Method for registering and splicing data of bamboo strips based on generalized T-Student kernel function

Abstract

The invention discloses a general T-Student kernel function-based bamboo strip broken simple data registration splicing method, which comprises the following steps of: taking to-be-spliced bamboo strip broken simple data as input of a point cloud splicing model of the bamboo strip broken simple to obtain a splicing result of the spliced bamboo strip broken simple; the model comprises a geometric feature extraction module, a texture feature extraction module and a joint optimization registration module. The geometric feature extraction module constructs a multi-scale geometric descriptor fused with region connected graph convolution by calculating a local normal vector, and generates a geometric label; a texture feature extraction module extracts a texture gradient vector and generates a binary direction mask; and the joint optimization registration module integrates the outputs of the first two modules, constructs a multi-modal error function fusing geometric-texture errors, performs weighted optimization by adopting a generalized T-Student kernel function, and finally outputs a splicing result through iterative calculation. According to the method, multi-scale geometric features, texture direction constraints and robust kernel function optimization are combined, and high-precision automatic splicing of the bamboo strips is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of point cloud stitching, and specifically relates to a method for registering and stitching fragmentary bamboo slip data based on a generalized T-Student kernel function. Background Art

[0002] Bamboo slips were narrow bamboo or wooden slips used for writing in ancient China, widely used from the Warring States period to the Wei and Jin dynasties (5th century BC to 4th century AD). Before the invention of paper, bamboo slips were the main carrier of written records. Their size was usually 15–30 cm long, 0.5–1.5 cm wide, and 1–3 mm thick, often tied together with ropes into volumes. The content recorded on bamboo slips was extremely extensive, including legal provisions, classical works, household registrations, and financial accounts. As a "subterranean archive" spanning thousands of years, the written content and material form of bamboo slips together constitute an important empirical basis for studying ancient social systems, the evolution of writing, and craftsmanship.

[0003] However, due to bamboo and wood being organic materials, most of the existing bamboo slips are fragments that have survived fortunately in deep underground strata. The currently successfully pieced and restored bamboo slips are as Figure 1 shown. The digital restoration of fragmented bamboo slips is not only a technical requirement for information reconstruction but also an urgent task for protecting intangible cultural heritage. According to statistics, the currently unearthed bamboo slip cultural relics have exceeded 300,000 pieces, and most of them have physical damages such as fractures and corrosion. Gansu Province, known for its rich unearthed quantity and high quality, especially Han Dynasty bamboo slips, has become one of the most representative bamboo slip resource libraries in the country. Although Liu et al. constructed the DeepJiandu dataset and collected infrared-visible images of bamboo slips, the piecing of bamboo slip fragments still faces many technical problems. Traditional restoration methods mainly rely on manual piecing, which is time-consuming and prone to causing secondary damage to fragile cultural relics. With the development of three-dimensional digital technology, non-contact restoration based on point clouds has gradually become a new path for bamboo slip protection, providing a more efficient and less damaging solution compared to traditional methods.

[0004] However, the current mainstream point cloud registration technologies face three major challenges in cultural heritage restoration: 1. High-precision registration requirements: The unique bamboo grain texture and micro-deformation caused by oxidation of bamboo slips require the registration accuracy to reach the sub-millimeter level; 2. Irregular fractures and sparse features: There are irregular material losses on the fracture surface, making it difficult to find enough feature points for robust matching; 3. Environmental noise interference: The inevitable environmental noise (such as light reflection artifacts and scanner quantization errors) during the digitalization of cultural relics seriously reduces the registration robustness.

[0005] In recent years, researchers have tried to introduce deep learning and probability models to improve performance, but there are still significant deficiencies in dealing with sparse data, adapting to complex surface morphologies, and suppressing noise interference. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, this invention provides a data registration and splicing method for fragmented bamboo and wooden slips based on the generalized T-Student kernel function. This method preserves the geometric structure and texture details of the fragmented bamboo and wooden slips, and ensures high precision and consistency in splicing through joint optimization.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A method for registering and stitching fragmented bamboo and wooden slips based on the generalized T-Student kernel function is proposed. The method obtains the fragmented bamboo and wooden slips data to be stitched, which includes point cloud data and texture image data of the fragmented bamboo and wooden slips. The fragmented bamboo and wooden slips data to be stitched are used as input to the point cloud stitching model of the fragmented bamboo and wooden slips, and the stitching result of the fragmented bamboo and wooden slips data to be stitched is output.

