A rapid texture mapping method for cross-section members such as bridges
By using image point cloud generation and multi-stage geometric prior registration, an efficient and structured bridge texture mapping model is generated, which solves the problems of computational redundancy and poor reconstruction quality in existing technologies, and realizes efficient defect measurement and geometric localization of bridge detection.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TAIYUAN UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2026-04-21
- Publication Date
- 2026-07-14
AI Technical Summary
Existing bridge inspection technologies suffer from a contradiction between computational overhead and effectiveness, a "utility mismatch" between reconstruction accuracy and engineering requirements, and fail to effectively utilize the prior information of regular geometric features of bridge components, resulting in computational redundancy and poor reconstruction surface quality.
A fast texture mapping method based on image point cloud generation, multi-stage geometric prior registration, and structured mesh generation is adopted. Sparse point clouds are generated using motion structure recovery algorithm, and efficient and structured texture mapping models are generated through geometric prior-driven registration framework and multi-stage optimization.
It significantly reduces computational overhead and improves processing efficiency. The generated model supports rapid defect measurement, provides a robust geometric basis, overcomes geometric distortion and noise problems in traditional methods, and meets the timeliness and ease of operation requirements of bridge inspection.
Smart Images
Figure CN122391454A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of bridge infrastructure inspection and maintenance technology, specifically relating to a fast texture mapping method for cross-sectional components such as bridges. Background Technology
[0002] As the lifeline of transportation infrastructure, the safety and durability of bridge structures are of paramount importance. However, during construction and long-term service, concrete structures inevitably suffer from environmental erosion and load effects, leading to defects such as cracks and spalling. If these defects are not detected and repaired in time, they may endanger structural safety or even cause serious accidents. Traditional bridge visual inspection mainly relies on manual inspection, which is not only inefficient and highly subjective, but also poses extremely high safety risks when dealing with complex structures such as high piers and long spans. Therefore, how to achieve efficient and reliable defect detection has become a focus of attention in the engineering and academic communities.
[0003] In recent years, the rapid development of computer vision and deep learning technologies has provided a new paradigm for intelligent bridge inspection, and detection methods have gradually shifted towards digital assessment based on visual data. Two-dimensional defect identification technology has matured, but it is essentially still processing pixel information, lacking the physical scale and spatial context of the real world. In practical engineering assessments, simply identifying the type of defect is insufficient; accurately acquiring the geometric features of the defects (such as true width and area) and their overall structural distribution is crucial for damage assessment and reinforcement design. Based on the sparse geometric framework established by the Motion Structure Restoration (SfM) algorithm, Multi-View Stereo (MVS) restores the fine geometric surface of the structure through dense pixel matching, which is a key step in realizing spatial quantitative analysis of defects. Depending on the algorithm logic and application focus, domestic and international scholars have conducted numerous representative studies on the application of MVS in the reconstruction of civil engineering components such as bridges. For example, in system integration, Perry et al. constructed an end-to-end bridge inspection system integrating automated defect analysis, human-machine collaborative learning, and 3D reconstruction, generating a component-level as-built model with geographic reference; Abdelazeem et al. developed a data fusion algorithm that, by optimizing the combination of ground laser scanning point clouds, UAV images, and ground camera images, reduced the registration error from 0.149 m to 0.130 m, achieving a significant improvement in the integrity of the building model; Qi et al. combined PatchMatchNet dense reconstruction with YOLOv11 detection and SeaFormer lightweight segmentation to achieve high-quality visualization of 3D crack distribution. Meanwhile, neural rendering technologies, represented by neural radiation fields and 3D Gaussian splashing, are changing the paradigm of defect manifestation through implicit expression.
[0004] Overall, while classic MVS, multi-source fusion, and deep learning reconstruction methods have made significant progress in accuracy and visual effects, they still face severe "implementation bottlenecks" in real-world bridge inspection tasks. First, there is an irreconcilable contradiction between computational overhead and timeliness. Traditional MVS dense matching processes heavily rely on high-performance GPU computing power, resulting in data processing cycles far exceeding acquisition cycles, making it difficult to achieve real-time results in resource-constrained inspection sites. Second, there is a significant "utility mismatch" between reconstruction accuracy and engineering requirements. Current MVS algorithms tend to focus on general arbitrary scene reconstruction, pursuing the ultimate detail restoration. However, the models generated by these algorithms are often unstructured dense point clouds or implicit voxels, whose surfaces often exhibit irregular "pitted" noise at the microscopic level. Finally, the lack of prior structural information leads to inefficient model construction. Existing reconstruction processes mostly follow the "no prior" principle, treating bridge components as unknown natural scenes. However, in actual engineering, bridge components have highly regular geometric characteristics, and even a large number of bridges on the same route often use standardized, similar drawings. This valuable strong geometric prior information has not been effectively utilized in existing MVS algorithms, forcing the system to deduce the known geometric topology from scratch through massive computations. This contradiction between "high computational requirements" and "unstructured output" compels us to find a lightweight reconstruction path that is more in line with engineering practice: that is, to use the geometric prior of regular components to constrain the reconstruction process, sacrificing unnecessary microscopic precision in exchange for extremely high processing efficiency and structured geometric output. Summary of the Invention
[0005] To address the problem that existing technologies cannot fully utilize geometric priors, resulting in serious computational redundancy and poor reconstructed surface quality when reconstructing a large number of components with highly repetitive geometric shapes pixel by pixel, this invention provides a fast texture mapping method for cross-sectional components such as bridges.
[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:
[0007] A fast texture mapping method for cross-sectional components such as bridges includes the following steps:
[0008] Step S1, image-based point cloud generation: The camera pose is recovered from the sequence of images using the structure-of-motion (SfM) algorithm and a preliminary sparse point cloud is generated. Then, the background environment and noise are removed through manual interactive cleaning to obtain the core point cloud data of the target bridge component.
[0009] Step S2, Multi-stage geometric prior registration: Construct a parametric prior model for the features of the component with equal cross-section. By performing axis-guided slicing on the sparse point cloud, and using a registration framework that includes coarse registration and multi-stage fine optimization, the preset model is aligned with the geometric features of the discrete point cloud.
[0010] Step S3, Structured Mesh Generation: Based on the registered cross-sectional parameters, a topologically regular structured mesh model is generated using lofting techniques;
[0011] Step S4, High-fidelity texture mapping: The generated mesh model is projected and mapped using the perspective consistency and stereo matching method of multi-view stereo vision, and a high-resolution texture map model with a realistic appearance is output.
[0012] Further, step S1 specifically includes: acquiring images of the target bridge components using an image acquisition device; performing spatial pose calculation on the images using a motion structure recovery algorithm, completing sparse reconstruction and generating the original sparse point cloud while restoring the camera's intrinsic and extrinsic parameters; and performing noise reduction processing on the original sparse point cloud using a manual interactive point cloud editing method to selectively remove irrelevant targets other than the target components.
