flat regions to simplify the model. Finally, these local Bezier curves are combined to form a complete parametric surface model. This model not only accurately describes the shape of the surface but also, due to the parametric nature of Bezier curves, offers good flexibility and operability, facilitating subsequent dimensional measurements and surface analysis.

[0048] The third step is dimensional measurement based on an error model. This aims to evaluate and adjust various error sources that arise during the measurement process by establishing a comprehensive error model, ensuring more accurate dimensional data. S3.1 First, a comprehensive error model is established, and multiple error sources are evaluated. Specifically, error sources can be categorized into several types, including geometric errors of the scanner itself, deformation caused by material properties, and the influence of environmental factors. Scanner geometric errors typically include systematic and random errors, caused by the equipment's accuracy, inaccurate sensor calibration, or any mechanical errors occurring during the scanning process. Furthermore, deformation caused by material properties includes surface deformation due to the material's elasticity, thermal expansion, or other physical properties. This error varies under different environmental conditions, such as temperature and humidity. The influence of environmental factors, such as temperature changes, lighting conditions, or air humidity, can also lead to inconsistencies in scanning data, thus affecting measurement accuracy. To comprehensively evaluate these error sources, experimental data is needed. Through analysis of multiple measurement results, an error propagation function is fitted. The error propagation function is a mathematical model used to describe the impact of each error source on the final measurement result, quantifying the contribution of each error source to the overall measurement accuracy. By analyzing the contribution of different error sources, we can accurately understand the specific impact of each error on the measurement results and provide a basis for subsequent error correction. S3.2 The least squares method is used to adjust the dimensional measurement. The least squares method is a commonly used mathematical optimization method, mainly used to find the parameters that best match the actual situation in data with large errors. During the dimensional measurement process, the measured data is compared with the expected true value through the established error model, and the error between the measured result and the true value is calculated. The basic principle of the least squares method is to obtain the optimal solution by minimizing the sum of squared errors, that is, by weighting all measurement data and adjusting the model parameters to minimize the error. In this way, deviations caused by various error sources can be eliminated, thereby improving the measurement accuracy. For example, when measuring the dimensions of curved surfaces, the least squares method can be used to adjust the scanning data to minimize deviations caused by scanner geometric errors or material deformation, ensuring that the final measured dimensions are more accurate. With the support of a comprehensive error model, the least squares method can effectively reduce the propagation of errors, making the measurement results more consistent with the geometric characteristics of the actual object, and improving the accuracy and reliability of curved surface dimensional measurement.

[0049] The fourth step is dynamic adjustment and feedback control, which aims to ensure that all conditions during the measurement process are always maintained in an optimal state by monitoring environmental changes in real time and dynamically adjusting scanning parameters, thereby improving the accuracy and stability of the measurement. S4.1 first introduces a real-time data acquisition and feedback system to continuously monitor changes in the measurement environment, especially factors such as temperature and humidity, which have a significant impact on the scanning results. For example, fluctuations in temperature and humidity affect the accuracy and stability of the laser scanner. In particular, the propagation characteristics of the laser beam, surface reflectivity, and physical properties of materials all change with environmental conditions during the scanning process. Therefore, these factors need to be monitored in real time. By placing temperature and humidity sensors in the measurement environment, real-time data of environmental parameters can be accurately acquired and transmitted to the system for processing. Based on the real-time temperature and humidity data, the system identifies environmental changes affecting measurement accuracy and makes corresponding adjustments. S4.1 involves adjusting scanning parameters, including scanning speed and light source brightness, using a PID controller (proportional-integral-derivative controller). The PID controller is a classic feedback control method widely used in the real-time adjustment of dynamic systems. By adjusting the control variables through feedback regulation of measurement errors, the system stabilizes and reaches its optimal operating state. In this application, the PID controller adjusts scanning parameters such as scanning speed and light source brightness based on real-time data of environmental changes to ensure the scanning process remains in optimal condition. Specifically, the PID controller calculates the necessary adjustments to the scanning parameters based on current environmental changes (such as temperature and humidity) and regulates these parameters through proportional, integral, and derivative components. The proportional component adjusts the parameters based on the current error magnitude, the integral component accumulates past errors to eliminate long-term deviations, and the derivative component predicts future error trends and responds in advance. Through this precise control, the PID controller can achieve rapid real-time adjustments, maintaining consistent scanning accuracy under changing environmental conditions. Ultimately, through the combined effect of real-time data acquisition, environmental monitoring, and PID control, scanning parameters can be dynamically adjusted during the measurement process, effectively offsetting the influence of the external environment on measurement accuracy and ensuring that the results of each scan remain within the required accuracy range.