[0009] The bamboo and wooden slip fragment point cloud stitching model includes a geometric feature extraction module, a texture feature extraction module, and a joint optimization registration module. The model transmits the input bamboo and wooden slip fragment data to the geometric feature extraction module and the texture feature extraction module, respectively. The geometric feature extraction module extracts the local normal vectors of the point cloud data and constructs a multi-scale geometric descriptor that integrates the region connectivity graph convolution to generate geometric labels. The texture feature extraction module extracts and calculates the texture gradient vector of the texture image data and generates a binary orientation mask. Then, the joint optimization registration module combines the outputs of the geometric and texture feature extraction modules to construct a multimodal error function that combines geometric and texture errors. The multimodal error function is weighted using a generalized T-Student kernel function, and the weighted multimodal error function is iterated to obtain the stitching result of the bamboo and wooden slip stitching data as the output.

[0010] Preferably, the specific processing steps of the geometric feature extraction module in the bamboo and wooden slip fragment point cloud splicing model include the following steps:

[0011] First, the point cloud data of the bamboo and wooden slips used as input... Each point cloud sampling point x i A k-nearest neighbor search is performed to obtain the local neighborhood point set, where N represents the number of point cloud sampling points contained in the point cloud data X of the bamboo and wooden slips. Then, the local normal vector is obtained by minimizing the sum of squared distances from the neighborhood points to the tangent plane. Finally, graph convolution is used to construct a connected graph of the region. Specifically, the set of point cloud sampling points in the point cloud data X of the bamboo and wooden slips fragments is constructed as a vertex set. The set of Euclidean distances between point cloud sampling points is used to construct an edge set ε, which is then used in the multi-scale regional connectivity graph. The graph convolution operation is used to extract multi-scale geometric descriptors, s = 1, 2, ..., S, where S is the total number of graph convolution layers. Finally, the multi-scale geometric descriptors are concatenated and classified by a multilayer perceptron to output geometric labels.

[0012] Preferably, the objective function of the local normal vector is:

[0013]

[0014] In the formula, n i This represents the i-th point cloud sampling point x in the point cloud data X of the bamboo and wooden slips fragments. i The corresponding local normal vector; Represents the sampling point x in the point cloud i The local neighborhood point set; Representation of neighborhood point set The centroid. Preferably, the processing procedure for the multi-scale geometric descriptor is expressed as follows:

[0015]

[0016] In the formula, f represents the multi-scale geometric descriptor of the graph convolution at layer s; j W represents the point cloud coordinates of point j. (s) With b (s) Let represent the weights and bias parameters of the graph convolution at layer s, respectively. This represents the edge weight between point i and point j. Let represent the local neighborhood point set of point i in the graph convolution of the s-th layer; σ represents the activation function.

[0017] Preferably, the specific processing steps of the texture feature extraction module in the bamboo and wooden slip fragment point cloud splicing model include the following steps:

[0018] First, the point cloud data of the bamboo and wooden slip fragments, which are used as input, are mapped to obtain the corresponding texture image data. Then, the horizontal and vertical gradients of the texture image are calculated using a Sobel convolution kernel to generate a texture gradient vector. Next, the gradient direction is calculated using an inverse tangent function, and the gradient direction is quantized into K discrete directions, thereby generating a binary direction mask for each discrete direction.

[0019] Preferably, the horizontal and vertical gradients of the texture image, and the generated texture gradient vector, are represented as follows:

[0020] G x (x i )=I(x i )*S x G y (x i )=I(xi )*S y ;

[0021]

[0022] In the formula, I(x) i ) represents the first point cloud data of bamboo and wooden slip fragments X. i x point cloud sampling points i Corresponding texture image; S x and S y Both represent Sobel convolution kernels; G x (x i ) and G y (x i ) represent the sampling points x in the point cloud, respectively. i Gradient along the horizontal and vertical directions in the texture image; g(x) i ) represents the sampling point x in the point cloud. i The texture gradient vector.