[0013] Further, step S2 specifically includes the following steps: after obtaining the sparse point cloud of the bridge component, a registration framework driven by geometric prior is introduced; utilizing the uniform cross-sectional characteristics of the component, the three-dimensional point cloud is discretized and sliced along the principal axis; in the two-dimensional projection plane of each slice, a preset polyline template is registered with the measured sparse point cloud in multiple stages; the geometric prior refers to the cross-sectional profile of the component extracted from the bridge design drawings, which is mathematically represented as a set of ordered polyline points.
[0014] Furthermore, the multi-stage registration specifically includes the following steps:
[0015] Step S2.1, Point cloud slicing and projection based on principal component analysis: The geometric center and axial vector of the component are identified by the principal component analysis algorithm, and the original point cloud is corrected to the standard coordinate system to obtain an aligned point cloud; the point cloud is discretized into multiple cross-sectional slices along the coordinate axis with a set step size, and each slice is projected onto a two-dimensional plane to obtain the observation point set;
[0016] Step S2.2, coarse registration of point cloud based on coherent point drift: using the component cross-sectional contour extracted from the design drawings as the source point cloud and the set of observation points obtained by cross-section projection as the target point cloud, rigid coarse registration is performed using the coherent point drift algorithm to obtain the initial pose parameters of each cross section.
[0017] Step S2.3, Refined registration based on 7-DOF transformation: Based on the coarse registration, a 7-DOF weak affine transformation including rotation, scaling, shearing and translation is used to refine the registration of each section, and the residual of the inlier rate and the median distance of the inlier point is output for each slice.
[0018] Step S2.4, Global Optimization: Based on the inlier rate and residual of each section, a comprehensive score is calculated, outlier sections are removed using robust statistical methods, and the translation parameters and rotation angles of the retained sections are optimized for global consistency.
[0019] Further, step S2.1, the specific method for point cloud slicing and projection based on principal component analysis, is as follows: Pose alignment is performed using the principal component analysis algorithm; the geometric center and axial vector of the component are automatically identified by statistically analyzing the spatial discrete distribution of the point cloud; a homogeneous transformation matrix is constructed using the extracted axial vectors; rotation and translation corrections are performed on the original point cloud, redirecting it to a standard right-handed coordinate system to obtain the aligned point cloud. In the standard coordinate system, along the X-axis with step sizes... Define a series of equally spaced cross-sectional sampling points. ;in, The number of slices, M is the total number of slices; The step size is the sampling frequency; for each numbered... The cross-section, with Define a half-width around the center. The spatial bounding box, from the global alignment point cloud Extract the corresponding local point cloud subset, denoted as the i-th subset. Target slice point cloud : For each individual slice Projecting the spatial points contained therein onto the YZ plane yields the corresponding two-dimensional set of observation points. .
[0020] Further, in step S2.2, the specific method for coarse registration of point clouds based on coherent point drift is as follows: after obtaining the two-dimensional observation point set of each section, the coherent point drift (CPD) algorithm is introduced to perform the first stage of rigid coarse registration; in the registration framework, the source point cloud is defined as... This represents the feature point set generated by resampling the cross-sectional polygonal lines of the components in the design drawings, representing the ideal geometric prior model, with a point count of [number missing]. Define the target point cloud corresponding to the first... The set of observation points obtained by cross-sectional projection If the number of observation points exceeds the preset threshold Then, a random sampling strategy is used to extract its subset, denoted as . Before registration, transform the target point cloud and source point cloud to a normalized space; calculate the center of the target point cloud. The center of Heyuan point cloud and the maximum distribution radius of the target point cloud. Maximum distribution radius of source point cloud Then perform the following transformation: The Coherence Point Shift (CPD) algorithm treats the registration problem as a probability density estimation problem, and considers the source point cloud... The point is used as the centroid of the Gaussian Mixture Model (GMM). By moving the centroid, the GMM generates the target point cloud. Maximize the probability;
[0021] In the rigid transformation model, the transformation function is defined as: ;in, Scaling factor For rotation matrix, The transformation vector is used; the algorithm employs an expectation-maximization (EM) strategy to solve it; in the E-step, the posterior probability between the source and target points is calculated based on the current parameters; in the M-step, the transformation parameters are updated by minimizing the negative log-likelihood function. After completing the registration in the normalized space, the calculated parameters will be... Mapping back to the original physical coordinate space yields the actual transformation parameters: , , For the k-th cross-section, the final output is the transformed template point cloud. Simultaneously output alignment parameter set ;
[0022] Furthermore, in step S2.3, the specific method for refined registration based on 7-DOF transformation is as follows: after obtaining the initial pose of the cross-section through coarse registration, a refined registration and global optimization framework based on 7-DOF weak affine transformation is used to further eliminate residual biases; the design logic of the framework follows "parameter decoupling". Adaptive parameters Energy function construction The progressive strategy of "serialization collaborative optimization" is as follows:
[0023] First, define a transformation vector with 7 degrees of freedom. ,in, The rotation angle representing the cross section; and These are the logarithmic scaling factors in the Y and Z directions, respectively; and It is the bidirectional shear coefficient. and These are two-dimensional displacement vectors in the Y and Z directions; directly inherited from the coherent point drift (CPD) algorithm. The target coordinates are obtained after bidirectional shear weak affine transformation. By statistically analyzing the residual distribution obtained from the coherent point drift (CPD) algorithm at the initial pose, the hyperparameters of the energy function are adaptively determined. After determining the robust statistical parameters, a comprehensive energy function based on a smooth distance field is constructed. A two-stage sequential optimization strategy, from local free evolution to global constraint guidance, is adopted to optimize the deformation parameters of the effective cross-section. The median is extracted and used as a shared parameter for the global cross-section; subsequently, fine registration is performed to forcibly lock the globally shared parameter. At this point, the optimization space is reduced from 7 dimensions to 3 dimensions, meaning it only applies to... Optimize and output the interior point rate for each slice. residuals of distance from median of interior points .
[0024] Further, in step S2.4, the specific method for global optimization is as follows: after completing the stepwise fine-grained registration of the entire sequence cross-sections, global consistency optimization is performed on the registration parameter sequence; firstly, based on the inlier rate... residuals of distance from median of interior points Soft weighting is applied to each cross-section; robust standardization of the entire series indicators is performed using the median absolute difference (MAD). , Standardized scores and Mapped to via the Sigmoid operator The interval is used to obtain the individual score. and The final comprehensive score for the cross-section is: , They are respectively and Weighting coefficients; introducing distance residual-based weighting coefficients. The criteria perform hard rejection of outlier cross-section interference; and apply translation parameters. Perform global optimization; use geometric continuity-based interpolation to complete the angular pose of the culling section. .