[0050] Example 1:

[0051] Combined with appendix Figure 2In this embodiment, intelligent feature recognition and parametric modeling are key technologies in the 3D dimensional measurement method applicable to curved surfaces. These technologies enable accurate extraction and modeling of the geometric features of the curved surface. In particular, the introduction of a multi-scale analysis strategy allows the neural network to extract local feature information at different scales, thereby improving the recognition capability of curved surface features. In practical applications, a complex metal component surface is considered, exhibiting different curvature regions, especially at curved edges and corners. The geometric features of these regions are crucial for the final dimensional measurement.

[0052] First, point cloud data of the target surface was acquired using a multi-view laser scanning device. This data contains detailed geometric information of different regions, and due to errors during the scanning process, the surface data contains some irregularities and noise. Therefore, the use of intelligent feature recognition and parametric modeling methods is crucial. To improve the accuracy of surface feature extraction, a multi-scale analysis strategy was adopted, introducing progressive extraction of features at different levels in different convolutional layers of the neural network, allowing information such as edges, angles, and curvature to be fully identified at a fine scale. For example, in higher-level convolutional layers, the neural network identifies large-scale features including the overall contour and large curvature regions of the surface, while in lower-level convolutional layers, it focuses on minute local changes and detailed features. This enables the extraction of accurate geometric information on complex surfaces, especially in areas with dramatic curvature changes.

[0053] For regions of local curvature on the surface, the second derivative is further calculated and adaptively adjusted. This process helps to capture local changes more accurately, especially in areas where the surface changes rapidly. The formula for calculating local curvature is as follows:

[0054]

[0055] In this formula, C local (x,y) represents the local curvature of the surface at position (x,y). and Let represent the second derivatives of the surface height function Z(x,y) in the x and y directions, respectively. These derivatives are used to calculate the curvature changes of the surface. The second derivative of a surface reflects its degree of curvature and can accurately capture the drastic nature of surface changes. i These are the weights of local features, representing the degree of influence of each feature within a specific region. They are typically dynamically adjusted based on the geometric properties of the surface. For example, weights are larger in regions of high curvature and smaller in flat regions. i This is the area of ​​region i, used to balance spatial factors in local curvature calculation. This area provides more precise spatial adjustments when the surface changes significantly, thereby further optimizing the calculation of local curvature.

[0056] Measurements were taken on a curved area of ​​a metal plate. First, point cloud data of the area was acquired through scanning, resulting in a 3D model containing multiple data points. When processing this data, a neural network extracted feature information of the curved area through multi-scale analysis, particularly noting the significant curvature changes at the edges. Then, the local curvature was calculated, and the height function at a specific location (x, y) was set as Z(x, y) = 3x. 2 +4y 2 Its second derivative is:

[0057]

[0058] Setting the weight at this location w1 = 0.8 and the area of ​​the region A1 = 2, the local curvature is calculated as follows:

[0059] C local (x,y)=0.8×(6+8)×2=22.4

[0060] This method allows for the accurate identification and adjustment of local features of a surface, particularly in areas with significant curvature variations. Thus, throughout the entire 3D dimensional measurement process, the fitting parameters of the scanning model can be adjusted based on changes in local curvature, ensuring more precise measurement results.