[0023] Preferably, the gradient direction is represented as:

[0024]

[0025] In the formula, θ(x) i ) represents the sampling point x in the point cloud. i The gradient direction; ∈ represents a preset positive constant;

[0026] The binary direction mask generated for each discrete direction is represented as follows:

[0027]

[0028] In the formula, M k (x i ) represents the sampling point x in the point cloud. i Directional mask; θ k This represents the central angle of the k-th discrete direction. Δ represents the directional tolerance.

[0029] Preferably, the specific processing steps of the joint optimization registration module in the bamboo and wooden slip fragment point cloud splicing model include the following steps:

[0030] S1. Obtain the source point cloud and target point cloud to be registered from the point cloud data of the bamboo and wooden slips, and perform downsampling, noise reduction and coordinate normalization preprocessing.

[0031] S2. For each point in the preprocessed source point cloud, based on the similarity between the multi-scale geometric descriptor and the geometric label, candidate point pairs are matched in the target point cloud through nearest point search.

[0032] S3. Based on the texture gradient vector of the candidate point pair and the corresponding binary orientation mask, calculate the texture gradient orientation difference of the candidate point pair, and filter out candidate point pairs that are greater than a preset angle threshold.

[0033] S4. Construct a multimodal error function that includes geometric error, label error, and texture error, and perform weighted processing based on the multimodal error function using the generalized T-Student kernel function; with the goal of optimizing the multimodal error function weighted by the generalized T-Student kernel function, use the optimization algorithm to calculate the rotation matrix and translation vector, and update the source point cloud based on the calculated rotation matrix and translation vector;

[0034] S5. Determine whether the weighted average registration error between the updated source point cloud and the target point cloud is less than a preset threshold. If it is satisfied, proceed to step S7; otherwise, proceed to step S6.

[0035] S6. Return to step S2 and continue iterative optimization based on the updated source point cloud;

[0036] S7. The optimization process converges, the iteration ends, and the final rotation matrix and translation vector, as well as the registered point cloud data, are output.

[0037] Preferably, in step S4, the multimodal error function, which includes geometric error, label error, and texture error, is expressed as:

[0038]

[0039] In the formula, E represents the multimodal error function; Indicates geometric error; Indicates labeling error; Represents texture error; R and t represent the rotation matrix and translation vector, respectively; x i Let y represent the i-th point in the source point cloud. c(i) Indicates the relationship between x and the target point cloud. i Corresponding candidate points; and These represent the two points in the CIELAB color space; w1 and w2 both represent weighting coefficients; g(x i ) and g(y d(i) )) represent the source point x i At the target point y c(i) The image gradient vector at that location; This represents the angle between two gradient vectors; Represents a binary indicator function; c(i) and d(i) both represent indices in the target point cloud; N y Represents the target point cloud number; θ th This indicates the preset threshold angle.

[0040] Preferably, in step S5, the objective function of the generalized T-Student kernel-weighted multimodal error function is expressed as:

[0041]

[0042] In the formula, E' represents the multimodal error function weighted by the generalized T-Student kernel function.

[0043] Compared with the prior art, the present invention has the following technical effects:

[0044] (1) Traditional local point cloud descriptors are limited by single-scale analysis and lack topological connections, resulting in insufficient recognition ability when dealing with complex fracture morphologies. This invention significantly improves the robustness of fracture surface morphology representation by using a geometric feature extraction method that combines multi-scale geometric descriptors with regional connected graphs. This method integrates local normal vector statistical features with regional topological constraints, representing the physical continuity of the fracture surface as a priori feature, reducing geometric errors caused by mismatches, and thus maintaining stable feature matching in the case of missing or eroded data, adapting to the registration requirements of complex fracture morphologies.

[0045] (2) Existing Iterative Closest Point (ICP) algorithms rely only on geometric distance metrics and ignore the semantic continuity of the surface texture of bamboo slips, which can easily lead to distortion of texture direction after registration. This invention introduces a hard constraint on texture gradient direction consistency. By extracting the texture gradient field of RGB-D data and embedding the direction consistency as a hard constraint into the ICP registration process, geometric alignment and texture continuity are achieved simultaneously.