[0025] Furthermore, step S2.3 also includes the following steps:
[0026] Step S2.3.1, Transformation Model Parameterization and Initial Value Mapping: Obtain the initial pose of the component cross-section using the Coherence Point Drift (CPD) algorithm. Then, a refined registration method based on a two-way shearing weak affine model is proposed; firstly, a transformation vector with 7 degrees of freedom is defined. These collectively define a two-dimensional affine transformation matrix, which translates, rotates, scales, and shears a component section template to make it accurately adapt to the geometric distortion of the measured point cloud data;
[0027] Initial value of the rotation angle of the given cross section ; and These are the logarithmic scaling factors in the Y and Z directions, respectively, with initial values set to... ; and It is the bidirectional shear coefficient. and The displacement vectors in the Y and Z directions are directly inherited from the CPD solution. ;
[0028] For any point in the template point set The target coordinates are obtained after bidirectional shear weak affine transformation. : ;
[0029] Step S2.3.2 Adaptive Parameter Estimation: Before performing nonlinear optimization iterations, statistical analysis is performed on the residual distribution obtained from the coherent point drift (CPD) algorithm under the initial pose to adaptively determine the hyperparameters of the energy function; kd-trees are used to retrieve observation points in the target point cloud. Construct the residual set by finding the shortest Euclidean distance to the polyline of the template after the initial transformation. The median absolute deviation (MAD) is introduced to robustly quantify the dispersion of the distribution. Based on this statistic, two key control parameters are defined: kernel width. Interior point cutoff threshold ; Defined as ,in It is a scaling factor that controls the degree of "softening" of the kernel function; It does not directly change the physical distance, but rather serves as the scale parameter of the kernel function, determining the rate at which the weight of the observation point decays with distance; Defined as , The tolerance limit of the algorithm for "interior points" was defined;
[0030] Step S2.3.3 Construction of Energy Function Based on Smooth Distance Field: After determining the robust statistical parameters, a comprehensive energy function combining the K-nearest neighbor smoothing minimum (k-NN Soft-min) operator and the Sigmoid kernel weighting is constructed. The synthesized energy function aims to address the problems of discontinuous objective functions and susceptibility to local minima in discrete point cloud registration, and to achieve automatic suppression of unstructured noise. A smoothing minimum operator (Soft-min) is introduced, constructing a continuously differentiable soft distance through the Log-Sum-Exp transformation of k nearest neighbors. ; );
[0031] in, Indicates the sampled points of the transformed template; Represents the set of observation points One point in the middle;
[0032] By applying confidence weights based on the Sigmoid kernel to each observation point This gives the algorithm the ability to identify and exclude outliers, as shown in the following formula:
[0033] ( );
[0034] When the observation point falls into the inner point region hour, The weight approaches 1; conversely, its weight decreases exponentially as the residual increases; at this point, for observations identified as outliers, i.e., 1- In part, the algorithm includes a constant term penalty in the total energy. This allows the optimization process to prioritize the alignment of high-confidence feature regions;
[0035] The final optimization objective function The terms consist of observation residuals, outlier penalty terms, and parameter space regularization terms. Together they constitute:
[0036] In the formula, This represents the total number of observation points in the current cross-section measured point cloud. The definition is as follows:
[0037] Step S2.3.4 Serialization Co-optimization Strategy: A two-stage serial optimization strategy is adopted, evolving from local free evolution to global constraint guidance. In the refinement stage, the algorithm treats each axial section as an independent observation and performs a 7-DOF affine transformation solution. A multi-starting-point global optimization mechanism is introduced to reduce the optimization space from 7 dimensions to 3 dimensions, only for... Optimize and output the interior point rate for each slice. residuals of distance from median of interior points .
[0038] Furthermore, the serialization collaborative optimization in step S2.3.4 specifically includes: using the coarse registration result as a benchmark, generating multiple initial solutions through Gaussian perturbation and solving them in parallel, selecting the parameter set with the lowest global energy as a provisional solution; extracting the median of the deformation parameters of the effective cross section as a globally shared parameter; and forcibly locking the globally shared parameter in the secondary optimization, optimizing only the rotation angle and the two-dimensional displacement vector.
[0039] Furthermore, the global optimization in step S2.4 specifically includes: hard-removing outlier sections using the 3σ criterion based on distance residuals; globally fitting the translation parameters of the retained valid sections using robust second-order polynomial regression with a soft-L1 loss function; and completing the angular pose of the removed sections by linear interpolation after unwinding the rotation angle sequence.
[0040] Furthermore, step S3 specifically includes:
[0041] Step S3.1, pose trajectory resampling: interpolation between every two adjacent observation sections. A virtual cross-section is used to encrypt the original discrete sequence into a high-density pose trajectory. , ;
[0042] Step S3.2, Cross-sectional point cloud topology generation: Resample the design template contour and refine the discrete feature points using linear interpolation. There are topological points, and the encrypted template point set is . Perform a two-dimensional affine transformation using globally shared deformation parameters to generate the deformed cross-sectional coordinates in the local coordinate system. To obtain the deformed two-dimensional contour;
[0043] According to the component along The physical properties of axis extension, for the first Encrypted locations The angle obtained by interpolation Translation vector The topological points are calculated. 3D coordinates:
[0044] Step S3.3, Skin Lofting and Triangular Mesh Reconstruction: Utilizing the index correspondence between points on the cross sections, a spatial quadrilateral is constructed by connecting corresponding points on adjacent cross sections and divided into triangular patches to generate a continuous three-dimensional shell mesh.
[0045] Furthermore, step S4 specifically includes: after acquiring the high-precision reconstructed mesh, performing texture mapping processing based on multi-view image data, the sparse reconstruction results of the Structure in Motion (SfM) algorithm, and the optimized geometric mesh; the prerequisite for texture mapping is the precise alignment of the mesh geometry and the camera pose in the same coordinate system; through pose restoration, the mesh in the local coordinate system is projected onto the global scene reconstructed by the Structure in Motion (SfM) algorithm; using the view consistency of multi-view stereo vision and the structural network model in the stereo matching method, the camera sequence with known intrinsic and extrinsic parameters is associated with the three-dimensional analytical mesh, providing spatial constraints for subsequent pixel-level fusion; the geometrically continuous surface is divided into several texture tiles and mapped to the two-dimensional UV coordinate space; using the tile packing algorithm, the complex surface image is efficiently rearranged into several high-resolution texture maps, realizing the decoupled storage of geometric data and image information.
[0046] Compared with the prior art, the present invention has the following advantages:
[0047] 1. Low computational overhead: This approach departs from the traditional three-step "sparse-dense-mesh" process, directly utilizing sparse point clouds recovered from moving structures to guide prior model construction. This process requires no GPU acceleration and can be completed on a CPU, reducing computational overhead by tens of times compared to traditional methods. While significantly improving processing efficiency and shortening delivery cycles, the generated texture model allows inspection personnel to quickly measure defects through intuitive human-computer interaction, improving timeliness and better meeting the current dual demands of bridge maintenance practices for both timeliness and ease of operation.