[0061] Not only is it necessary to accurately capture surface features, but it's also crucial to efficiently fit and model the surface. In this process, the parametric modeling method using Bezier curves plays a vital role, especially for surface regions with complex variations. Consider a metal component being measured, containing multiple surface variations, some areas exhibiting high curvature while others are relatively flat. In this case, using Bezier curves helps to better adapt to the geometric characteristics of different regions.

[0062] First, when modeling the surface, Bezier curves are used to fit local regions. Bezier curves themselves have good interpolation performance and can accurately describe the geometry of the surface. Each local region is first segmented, and then Bezier curves of different orders are selected for fitting based on the curvature characteristics of each region. For high-curvature regions, the order of the Bezier curve is usually higher to more accurately describe the abrupt changes in the surface, while for flat regions, the order of the Bezier curve is lower to simplify calculations and improve efficiency.

[0063] The model is designed to fit a region with high curvature using a fourth-order Bezier curve. The formula for the Bezier curve is:

[0064]

[0065] Among them, S Bezier (u,v) represents the values ​​of the Bezier surface with respect to parameters u and v, i.e., the geometry of the local surface; P ij These are the coordinates of the control points, representing the specific shape of the surface; and These are the Bezier basis functions, the i-th and j-th basis functions in the u and v directions, with orders m and n respectively; m and n represent the order of the surface in the u and v directions, which are usually adjusted according to the changes in the surface characteristics.

[0066] When the surface is in a high-curvature region, the density of control points is increased. For example, if there are 16 control points in a certain region, these control points will be distributed more densely to better fit the surface. The settings of m=4 and n=4 mean that fourth-order Bezier basis functions are used for fitting in the u and v directions respectively. By comparison, the Bezier fitting results set in this region closely match the actual surface, significantly reducing errors caused by low-order curve fitting.

[0067] On the other hand, for flat regions, low-order Bezier curves (such as second-order curves) are used for fitting. In such regions, the surface changes little, and low-order curves can meet the requirements while reducing computational complexity. For example, if a second-order Bezier curve is used to fit a flat region, the number of control points is reduced to 4, and its parameters are set as follows:

[0068]

[0069] In this way, the density of control points can be dynamically adjusted to adapt to different surface features, ensuring the accuracy of the fitting results.

[0070] First, the scanned point cloud data is used to extract local features at different scales through a multi-scale analysis strategy in a neural network. Then, an appropriate Bezier curve order and control point density are selected based on the changes in the curved region. In regions with high curvature, fine fitting is achieved by increasing the density of control points and the order of the Bezier curve, while in flat regions, the modeling is simplified by reducing the order and control point density, thus balancing accuracy and computational efficiency.

[0071] The surface of a metal gear is measured. The edges of the gear have a large curvature, while the tooth surface is relatively flat. In the edge region, a fourth-order Bezier curve is selected, and the density of control points is increased through algorithms to make it more accurate in subtle surface changes. In the tooth surface region, a second-order Bezier curve is used for fitting, which reduces the amount of computation while maintaining relatively accurate modeling results.

[0072] The dynamic control point adjustment mechanism of Bezier curves is crucial for applications across different surface regions, especially when the geometric characteristics of the surfaces vary significantly. Previous steps have introduced how to select an appropriate Bezier curve order based on surface curvature. The key at this stage is to dynamically adjust the number and density of control points according to the angle and curvature changes of the surface region, thereby ensuring a more accurate and efficient fitting effect for each local region.

[0073] The scenario involves 3D dimensional measurement of a metal mold, which contains multiple curved surface regions of varying shapes: the outer contour of the mold has significant curvature and exhibits subtle deformation, while the inner surface is relatively flat. To handle this complex surface morphology, a dynamic adjustment mechanism is needed to adjust the density of control points based on local curvature and angle variations. In this process, the density of control points is calculated by analyzing the second derivative of the surface at different locations, and this density value is used to determine the number and spacing of control points, thereby achieving accurate local fitting.