[0046] (3) Traditional Gaussian kernel functions are sensitive to heavy-tailed noise, which can easily cause nonlinear divergence in registration errors. This invention replaces the traditional least squares metric with a generalized T-Student kernel, significantly improving the robustness and convergence speed of point cloud registration. During the iteration process, the generalized T-Student kernel can effectively handle outliers and noise, improving the stability and accuracy of registration. By combining geometric and texture features, the method of this invention can fully utilize the multi-dimensional information of the fragmented bamboo and wooden slips to achieve high-precision and high-efficiency splicing, providing strong technical support for the digital protection and restoration of bamboo and wooden slip artifacts. In addition, this method also has good scalability and adaptability, and can be applied to data registration and splicing tasks of other similar artifacts. Attached Figure Description

[0047] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0048] Figure 1 The successful reassembly of the capital city fragment diagram disclosed in the background art of this invention;

[0049] Figure 2 This is a flowchart of a method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function disclosed in this invention;

[0050] Figure 3 This is a schematic diagram of the curve of the generalized T-Student kernel function of this invention;

[0051] Figure 4 A schematic diagram illustrating data acquisition using three-dimensional scanning technology in an embodiment of the invention;

[0052] Figure 5 This is a three-dimensional data example of broken bamboo and wooden slips according to an embodiment of the present invention;

[0053] Figure 6 This is a comparison chart of experimental results from embodiments of the present invention;

[0054] Figure 7 This is a comparison chart of other experimental results from embodiments of the present invention;

[0055] Figure 8 This is a comparison chart of multimodal experimental results in an embodiment of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but only to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0057] The present invention will now be described in further detail with reference to the accompanying drawings.

[0058] Point cloud registration is a fundamental research problem in computer vision and pattern recognition, with important applications in the digital preservation and restoration of cultural heritage. In recent years, with the increasing demand for efficient reconstruction of historical artifacts, especially in the digital restoration of bamboo slips, pottery, and ancient manuscripts, the value of point cloud registration technology has become increasingly prominent. It can achieve precise alignment and fusion of high-resolution scan data of artifact fragments, thereby promoting their digital restoration and physical reconstruction. In cultural heritage preservation, point cloud registration can effectively reduce human intervention, lower restoration errors, and generate accurate digital archives, which is of great significance. Through the registration and fusion of multi-source data (such as 3D laser scanning, infrared imaging, and high-resolution photography), not only can the accuracy of digital models be improved, but previously invisible details of artifacts can also be revealed. These technological advancements promote the implementation of more scientific and effective cultural heritage preservation strategies, while also enhancing public accessibility and understanding of ancient artifacts through digital exhibitions and interactive experiences.

[0059] Although point cloud registration algorithms have made significant progress in matching rigid and some non-rigid targets, they still have many limitations when applied to bamboo and wooden slips. Most algorithms (such as CPD and GLTP), while possessing some non-rigid processing capabilities, are largely based on targets with good local topology, making them ill-suited to the significant bending, warping, and even breakage caused by long-term burial, corrosion, or compression of bamboo and wooden slips. Furthermore, bamboo and wooden slips are extremely sensitive to noise, and traditional ICP and its improvements are also relatively vulnerable to noise and outliers, easily leading to registration errors. Therefore, as a fragile, highly deformable, and noise-sensitive cultural relic, bamboo and wooden slips require more targeted optimization strategies, such as enhancing robustness to deformation, fusing texture information, and improving noise suppression capabilities, to achieve higher accuracy and greater adaptability in point cloud registration.

[0060] To address the aforementioned problems and shortcomings, this invention proposes a data registration and stitching method for fragmented bamboo and wooden slips based on the generalized T-Student kernel function. In terms of geometric processing, this method combines multi-scale geometric descriptors with region graph convolution to effectively compensate for the sparsity of geometric features on the fracture surface. Regarding texture processing, a hard constraint mechanism on texture gradient direction ensures the continuity of texture direction during registration. In terms of optimization algorithm, the generalized T-Student kernel function, which has heavy-tailed distribution characteristics, is employed to achieve adaptive suppression of noise and outliers.