[0048] 2. High-quality reconstructed surface: The structured mesh surface generated by this patented method is smooth and has clear texture mapping, effectively overcoming the geometric distortion and surface noise commonly found in traditional multi-view stereo vision reconstruction. Geometric measurements can be performed directly on the mesh surface, providing a robust geometric basis for interactive location and dimensional verification of defects. For the first time, an equal-section prior is introduced into bridge component reconstruction, and a multi-stage optimization framework including "CPD coarse registration, fine-grained constraint registration, and overall topology optimization" is designed. This algorithm ensures high-precision fitting between the preset geometric template and the discrete sparse point cloud, effectively solving the reconstruction voids and noise problems easily generated by weakly textured concrete surfaces, and achieving smooth geometric output with structured topological features. Attached Figure Description
[0049] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0050] Figure 1 This is the overall technical roadmap of the present invention;
[0051] Figure 2 This is a sparse three-dimensional point cloud according to an embodiment of the present invention;
[0052] Figure 3 This demonstrates the coarse registration and fine registration processes according to an embodiment of the present invention;
[0053] Figure 4 This is the result of global optimization in the embodiments of the present invention;
[0054] Figure 5 This refers to the mesh generation and texture mapping in an embodiment of the present invention;
[0055] Figure 6 This is a comparison of the visual effects of the embodiments of the present invention with those of traditional methods. Detailed Implementation
[0056] To gain a deeper understanding of this invention, we will provide a comprehensive and detailed description. However, this invention has various implementations and is not limited to the specific examples listed herein. These examples are presented to enhance a full understanding of the disclosure of this invention.
[0057] Example 1
[0058] This embodiment uses a bridge pier as a case study to conduct experimental verification, providing a fast texture mapping method for cross-sectional components such as bridges. The method includes the following steps:
[0059] Step S1: Image-based point cloud generation: The camera pose is recovered from the sequence of images using the Structure in Motion (SfM) algorithm and a preliminary sparse point cloud is generated. Then, the background environment and noise are removed through manual interaction to extract the core point cloud data of the bridge component.
[0060] Image acquisition equipment was used to collect on-site images of the target bridge components. Specific data was collected by DJI drones, ensuring a safe operating distance from the bridge pier surface and minimizing the risk of collision. The photos had a resolution of 6144*3456 pixels, and a total of 461 photos were taken. The computing hardware configuration was an 11th Gen Intel(R) Core(TM) i9-11900K, 48GB of RAM, and an RTX 3090 graphics card. The computing language was Python.
[0061] Spatial pose calculation was performed on the acquired images using a motion structure reconstruction algorithm. Simultaneously, sparse reconstruction was completed and an original sparse point cloud was generated while restoring the camera's intrinsic and extrinsic parameters. An interactive point cloud editing method was used to denoise the original sparse point cloud, selectively removing irrelevant targets other than the target structure. A feature point extraction and matching (superpoint + superglue) algorithm was employed to complete the sparse reconstruction of the structure. The initial reconstruction yielded 152,905 points; after interactive editing, only the point cloud of the target bridge pier was retained, totaling 129,387 points. Figure 2 As shown.
[0062] Step S2, Multi-stage Geometric Prior Registration: Construct a parametric prior model for the features of the uniform cross-section component. By performing axis-guided slicing on the sparse point cloud, design a registration framework that includes coarse registration and multi-stage fine-tuning optimization, so that the preset model accurately aligns with the geometric features of the discrete point cloud; the specific operation is as follows:
[0063] After obtaining the core sparse point cloud of the bridge components, a registration framework driven by geometric priors is introduced. The geometric priors refer to the cross-sectional contours of the components extracted from the bridge design drawings, which are mathematically represented as a set of ordered polyline points. Utilizing the iso-section characteristics of the components, the three-dimensional point cloud is discretized and sliced along the principal axis. In the two-dimensional projection plane of each slice, the preset polyline template is registered with the measured sparse point cloud in multiple stages.
[0064] The specific operation of multi-stage registration includes the following steps:
[0065] Step S2.1 Point Cloud Slicing and Projection Based on Principal Component Analysis (PCA): The Principal Component Analysis (PCA) algorithm is introduced to perform pose alignment. By statistically analyzing the spatial discrete distribution of the point cloud, the geometric center and axial vector of the component are automatically identified. A homogeneous transformation matrix is constructed using the extracted direction vectors, and rotation and translation corrections are performed on the original point cloud, redirecting it to a standard right-handed coordinate system to obtain the aligned point cloud. In the standard coordinate system, along the X-axis with step sizes... Define a series of equally spaced cross-sectional sampling points. , among which, The number of slices, Step size (sampling frequency) This represents the total number of slices. For each slice numbered... The cross-section, with Define a half-width around the center. Spatial bounding box, from global point cloud Extract the corresponding local point cloud subset, denoted as the i-th subset. Target slice point cloud :
[0066] For each individual slice Projecting the spatial points contained therein onto the YZ plane yields the corresponding two-dimensional observation point set. .
[0067] Step S2.2 Coarse registration of point cloud based on coherent point drift (CPD): After obtaining the two-dimensional observation point set of each section, the coherent point drift (CPD) algorithm is introduced to perform the first stage of rigid coarse registration.
[0068] In the registration framework, the source point cloud is defined as a set of feature points generated by resampling the cross-sectional polylines of components in the design drawings, representing an ideal geometric prior model, with a point count of [missing information]. , represented as Define the target point cloud corresponding to the first... The set of observation points obtained by cross-sectional projection If the number of observation points exceeds the preset threshold Then, a random sampling strategy is used to extract its subset, denoted as . Before registration, transform the target point cloud and source point cloud to a normalized space; calculate the center of the target point cloud. The center of Heyuan point cloud and the maximum distribution radius of the target point cloud. Maximum distribution radius of source point cloud Then perform the following transformation:
[0069] CPD treats the registration problem as a probability density estimation problem. Assume a source point cloud. The point is used as the centroid of the Gaussian Mixture Model (GMM), and the target point cloud is generated by moving the centroid. The probability is maximized. In the rigid transformation model, the transformation function is defined as: ;
[0070] in, Scaling factor For rotation matrix, It is a translation vector.
[0071] The algorithm employs an expectation-maximization (EM) strategy for solving the problem. In the E-step, the posterior probability (i.e., the correspondence coefficient) between the source and target points is calculated based on the current parameters; in the M-step, the negative log-likelihood function (i.e., ...) is minimized. Value) Update transformation parameters After completing the registration in the normalized space, the calculated parameters will be... Mapping back to the original physical coordinate space yields the actual transformation parameters: , , For the k-th cross-section, the final output is the transformed template point cloud. Simultaneously output alignment parameter set .
[0072] Step S2.3 Refined registration based on 7-DOF transformation: After obtaining the initial pose of the cross section through coarse registration, a refined registration and global optimization framework based on 7-DOF weak affine transformation is adopted to further eliminate residual bias.