[0074] Specifically, the formula for calculating the local curvature of a surface is:

[0075]

[0076] In this formula, Density controlpoints The density of control points reflects the spacing or density of control points within the curved surface region; and These are the second derivatives of the surface in the x and y directions, respectively, representing the degree of change of the surface in these two directions; while n represents the number of sample points in the computational region, i.e., the total number of local feature points.

[0077] Measurements were taken at a highly curved edge region of the mold, revealing that the second derivative of this region varied by 0.15 in the x-direction and 0.2 in the y-direction. Substituting these values ​​into the formula above, the control point density for this region can be calculated.

[0078]

[0079] This means that a relatively dense set of control points is needed in this area to accurately fit the surface shape, thereby ensuring that the modeling of the high curvature section does not produce large errors.

[0080] Next, the control point density is applied to the actual Bezier curve fitting. A fourth-order Bezier curve is selected for this high-curvature region, and based on the calculated control point density, the number of control points is set to 16. Increasing the control point density allows for better capture of subtle curvature variations in this region. The formula for the Bezier curve is as follows:

[0081]

[0082] Among them, P ij It refers to the location of the control points. and These are Bezier basis functions, where m and n are the orders of the Bezier curve in the u and v directions, respectively. A fourth-order curve is chosen for fitting, therefore the values ​​of m and n are both 4.

[0083] For relatively flat areas inside the mold, the value of the second derivative will be smaller; for example, the second derivative in the x-direction is 0.05, and the second derivative in the y-direction is also 0.05. Based on the formula, the density of control points is calculated as follows:

[0084]

[0085] In this flat region, the density of control points is high, so a lower-order Bezier curve (such as a second-order curve) can be used for fitting, thereby reducing the computational cost. In the fitting process, a second-order Bezier curve was selected, reducing the number of control points to four, and the geometry of the region was calculated.

[0086] By dynamically adjusting the density of control points, Bezier curves of different orders were used to accurately fit the surface in different curvature regions. In high curvature regions, dense control points and high-order Bezier curves ensured measurement accuracy; while in flat regions, lower-order Bezier curves and sparse control points reduced computational complexity while still maintaining relatively accurate modeling results.

[0087] Ultimately, this method not only improved the overall measurement accuracy but also effectively reduced the computational burden, enabling the completion of 3D dimensional measurement of the metal mold.

[0088] Example 2:

[0089] See Figure 3This embodiment will illustrate how a comprehensive error model can be used to evaluate and adjust the combined effects of scanner, material properties, and environmental factors on the final measurement results through the 3D dimensional measurement process of a metal mold. In applications, the complexity of the mold and the variable working environment result in a variety of error sources, including geometric errors of the scanner itself, thermal expansion and elasticity changes caused by material properties, and the influence of environmental changes (such as temperature and humidity). Therefore, by establishing a comprehensive error model, these error sources can be effectively combined, thereby optimizing the measurement results.

[0090] First, let's start with the error E caused by the scanner. The scanner used is a high-precision laser scanner, which...

[0091] scanner

[0092] Even after calibration, minor geometric errors may still exist, typically including equipment accuracy errors and equipment calibration errors. For example, a scanner's calibration error can cause deviations between measurement points, with an error set at ±0.05 mm. This error can be determined by the equipment's resolution and calibration error model; generally, the hardware error of a scanner under standard test conditions ranges from 0.01 mm to 0.1 mm.

[0093] Next is the error E caused by material properties. material The measurement was conducted on an aluminum alloy mold, whose elastic modulus and coefficient of thermal expansion are significantly affected by temperature changes. In actual measurements, with fluctuations in ambient temperature, the coefficient of thermal expansion of the aluminum alloy was approximately α. Al =23×10 -6 ℃ -1 This means that for every 1°C increase, the length of the aluminum alloy will expand by approximately 0.023 mm. By setting the mold temperature to increase from 20°C to 25°C, the thermal expansion error of the material can be calculated using the formula:

[0094] ΔL=L0·α Al ·ΔT

[0095] Where L0 = 500mm is the initial length of the mold, and ΔT = 5℃ is the temperature change. Substituting the data, the thermal expansion error is:

[0096] ΔL=500mm×23×10 -6 ℃ -1 ×5℃=0.0575mm

[0097] This means that under this temperature change, the size of the aluminum alloy mold will increase by approximately 0.0575 mm.