[0061] Specifically, this invention proposes a method for registering and stitching fragmented bamboo and wooden slips based on the generalized T-Student kernel function. This method acquires the fragmented bamboo and wooden slips data to be stitched, which includes point cloud data and texture image data of the fragmented bamboo and wooden slips. The fragmented bamboo and wooden slips data to be stitched are used as input to the point cloud stitching model of the fragmented bamboo and wooden slips, and the stitching result of the fragmented bamboo and wooden slips data to be stitched is output. The bamboo and wooden slip fragment point cloud stitching model includes a geometric feature extraction module, a texture feature extraction module, and a joint optimization registration module. The model transmits the input bamboo and wooden slip fragment data to the geometric feature extraction module and the texture feature extraction module, respectively. The geometric feature extraction module extracts the local normal vectors of the point cloud data and constructs a multi-scale geometric descriptor that integrates the region connectivity graph convolution to generate geometric labels. The texture feature extraction module extracts and calculates the texture gradient vector of the texture image data and generates a binary orientation mask. Then, the joint optimization registration module combines the outputs of the geometric and texture feature extraction modules to construct a multimodal error function that combines geometric and texture errors. The multimodal error function is weighted using a generalized T-Student kernel function, and the weighted multimodal error function is iterated to obtain the stitching result of the bamboo and wooden slip stitching data as the output.

[0062] As can be seen, this invention introduces a correction algorithm based on point cloud local normal vectors and region connectivity, which improves the robustness of fracture surface morphology representation through multi-scale geometric descriptors; secondly, it designs a texture gradient direction consistency verification rule, which uses the spatial continuity of RGB-D data to extract semantic texture information of fracture surface; finally, it constructs a generalized T-Student kernel function, which effectively suppresses noise and outlier interference through an adaptive weight adjustment mechanism.

[0063] The following section provides a more detailed description of the point cloud stitching model for bamboo and wooden slips in the method for registering and stitching bamboo and wooden slips based on the generalized T-Student kernel function of this invention.

[0064] 1. Registration of fracture surfaces of bamboo slips based on weighted geometry-label joint constraints

[0065] Since the point clouds of bamboo and wooden slips lack significant structural variations, relying solely on geometric information for point cloud alignment often leads to registration failure. To address this, this invention proposes an innovative correction algorithm based on multi-scale geometry-topology joint optimization. This method constructs a dynamically adaptable geometric representation model of the fracture surface by integrating the multi-scale representation capability of local normal vector statistical features with the topology-preserving property of regional connectivity constraints.

[0066] In practice, before registering the fracture surfaces of the bamboo slips based on weighted geometry-label joint constraints, the geometric feature extraction module generates local normal vectors, multi-scale geometric descriptors, and geometric labels. The specific processing steps include the following:

[0067] First, the point cloud data of the bamboo and wooden slips used as input... Each point cloud sampling point x i A k-nearest neighbor search is performed to obtain the local neighborhood point set, where N represents the number of point cloud sampling points contained in the point cloud data X of the bamboo and wooden slips. Then, the local normal vector is obtained by minimizing the sum of squared distances from the neighborhood points to the tangent plane. Finally, graph convolution is used to construct a connected graph of the region. Specifically, the set of point cloud sampling points in the point cloud data X of the bamboo and wooden slips fragments is constructed as a vertex set. The set of Euclidean distances between point cloud sampling points is used to construct an edge set ε, which is then used in the multi-scale regional connectivity graph. The graph convolution operation is used to extract multi-scale geometric descriptors, s = 1, 2, ..., S, where S is the total number of graph convolution layers. Finally, the multi-scale geometric descriptors are concatenated and classified by a multilayer perceptron to output geometric labels.

[0068] The objective function of the local normal vector is:

[0069]

[0070] In the formula, n i This represents the i-th point cloud sampling point x in the point cloud data X of the bamboo and wooden slips fragments. i The corresponding local normal vector; Represents the sampling point x in the point cloud i The local neighborhood point set; Representation of neighborhood point set The center of mass.

[0071] The processing procedure for the multi-scale geometric descriptor is expressed as follows:

[0072]

[0073] In the formula, f represents the multi-scale geometric descriptor of the graph convolution at layer s; j W represents the point cloud coordinates of point j. (s) With b (s) Let represent the weights and bias parameters of the graph convolution at layer s, respectively. This represents the edge weight between point i and point j. Let represent the local neighborhood point set of point i in the graph convolution of the s-th layer; σ represents the activation function.