[0073] The design logic of the framework follows the principle of "parametric decoupling". Adaptive parameters Energy function construction A progressive strategy of "serialization collaborative optimization".
[0074] The complete algorithm execution flow for step S2.3 is as follows:
[0075] Step S2.3.1 Transformation Model Parameterization and Initial Value Mapping: Obtain the initial pose of the component cross-section using the Coherence Point Drift (CPD) algorithm. Then, a refined registration method based on a two-way shearing weak affine model is proposed; firstly, a transformation vector with 7 degrees of freedom is defined. These collectively define a two-dimensional affine transformation matrix, which translates, rotates, scales, and shears the standard box girder section template, enabling it to accurately adapt to the geometric distortions of the measured point cloud data; among which The rotation angle representing the cross section, given an initial value. ; and These are the logarithmic scaling factors in the Y and Z directions, respectively, with initial values set to... ; and It is the bidirectional shear coefficient. and For the two-dimensional displacement vectors in the Y and Z directions, directly inherit the values calculated by CPD. For any point in the template point set The target coordinates are obtained after bidirectional shear weak affine transformation. : .
[0076] S2.3.2 Adaptive Parameter Estimation: Before performing nonlinear optimization iterations, the hyperparameters of the energy function are adaptively determined by statistically analyzing the residual distribution under the initial pose obtained from the CPD; kd-trees are used to retrieve observation points in the target point cloud. Construct the residual set by finding the shortest Euclidean distance to the polyline of the template after the initial transformation. The median absolute deviation (MAD) is introduced to robustly quantify the dispersion of the distribution. Based on this statistic, the algorithm defines two key control parameters: kernel width. Interior point cutoff threshold . Defined as ,in It is a scaling factor that controls the degree of "softening" of the kernel function. It does not directly change the physical distance, but rather serves as the scale parameter of the kernel function, determining the rate at which the weight of the observation point decays with distance. Defined as , The tolerance limit of the algorithm for "interior points" was defined.
[0077] S2.3.3 Construction of Energy Function Based on Smooth Distance Field: After determining the robust statistical parameters, a comprehensive energy function is constructed that combines the K-nearest neighbor smooth minimum (k-NN Soft-min) operator with a Sigmoid kernel weighted sum. The function aims to address the problems of discontinuous objective functions and susceptibility to local minima in discrete point cloud registration, and to achieve automatic suppression of unstructured noise. It introduces a smoothing minimum operator (Soft-min) and constructs a continuously differentiable soft distance using the Log-Sum-Exp transformation of k nearest neighbors. : );
[0078] in, This represents the transformed template sampling points. Represents the set of observation points One point in the middle;
[0079] To enable the algorithm to identify and exclude outliers, a confidence weight based on the Sigmoid kernel is applied to each observation point. As shown in the following formula: ( );
[0080] When the observation point falls into the inner point region ( )hour, The weight approaches 1; conversely, its weight decreases exponentially as the residual increases. At this point, for observations identified as outliers (i.e., 1-...), the weight decreases. (Partially), the algorithm includes a constant term penalty in the total energy. This allows the optimization process to prioritize the alignment of high-confidence feature regions.
[0081] The final optimization objective function The terms consist of observation residuals, outlier penalty terms, and parameter space regularization terms. Together they constitute: In the formula, This represents the total number of observation points in the current cross-section measured point cloud. The definition is as follows:
[0082] S2.3.4 Serialization Co-optimization Strategy: A two-stage serial optimization strategy is adopted, evolving from local free evolution to global constraint guidance. In the refinement stage, the algorithm treats each axial section as an independent observation and performs a 7-DOF affine transformation solution. A multi-starting-point global optimization mechanism is introduced to reduce the optimization space from 7 dimensions to 3 dimensions, only for... Optimize and output the interior point rate for each slice. residuals of distance from median of interior points .
[0083] The specific operation of the multi-starting point global optimization mechanism in step S2.3.4 is as follows:
[0084] Based on the CPD coarse registration solution, the parameter boundary space is generated by Gaussian perturbation. The initial solution vectors are set, and the first initial solution is strictly aligned with the coarse registration result. For each set of initial values, the L-BFGS-B solver is started in parallel, and the parameter set with the lowest global energy is selected as the provisional solution for that section. The internal point ratio of the section is calculated, and an early rejection mechanism is introduced. If the initial internal point ratio of the section is lower than a preset threshold, the section is determined to be severely obstructed or subject to noise interference, and its solution will not participate in the subsequent statistical modeling of the geometric features of the components. Based on the physical assumption of constant cross-section followed by bridge components in design and construction, the deformation parameters of the effective section are calculated. The median is extracted and used as a shared parameter for the global cross-section; a second-stage fine registration is performed to forcibly lock the globally shared parameter. Only for Optimize and output the interior point rate for each slice. residuals of distance from median of interior points .
[0085] S2.4 Global Optimization: After completing the stepwise fine-grained registration of the entire sequence of cross-sections, global consistency optimization is performed on the registration parameter sequence; firstly, based on the output of S2.3... Soft weighting is applied to each cross-section; robust standardization of the entire series indicators is performed using the median absolute difference (MAD). , Standardized scores and Mapped to via the Sigmoid operator The interval is used to obtain the individual score. and The final comprehensive score for the cross-section is defined as follows: , They are respectively and The weighting coefficients.
[0086] The specific operation of global optimization in step S2.4 is as follows:
[0087] Introducing distance residual-based The criteria perform hard removal of outliers causing interference with the global linearity due to severe distortion or occlusion; and utilize the median residual of the entire sequence. Calculate robust standard deviation Define the filtering threshold If the residual of section k Exceeded If the cross-section is not a physical observation, it needs to be removed and will not participate in the subsequent centerline regression fitting.
[0088] For the retained set of valid cross-sections, the translation parameters are... Perform global optimization; unlike simple smoothing filtering, use robust second-order polynomial regression with a soft-L1 loss function, specifically as follows: Construct a model for the axial position of the cross-section. Fitted curve To further mitigate the impact of residual errors, the objective function is optimized by introducing section confidence. With Soft-L1 kernel function : ;
[0089] In the formula, This represents the t value calculated for the k-th cross section without global smoothing, solely based on the point cloud registration of that cross section itself. Defined as When the residual r is small, This is equivalent to the least squares method; when the residual r is large, That is, the loss increases linearly with the error. To avoid excessive interference from outliers on the fitted curve, the optimal coefficients are obtained through nonlinear least squares solution. Afterwards, the final translational pose of the k-th section is updated to the projection point on the regression curve;
[0090] For rotation angle An interpolation repair method based on geometric continuity is employed to unwrap the phase of the angle sequence of the preserved cross-section to eliminate the periodic boundary effects. Phase jump, using linear interpolation to complete and eliminate the angular pose of the cross-section. .