[0098] Finally, consider the error E caused by environmental factors. environmentEnvironmental temperature and humidity changes have a significant impact on measurement results. The measured environment was designed to have a large humidity variation, ranging from 50% to 80%, which can cause minute deformations in the metallic material or amplify scanning errors. For example, humidity changes can lead to variations in moisture adsorption in the material, causing slight deviations in the measurement point's location. The error caused by this humidity variation was set at ±0.03 mm, obtained through modeling environmental condition changes and actual experimental data.

[0099] Now, the total error is estimated by incorporating the above error sources into a comprehensive error model. Based on the given model:

[0100] E total =f(E scanner E material E environment )

[0101] The error propagation function f is set to be a linear weighted sum, where the weight of each error source depends on its contribution to the final measurement. The scanner error is weighted at 0.6, the material error at 0.3, and the environmental error at 0.1. Thus, the total error can be expressed by the following formula:

[0102] E total =0.6·E scanner +0.3·E material +0.1·E environment

[0103] After substituting the values, we get:

[0104] E total =0.6·0.05mm+0.3·0.0575mm+0.1·0.03mm

[0105] =0.03mm+0.01725mm+0.003mm=0.05025mm

[0106] Therefore, the final overall error is approximately 0.05025 mm. This means that after comprehensively considering the effects of scanner error, material thermal expansion error, and changes in ambient humidity, the measurement error is approximately 0.05025 mm. In this way, errors caused by different factors can be estimated and corrected more accurately, thereby improving the overall measurement accuracy.

[0107] To further improve the model's accuracy, experimental data will be used to dynamically adjust the error propagation function under different material and environmental conditions, thereby achieving adaptability to various measurement conditions. This process utilizes regression analysis to fit the error propagation function, enabling the model to dynamically reflect error performance under different conditions.

[0108] The mold dimensions were measured using three different materials (aluminum alloy, stainless steel, and carbon fiber), each exhibiting varying behavior under environmental factors such as temperature and humidity. To quantify the impact of each factor on the final error, multiple experimental measurements were conducted on each material, collecting error data under different environmental conditions (e.g., temperature between 20°C and 30°C, and humidity between 40% and 80%). This experimental data will provide the model with a realistic representation of the error, thereby supporting the fitting of the error propagation function.

[0109] In model fitting, the error propagation function takes the form:

[0110] ΔD=α1·E scanner +α2·E material +α3·E environment +∈

[0111] Where ΔD represents the measurement bias, i.e., the difference between the corrected measurement result and the true value; α1, α2, and α3 are regression coefficients, obtained by fitting experimental data, representing the degree of influence of each error source on the measurement bias. E scanner E material and E environment These represent errors caused by scanner, material, and environmental factors, respectively, while ∈ represents the fitting error, reflecting the deviation between the error propagation function and the actual experimental data.

[0112] After experimental fitting, the following regression coefficient ranges were obtained: α1 between 0.5 and 0.7, α2 between 0.2 and 0.4, and α3 between 0.1 and 0.2. These different ranges reflect the degree of contribution of each error source to the final measurement error. In a certain measurement, the scanner's geometric error was set to 0.06 mm, the material's thermal expansion error to 0.04 mm, and the error caused by environmental humidity to 0.02 mm.

[0113] Based on the form of the error propagation function fitted in the experiment, substitute the data into the formula and select the intermediate values ​​for calculation. Set α1 = 0.6, α2 = 0.3, and α3 = 0.15, then the total error deviation is:

[0114] ΔD=0.6·0.06mm+0.3·0.04mm+0.15·0.02mm=0.036mm+0.012mm+0.003mm

[0115] =0.051mm

[0116] In this way, the total measurement error deviation can be obtained as 0.051 mm. This indicates that the error propagation function, after fitting experimental data under different conditions, has the ability to dynamically adjust the model's error assessment capability under various environmental and material conditions.