[0074] The core objective function based on the weighted geometry-label joint constraint is defined as follows:

[0075]

[0076] To fully utilize normal vector features and region connectivity to establish accurate point correspondences between two sets of point clouds, determining a suitable weighting parameter is crucial. This parameter balances geometric alignment and label consistency. When the weighting parameter is large, the algorithm focuses more on semantic matching of local geometric features (such as curvature and flatness), making it suitable for scenarios with severe fracture surface defects. Conversely, when the weighting parameter is small, the algorithm relies more on coordinate distance alignment, making it more suitable for registration tasks with lower defects and relatively intact surfaces.

[0077] 2. Semantic alignment optimization based on hard constraints of texture gradient direction

[0078] To address the core requirement of restoring the surface texture continuity of broken bamboo and wooden slips, this invention proposes a multimodal registration algorithm driven by hard constraints on texture gradient direction consistency. This method breaks through the traditional pure geometric registration framework by integrating semantic information from the texture gradient field of RGB-D data, constructing a multimodal error function jointly optimized by geometry and texture. This significantly improves the visual consistency of broken surface registration and better preserves the integrity of cultural information.

[0079] In practice, before semantic alignment optimization based on hard constraints of texture gradient direction, the texture gradient vector of the texture image data corresponding to the point cloud data is extracted using the texture feature extraction module, and a binary orientation mask is generated. The specific processing steps include the following:

[0080] First, the point cloud data of the bamboo and wooden slip fragments, which are used as input, are mapped to obtain the corresponding texture image data. Then, the horizontal and vertical gradients of the texture image are calculated using a Sobel convolution kernel to generate a texture gradient vector. Next, the gradient direction is calculated using an inverse tangent function, and the gradient direction is quantized into K discrete directions, thereby generating a binary direction mask for each discrete direction.

[0081] The horizontal and vertical gradients of the texture image, and the generated texture gradient vector, are represented as follows:

[0082] G x (x i )=I(x i )*S x G y (x i )=I(x i )*S y ;

[0083]

[0084] In the formula, I(x) i ) represents the i-th point cloud sampling point x in the point cloud data X of the bamboo and wooden slip fragments. i Corresponding texture image; S x and S y Both represent Sobel convolution kernels; G x (x i ) and G y (x i ) represent the sampling points x in the point cloud, respectively. i Gradient along the horizontal and vertical directions in the texture image; g(x) i ) represents the sampling point x in the point cloud. i The texture gradient vector.

[0085] The gradient direction is represented as:

[0086]

[0087] In the formula, θ(x) i ) represents the sampling point x in the point cloud. i The gradient direction; ∈ represents a preset positive constant, which is a sufficiently small positive constant value, and its function is to prevent the denominator from being zero.

[0088] The binary direction mask generated for each discrete direction is represented as follows:

[0089]

[0090] In the formula, M k (x i ) represents the sampling point x in the point cloud. i Directional mask; θ k This represents the central angle of the k-th discrete direction. Δ represents the directional tolerance.

[0091] The core optimization function based on hard constraints in the texture gradient direction is defined as follows:

[0092]

[0093] First, the first term of the objective function is a joint geometric and color error term, designed to evaluate the spatial coordinate difference between the transformed source point and its corresponding point in the target point cloud, while incorporating color space information to enhance semantic consistency. Specifically, Indicates geometric error; Represents the labeling error; R and t represent the rotation matrix and translation vector, respectively; x i Let y represent the i-th point in the source point cloud. c(i)Indicates the relationship between x and the target point cloud. i The corresponding candidate points; w1 represents the weighting coefficient; and These represent the two points in the CIELAB color space. By jointly optimizing the Euclidean distance and perceived color difference, this not only ensures the registration accuracy in the geometric structure but also improves the alignment effect in the material properties, thereby enhancing the visual continuity of the fracture surface.

[0094] Secondly, the objective function introduces a hard constraint mechanism based on the consistency of texture gradient direction, aiming to avoid mismatch of surface textures in the fracture region. Specifically, Indicates texture error; g(x) i ) and g(y d(i) )) represent the source point x i At the target point y c(i) The image gradient vector at that location is used to capture the main direction of the surface texture; This represents the angle between two gradient vectors; Represents a binary indicator function; θ th This indicates the preset threshold angle, which is only considered when the angle difference... (e.g., 15°) takes a value of 1, thus forcing directional consistency; c(i) and d(i) both represent indices in the target point cloud; N y Indicates the target point cloud number;

[0095] This constraint mechanism ensures the continuity of texture direction during registration, which is particularly important for key features such as ink strokes and lacquer lines on the surface of bamboo and wooden slips. At the same time, this mechanism exhibits strong robustness in the face of real-world degradation conditions (such as blurring, tilting, and surface erosion).