[0091] Based on the theory in step S2, multi-stage geometric prior registration is adopted, and the relevant parameters are set as follows: The value is 1.0. The value is 2.5, and k takes the value 16. , , , All values are 1.
[0092] The point cloud is sliced into 21 sections along the main direction determined by PCA. Figure 3 The output of typical cross-sections in the multi-stage registration process is shown, representing coarse registration using CPD and fine registration using 7 degrees of freedom. The blue line represents the CPD result, and the red line represents the fine registration result. At section 0, which is the bottom of the pier, the area is obscured by trees, so the point cloud is the point cloud of the trees surrounding the pier, resulting in significantly poor matching at section 0. For the other sections, since the pier itself has a relatively simple cross-section, CPD can achieve better registration results. In terms of computation time, the CPD stage takes 68 seconds, and the fine registration stage takes 24 seconds.
[0093] Figure 4 The results of global optimization are shown. The calculation took 13 seconds. It can be seen that the fitting accuracy of the cross-section at the upper and lower ends of the pier is poor. The cross-section is extracted and the final value is obtained by fitting. In the y and z directions, the line connecting the centroids of the cross-sections is almost a straight line.
[0094] Step S3, Structured Mesh Generation: Based on the registered cross-sectional parameters, a topologically regular structured mesh model is directly generated using lofting techniques. The specific operation is as follows:
[0095] S3.1 Pose Trajectory Resampling: Interpolation between every two adjacent observation sections A virtual cross-section is used to encrypt the original discrete sequence into a high-density pose trajectory. , .
[0096] S3.2 Section Point Cloud Topology Generation: First, the design template contour is resampled, and the discrete feature points are densified through linear interpolation. There are n topological points; let the encrypted template point set be . By utilizing a globally shared parameter-based two-dimensional affine transformation, the deformed cross-sectional coordinates in the local coordinate system are generated. The calculation is as follows: ;
[0097] After obtaining the deformed two-dimensional contour, it is projected onto the three-dimensional design coordinate system; based on the component along... The physical properties of axis extension, for the first Encrypted locations The angle obtained by interpolation Translation vector The topological points are calculated. 3D coordinates: ;
[0098] Through this mapping process, the original static two-dimensional design template is transformed into a series of three-dimensional topological rings that dynamically evolve along the spatial axis.
[0099] S3.3 Skin Lofting and Triangular Mesh Reconstruction: After completing the full sequence of encrypted section topology points After spatial mapping, topological connections between points are established using skin lofting technology, thereby transforming the discrete point lattice into a continuous three-dimensional shell mesh. The core of mesh construction lies in generating topological patches using the index correspondence between points on cross sections. For any adjacent cross sections... and and its corresponding encrypted index points and By connecting four adjacent vertices to construct a spatial quadrilateral, the spatial quadrilateral is divided into two equivalent triangular facets. and : ;
[0100] Through topological connectivity and geometric reconstruction, discrete cross-sectional parameters are transformed into a high-quality 3D surface mesh model. The pier mesh is generated based on the theory from step S3, and settings are configured. =5, set =60, directly replace the previous template with the template containing the chamfer, such as Figure 5 As shown.
[0101] S4, High-fidelity texture mapping: The generated mesh model is projected and mapped using a multi-view stereo vision method that combines viewpoint consistency and stereo matching, outputting a high-resolution texture map model with a realistic appearance. The specific steps are as follows:
[0102] After acquiring a high-precision reconstructed mesh, texture mapping is performed based on multi-view image data, SfM sparse reconstruction results, and optimized geometric meshes. Texture mapping requires precise alignment of the mesh geometry and camera pose within the same coordinate system. Through pose restoration, the mesh in the local coordinate system is projected onto the global scene reconstructed by SfM. Utilizing the viewpoint consistency of multi-view stereo vision and the structural network model in stereo matching methods, camera sequences with known intrinsic and extrinsic parameters are associated with the 3D analytical mesh, providing spatial constraints for subsequent pixel-level fusion. Geometrically continuous patches are divided into several texture tiles and mapped to a 2D UV coordinate space. Using a tile packing algorithm, complex surface images are efficiently rearranged into several high-resolution texture maps, achieving decoupled storage of geometric data and image information.
[0103] After obtaining the mesh, multi-view texture mapping is further performed on the mesh model based on the original image to generate a realistic textured mesh that can be used for 3D measurement and inspection display. Texture mapping is completed using a structural network model from the perspective consistency and stereo matching methods of multi-view stereo vision. Its inputs include: camera pose, mesh model, and the corresponding set of original images. Under the condition of known camera pose and mesh geometry, the structural network model performs view selection for each mesh facet and generates a texture atlas. Then, cross-view color fusion and seam optimization are used to reduce color jumps and seam artifacts caused by perspective differences, ultimately outputting a textured mesh model. Regarding parameter settings, a high-quality texture configuration is used to preserve texture details as much as possible: first, the resolution level is set to 0 to use the highest resolution level of the original image, and the minimum resolution is set to 2000 to constrain the minimum texture sampling resolution. Simultaneously, a smoothing ratio of 0.3 is used to introduce a smoothing term weight into the texture cost to achieve a balance between texture sharpness and cross-facet consistency. Mesh generation takes 1.1 seconds, and texture mapping takes 3.1 seconds.
[0104] Figure 6 The visualization effects of the patented method and conventional methods are shown from different perspectives. For textures whose structures lie within a plane, the two methods are almost identical. Figure 6 The last line shows a magnified view of the localized defects. Under the same computer configuration, the texture generated by this patented method is significantly clearer than that of traditional methods. In terms of time efficiency, this patented method takes 3 minutes and 1 second to compute. Traditional methods, using the same parameters, take 15 minutes and 58 seconds for dense reconstruction, 20 minutes and 29 seconds for mesh reconstruction, and 24 minutes and 50 seconds for texture mapping in the dense reconstruction and mesh generation stages.
[0105] Contents not described in detail in this specification are prior art known to those skilled in the art. Although illustrative specific embodiments of the invention have been described above to facilitate understanding by those skilled in the art, it should be understood that the invention is not limited to the scope of the specific embodiments. Various modifications are readily apparent to those skilled in the art as long as they fall within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of this invention are protected.
Claims
1. A fast texture mapping method for cross-sectional components such as bridges, characterized in that, Includes the following steps: Step S1, image-based point cloud generation: The camera pose is recovered from the sequence of images using a motion structure recovery algorithm and a preliminary sparse point cloud is generated. Then, the background environment and noise are removed through manual interactive cleaning to obtain the core point cloud data of the target bridge component. Step S2, Multi-stage geometric prior registration: Construct a parametric prior model for the features of the component with equal cross-section. By performing axis-guided slicing on the sparse point cloud, and using a registration framework that includes coarse registration and multi-stage fine optimization, the preset model is aligned with the geometric features of the discrete point cloud. Step S3, Structured Mesh Generation: Based on the registered cross-sectional parameters, a topologically regular structured mesh model is generated using lofting techniques; Step S4, High-fidelity texture mapping: The generated mesh model is projected and mapped using the perspective consistency and stereo matching method of multi-view stereo vision, and a high-resolution texture map model with a realistic appearance is output.