[0117] Continuing with the application of 3D dimensional measurement of the aforementioned metal mold, the contribution of different error sources to the measurement deviation has been estimated by fitting the error propagation function and regression coefficients, yielding a total error deviation of 0.051 mm. Next, these data will be used for dimensional correction, and the least squares method will be introduced to further optimize the results, making the measured values ​​closer to the true dimensions.

[0118] In this step, size correction optimizes parameters by minimizing the sum of squared errors between model predictions and actual measurements. The measurements are adjusted using the least squares method, with the goal of minimizing the sum of squared errors across all experimental data points. The least squares method helps find the optimal measurement result that minimizes the overall error, thereby improving measurement accuracy.

[0119] In this series of measurements, n experimental data points were obtained under different environmental conditions and material types, and the uncorrected measurement result for each data point is D. i Based on the error propagation function model, the predicted value... It can be represented as:

[0120]

[0121] Where α1, α2, and α3 are the regression coefficients obtained through experimental fitting, and ∈ represents the fitting error. By comparing these predicted values ​​with the actual measured values, a least-squares objective function can be established:

[0122]

[0123] In this formula, This is the corrected dimensional measurement result, with the goal of minimizing the sum of squared errors across all experimental data points. D i These are the raw data points from the experiment, the measurement results without error correction. These are predicted values ​​calculated using the error propagation function. Adjusting these values ​​using the least squares method can minimize the error.

[0124] The collected measurement data will include the following samples:

[0125] Data point 1: D1 = 100.12 mm

[0126] Data point 2: D2 = 100.08 mm

[0127] Data point 3: D3 = 100.15mm

[0128] At each data point, a predicted value can be obtained using the previously fitted error propagation function. The predicted values ​​for these data points are calculated as follows:

[0129]

[0130] Next, calculate the sum of squared least-squares errors:

[0131] Sum of squared errors = (100.12 - 100.10) 2 +(100.08-100.07) 2 +(100.15-100.12) 2

[0132] =(0.02) 2 +(0.01) 2 +(0.03) 2 =0.0004 + 0.0001 + 0.0009 = 0.0014

[0133] By minimizing the sum of squared errors, the optimal size correction value can be found, making the overall measurement results more accurate. This process can be continuously iterated and optimized using new experimental data, further improving the model's accuracy under different conditions. The use of the least squares method not only improves the accuracy of the measurement data but also further reduces the deviation caused by different error sources, providing a reliable foundation for the final 3D size measurement. Therefore, using the least squares method to correct the size of the measured values ​​can make the measurement results closer to the actual size.

[0134] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A 3D dimension measurement method applicable to curved surface structures, characterized in that... Includes the following steps: S1. Multi-view surface reconstruction: S1.

1. Use a camera and laser scanner to capture the target surface; use structured light to generate point cloud data; S1.2 Using the SIFT feature matching algorithm, point cloud registration is performed between multiple views to generate a unified point cloud model; S2, Intelligent Feature Recognition and Parametric Modeling: S2.1 Utilize deep learning algorithms to train a feature recognition model and extract key geometric features of the surface; S2.

2. Identify surface features with different edges, angles, and curvatures through labeling and classification, and transform the features into mathematical representations using the parametric modeling method of Bezier curves; S3. Size measurement based on error model: S3.1 Establish a comprehensive error model to evaluate multiple error sources, including the geometric error of the scanner itself, deformation caused by material properties, and the influence of environmental factors; fit the error propagation function using experimental data; S3.