2. The method for rapid texture mapping of cross-sectional components such as bridges according to claim 1, characterized in that, Step S1 specifically includes: acquiring images of the target bridge components using an image acquisition device; performing spatial pose calculation on the images using a motion structure recovery algorithm, completing sparse reconstruction and generating the original sparse point cloud while restoring the camera's intrinsic and extrinsic parameters; and performing noise reduction processing on the original sparse point cloud using a manual interactive point cloud editing method to selectively remove irrelevant targets other than the target components.
3. The method for rapid texture mapping of cross-sectional components such as bridges according to claim 1, characterized in that, Step S2 specifically includes the following steps: After acquiring the sparse point cloud, a geometric prior-driven registration framework is introduced; the 3D point cloud is discretized and sliced along the principal axis by utilizing the isosectional properties of the components; in the 2D projection plane of each slice, the preset polyline template is registered with the measured sparse point cloud in multiple stages. The geometric prior refers to the cross-sectional profile of the component extracted from the design drawings, which is mathematically represented as an ordered set of polyline points.
4. The method for rapid texture mapping of cross-sectional components such as bridges according to claim 3, characterized in that, The multi-stage registration specifically includes the following steps: Step S2.1, Point cloud slicing and projection based on principal component analysis: The geometric center and axial vector of the component are identified by the principal component analysis algorithm, and the original point cloud is corrected to the standard coordinate system to obtain an aligned point cloud; the point cloud is discretized into multiple cross-sectional slices along the coordinate axis with a set step size, and each slice is projected onto a two-dimensional plane to obtain the observation point set; Step S2.2, coarse registration of point cloud based on coherent point drift: using the component cross-sectional contour extracted from the design drawings as the source point cloud and the set of observation points obtained by cross-section projection as the target point cloud, rigid coarse registration is performed using the coherent point drift algorithm to obtain the initial pose parameters of each cross section. Step S2.3, Refined registration based on 7-DOF transformation: Based on the coarse registration, a 7-DOF weak affine transformation including rotation, scaling, shearing and translation is used to refine the registration of each section, and the residual of the inlier rate and the median distance of the inlier point is output for each slice. Step S2.4, Global Optimization: Based on the inlier rate and residual of each section, a comprehensive score is calculated, outlier sections are removed using robust statistical methods, and the translation parameters and rotation angles of the retained sections are optimized for global consistency.
5. A fast texture mapping method for cross-sectional components such as bridges according to claim 4, characterized in that, Step S2.1, the specific method for point cloud slicing and projection based on principal component analysis, is as follows: Pose alignment is performed using the principal component analysis algorithm; the geometric center and axial vector of the component are automatically identified by statistically analyzing the spatial discrete distribution of the point cloud; a homogeneous transformation matrix is constructed using the extracted axial vectors; rotation and translation corrections are performed on the original point cloud, redirecting it to the standard right-handed coordinate system to obtain the aligned point cloud. In the standard coordinate system, along the X-axis with step sizes... Define a series of equally spaced cross-sectional sampling points. ;in, The number of slices, M is the total number of slices; The step size is the sampling frequency; for each numbered... The cross-section, with Define a half-width around the center. The spatial bounding box, from the global alignment point cloud Extract the corresponding local point cloud subset, denoted as the i-th subset. Target slice point cloud : For each individual slice Projecting the spatial points contained therein onto the YZ plane yields the corresponding two-dimensional set of observation points. ; The specific method for coarse registration of point clouds based on coherent point drift in step S2.2 is as follows: after obtaining the two-dimensional observation point set of each section, the coherent point drift (CPD) algorithm is introduced to perform the first stage of rigid coarse registration; in the registration framework, the source point cloud is defined as... This represents the feature point set generated by resampling the cross-sectional polygonal lines of the components in the design drawings, representing the ideal geometric prior model, with a point count of [number missing]. Define the target point cloud corresponding to the first... The set of observation points obtained by cross-sectional projection If the number of observation points exceeds the preset threshold Then, a random sampling strategy is used to extract its subset, denoted as . Before registration, transform the target point cloud and source point cloud to a normalized space; calculate the center of the target point cloud. The center of Heyuan point cloud and the maximum distribution radius of the target point cloud. Maximum distribution radius of source point cloud Then perform the following transformation: ; In the rigid transformation model, the transformation function is defined as: ； in, Scaling factor Let be a rotation matrix. The vector is the translation vector; the algorithm uses an expectation-maximization strategy to solve it; in the E-step, the posterior probability between the source and target points is calculated based on the current parameters; in the M-step, the transformation parameters are updated by minimizing the negative log-likelihood function. After completing the registration in the normalized space, the calculated parameters will be... Mapping back to the original physical coordinate space yields the actual transformation parameters: , , For the k-th cross-section, the final output is the transformed template point cloud. Simultaneously output alignment parameter set ; Step S2.3, the specific method of fine registration based on 7-DOF transformation, is as follows: after obtaining the initial pose of the cross-section through coarse registration, a fine registration and global optimization framework based on 7-DOF weak affine transformation is used to further eliminate residual bias; the design logic of the framework follows "parameter decoupling". Adaptive parameters Energy function construction The progressive strategy of "serialization collaborative optimization" is as follows: First, define a transformation vector with 7 degrees of freedom. ,in, The rotation angle representing the cross section; and These are the logarithmic scaling factors in the Y and Z directions, respectively; and It is the bidirectional shear coefficient. and These are two-dimensional displacement vectors in the Y and Z directions; directly inherited from the coherent point drift (CPD) algorithm. The target coordinates are obtained after bidirectional shear weak affine transformation. By statistically analyzing the residual distribution obtained from the coherent point drift (CPD) algorithm at the initial pose, the hyperparameters of the energy function are adaptively determined. After determining the robust statistical parameters, a comprehensive energy function based on a smooth distance field is constructed. A two-stage sequential optimization strategy, from local free evolution to global constraint guidance, is adopted to optimize the deformation parameters of the effective cross-section. The median is extracted and used as a shared parameter for the global cross-section; subsequently, fine registration is performed to forcibly lock the globally shared parameter. At this point, the optimization space is reduced from 7 dimensions to 3 dimensions, meaning it only applies to... Optimize and output the interior point rate for each slice. residuals of distance from median of interior points ; The specific method for global optimization in step S2.4 is as follows: after completing the stepwise fine-grained registration of the entire sequence cross-section, global consistency optimization is performed on the registration parameter sequence; firstly, based on the inlier rate... residuals of distance from median of interior points Soft weighting is applied to each cross-section; robust standardization of the entire series indicators is performed using the absolute median difference. , Standardized scores and Mapped to via the Sigmoid operator The interval is used to obtain the individual score. and The final comprehensive score for the cross-section is: , They are respectively and Weighting coefficients; introducing distance residual-based weighting coefficients. The criteria perform hard rejection of outlier cross-section interference; and apply translation parameters. Perform global optimization; use geometric continuity-based interpolation to complete the angular pose of the culling section. .
6. The method for rapid texture mapping of cross-sectional components such as bridges according to claim 5, characterized in that, Step S2.3 further includes the following steps: Step S2.3.1, Transformation Model Parameterization and Initial Value Mapping: Obtain the initial pose of the component cross-section using the Coherence Point Drift (CPD) algorithm. Then, a refined registration method based on a two-way shearing weak affine model is proposed; firstly, a transformation vector with 7 degrees of freedom is defined. These collectively define a two-dimensional affine transformation matrix, which translates, rotates, scales, and shears a component section template to make it accurately adapt to the geometric distortion of the measured point cloud data; Initial value of the rotation angle of the given cross section ; and These are the logarithmic scaling factors in the Y and Z directions, respectively, with initial values set to... ; and It is the bidirectional shear coefficient. and The displacement vectors in the Y and Z directions are directly inherited from the CPD solution. ; For any point in the template point set The target coordinates are obtained after bidirectional shear weak affine transformation. : ； Step S2.3.2 Adaptive Parameter Estimation: Before performing nonlinear optimization iterations, statistical analysis is performed on the residual distribution obtained from the coherent point drift (CPD) algorithm under the initial pose to adaptively determine the hyperparameters of the energy function; kd-trees are used to retrieve observation points in the target point cloud. Construct the residual set by finding the shortest Euclidean distance to the polyline of the template after the initial transformation. The median absolute deviation (MAD) is introduced to robustly quantify the dispersion of the distribution. Based on this statistic, two key control parameters are defined: kernel width. Interior point cutoff threshold ; Defined as ,in It is a scaling factor that controls the degree of "softening" of the kernel function; It does not directly change the physical distance, but rather serves as the scale parameter of the kernel function, determining the rate at which the weight of the observation point decays with distance; Defined as , The tolerance limit of the algorithm for "interior points" was defined; Step S2.3.3 Construction of Energy Function Based on Smooth Distance Field: After determining the robust statistical parameters, a comprehensive energy function combining the K-nearest neighbor smoothing minimum operator and the Sigmoid kernel weighting is constructed. The integrated energy function aims to address the problems of discontinuous objective functions and susceptibility to local minima in discrete point cloud registration, and to achieve automatic suppression of unstructured noise. A smoothing minimum operator is introduced, and a continuously differentiable soft distance is constructed through the Log-Sum-Exp transformation of k nearest neighbors. : ） in, Indicates the sampled points of the transformed template; Represents the set of observation points One point in the middle; By applying confidence weights based on the Sigmoid kernel to each observation point This gives the algorithm the ability to identify and exclude outliers, as shown in the following formula: ( )； When the observation point falls into the inner point region hour, The weight approaches 1; conversely, its weight decreases exponentially as the residual increases; at this point, for observations identified as outliers, i.e., 1- In part, the algorithm includes a constant term penalty in the total energy. This allows the optimization process to prioritize the alignment of high-confidence feature regions; The final optimization objective function The terms consist of observation residuals, outlier penalty terms, and parameter space regularization terms. Together they constitute: ； In the formula, This represents the total number of observation points in the current cross-section measured point cloud. The definition is as follows: ； Step S2.3.4 Serialization Co-optimization Strategy: A two-stage serial optimization strategy is adopted, evolving from local free evolution to global constraint guidance. In the refinement stage, the algorithm treats each axial section as an independent observation and performs a 7-DOF affine transformation solution. A multi-starting-point global optimization mechanism is introduced to reduce the optimization space from 7 dimensions to 3 dimensions, only for... Optimize and output the interior point rate for each slice. residuals of distance from median of interior points .
7. The method for rapid texture mapping of cross-sectional components such as bridges according to claim 4, characterized in that, The serialization collaborative optimization in step S2.3.4 specifically includes: using the coarse registration result as a benchmark, generating multiple initial solutions through Gaussian perturbation and solving them in parallel, selecting the parameter set with the lowest global energy as a provisional solution; extracting the median of the deformation parameters of the effective cross section as a globally shared parameter; and forcibly locking the globally shared parameter in the secondary optimization, optimizing only the rotation angle and the two-dimensional displacement vector.
8. The method for rapid texture mapping of cross-sectional components such as bridges according to claim 3, characterized in that, The global optimization in step S2.4 specifically includes: hard-removing outlier sections using the 3σ criterion based on distance residuals; globally fitting the translation parameters of the retained valid sections using robust second-order polynomial regression with a soft-L1 loss function; and completing the angular pose of the removed sections by linear interpolation after unwinding the rotation angle sequence.
9. The method for rapid texture mapping of cross-sectional components such as bridges according to claim 1, characterized in that, Step S3 specifically includes: Step S3.1, pose trajectory resampling: interpolation between every two adjacent observation sections. A virtual cross-section is used to encrypt the original discrete sequence into a high-density pose trajectory. , ; Step S3.2, Cross-sectional point cloud topology generation: Resample the design template contour and refine the discrete feature points using linear interpolation. There are topological points, and the encrypted template point set is . Perform a two-dimensional affine transformation using globally shared deformation parameters to generate the deformed cross-sectional coordinates in the local coordinate system. To obtain the deformed two-dimensional contour; ； According to the component along The physical properties of axis extension, for the first Encrypted locations The angle obtained by interpolation Translation vector The topological points are calculated. 3D coordinates: ； Step S3.3, Skin Lofting and Triangular Mesh Reconstruction: Utilizing the index correspondence between points on the cross sections, a spatial quadrilateral is constructed by connecting corresponding points on adjacent cross sections and divided into triangular patches to generate a continuous three-dimensional shell mesh.
10. A fast texture mapping method for cross-sectional components such as bridges according to claim 1, characterized in that, Step S4 specifically includes: after acquiring a high-precision reconstructed mesh, performing texture mapping processing based on multi-view image data, sparse reconstruction results of the motion structure recovery algorithm, and optimized geometric mesh; the prerequisite for texture mapping is the precise alignment of mesh geometry and camera pose in the same coordinate system; through pose restoration, the mesh in the local coordinate system is projected onto the global scene reconstructed by the motion structure recovery algorithm; using the view consistency of multi-view stereo vision and the structural network model in the stereo matching method, the camera sequence with known intrinsic and extrinsic parameters is associated with the three-dimensional analytical mesh, providing spatial constraints for subsequent pixel-level fusion; geometrically continuous patches are divided into several texture tiles and mapped to a two-dimensional UV coordinate space; using a tile packing algorithm, complex surface images are efficiently rearranged into several high-resolution texture maps, achieving decoupled storage of geometric data and image information.