2. Adjust the dimensional measurements using the least squares method; S4. Dynamic Adjustment and Feedback Control: S4.1 Introduce a real-time data acquisition and feedback system, using temperature and humidity sensors to monitor environmental changes, and adjust scanning parameters including scanning speed and light source brightness through a PID controller; The intelligent feature recognition and parameter modeling include: A multi-scale analysis strategy is introduced to enable the neural network to extract local feature information at different scales. The multi-scale strategy extracts features at different levels step by step by introducing convolutional layers, so that the edge, angle and curvature information in the surface can be identified at a fine scale. For the local curvature region of the surface, the second derivative of the height function at multiple sampling points is calculated to identify the local surface features. The local curvature C local Calculated using the following formula: in: N represents the total number of sample points involved in the curvature calculation; i is the number of the i-th sample point, (x i ,y i Z(x,y) represents the location; Z(x,y) is the surface height function. and Let w represent the second derivatives of the height function along the x and y directions at point i, respectively; i The local weight of point i is dynamically adjusted based on geometric feature strength or distance attenuation; A i The area of ​​the region corresponding to point i is used to balance the spatial factors in the calculation of local curvature; Local surface fitting is performed by selecting Bezier curves; the density of control points is dynamically adjusted according to different requirements of surface characteristics; high-order Bezier curves are used for fitting in high curvature regions, while low-order Bezier curves are used to simplify modeling in flat or low-curvature regions. By analyzing the changes in angle and curvature in different regions of the surface, the number and density of control points are dynamically adjusted; the adjustment mechanism of the control point density can be expressed by the following formula: in: Density controlpoints Z(x,y) represents the density of control points, i.e., the spacing or density between control points; Z(x,y) is the surface height function; N represents the total number of sample points involved in the calculation; and i is the number of the i-th sample point.

2. The 3D dimension measurement method for curved surface structures according to claim 1, characterized in that... The fitting process employs a parametric modeling method using Bezier curves, performing control point interpolation and surface fitting in each local region using the following formula: in: S Bezier (u,v) represents the function values ​​of the Bezier surface at parameters u and v, representing the local surface geometry at that point; P ij These represent control points, the position and number of which adaptively change according to the surface characteristics. and These are the Bezier basis functions in the directions of parameters u and v, respectively, with orders m1 and m2; m1 and m2 represent the orders of the Bezier curves in the u and v directions, which are adjusted according to the local curvature.

3. The 3D dimension measurement method for curved surface structures according to claim 1, characterized in that... The error model-based dimensional measurement method includes: establishing a comprehensive error model to integrate the combined effects of the scanner, material, and environment on the measurement results; the model is represented in the following form: AND total =f(E scanner ,AND material ,AND environment ) Among them, E total E represents the final overall error, indicating the deviation between the measured result and the true value. scanner Geometric errors caused by the scanner originate from hardware problems or improper calibration of the scanner; E material This indicates the error caused by material properties, including changes in thermal expansion and elastic modulus at different temperatures; E environment Errors caused by environmental factors include the impact of changes in temperature and humidity on the measurement; f(·) is the error propagation function, which describes the interaction between different error sources and their contribution to the final measurement error.

4. The 3D dimension measurement method for curved surface structures according to claim 3, characterized in that... The dimension measurement method based on the error model includes: Experimental data provides error performance under different conditions and with different materials, allowing the error propagation function to be dynamically adjusted according to actual measurement conditions. Through regression analysis, the form of the error propagation function is fitted, expressed as: ΔD=α1·E scanner +α2·E material +α3·E environment +∈ Where ΔD represents the deviation in dimensional measurement, i.e., the difference between the corrected measurement result and the true value; α1, α2, and α3 are regression coefficients, representing the degree of influence of scanner, material, and environmental factors on the measurement deviation, respectively; the regression coefficients are obtained by fitting experimental data and quantify the contribution of each error source to the final error; E scanner E material E environment These represent errors caused by the scanner, materials, and environmental factors, respectively; ∈ represents the fitting error, indicating the deviation between the error propagation function and the actual experimental data.

5. The 3D dimension measurement method for curved surface structures according to claim 4, characterized in that... The dimension measurement method based on the error model includes: obtaining the error propagation function, fitting regression coefficients based on experimental data, and then using the data to correct the dimensions; optimizing parameters by minimizing the sum of squared errors between the model predictions and the actual measurements; and adjusting the dimension measurements using the least squares method.

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