[0096] 3. Error optimization based on generalized T-Student kernel

[0097] In the process of registering point clouds of bamboo and wooden slips, due to their thin-walled structure being easily deformable, having large curvature of fracture surfaces, and the unavoidable presence of noise in actual acquisition and fusion, traditional least squares error metrics are difficult to effectively distinguish between normal data, noise, and outliers. These outliers will significantly affect the registration accuracy of the standard ICP (Iterative Closest Point) algorithm.

[0098] To address this issue, this invention proposes a robust error optimization framework based on the generalized T-Student kernel function. This method effectively suppresses outlier interference through an adaptive weight allocation mechanism and heavy-tailed distribution characteristics, enabling the algorithm to maintain strong registration accuracy and robustness when processing real bamboo and wooden slip point clouds, thereby significantly improving its practicality in cultural heritage protection.

[0099] In other words, this invention constructs a multimodal error function that combines geometric and texture errors based on the joint optimization registration module and the outputs of the geometric feature extraction module and the texture feature extraction module. The multimodal error function is weighted by the generalized T-Student kernel function and iterated over to obtain the splicing result of the bamboo and wooden slip splicing data.

[0100] In specific implementation, the specific processing procedure of the joint optimization registration module is as follows: Figure 2 As shown, it includes the following steps:

[0101] S1. Obtain the source point cloud and target point cloud to be registered from the point cloud data of the bamboo and wooden slips, and perform downsampling, noise reduction and coordinate normalization preprocessing.

[0102] S2. For each point in the preprocessed source point cloud, based on the similarity between the multi-scale geometric descriptor and the geometric label, candidate point pairs are matched in the target point cloud through nearest point search.

[0103] S3. Based on the texture gradient vector of the candidate point pair and the corresponding binary orientation mask, calculate the texture gradient orientation difference of the candidate point pair, and filter out candidate point pairs that are greater than a preset angle threshold.

[0104] S4. Construct a multimodal error function that includes geometric error, label error, and texture error, and perform weighted processing based on the multimodal error function using the generalized T-Student kernel function; with the goal of optimizing the multimodal error function weighted by the generalized T-Student kernel function, use the optimization algorithm to calculate the rotation matrix and translation vector, and update the source point cloud based on the calculated rotation matrix and translation vector;

[0105] S5. Determine whether the weighted average registration error between the updated source point cloud and the target point cloud is less than a preset threshold. If it is satisfied, proceed to step S7; otherwise, proceed to step S6.

[0106] S6. Return to step S2 and continue iterative optimization based on the updated source point cloud;

[0107] S7. The optimization process converges, the iteration ends, and the final rotation matrix and translation vector, as well as the registered point cloud data, are output.

[0108] like Figure 3 As shown, the generalized T-Student kernel is introduced into the registration algorithm. The generalized T-Student kernel function achieves robust optimization by maximizing the reciprocal of the fraction of the multimodal error function. Its effect is equivalent to adaptive weighting of the error term: large error terms will significantly reduce the fraction value, thus being automatically suppressed by the optimization process.

[0109] It is represented as:

[0110]

[0111] 4. Example

[0112] To better illustrate the effectiveness of this method, a specific example will be used to illustrate the method of this invention below.

[0113] This embodiment designs a comprehensive set of experiments to evaluate the performance and robustness of the proposed point cloud registration method in real-world scenarios. The experiments cover multiple settings, including ablation experiments, rotation simulations, and noise simulations, aiming to verify the effectiveness of the algorithm in dealing with challenges such as initial pose rotation, environmental noise, and outliers.

[0114] By comparing this method with a variety of advanced point set registration algorithms, such as ICP, Picky-ICP, Robust-ICP, Correntropy-ICP, and Color-ICP, as well as deep learning-based methods (such as PCRNet, RPM-Net, and DeepGMR), this embodiment highlights the unique advantages and innovative contributions of this method in achieving high-precision and high-robust registration in practical applications, which is of great significance for achieving accurate reconstruction of bamboo and wooden slips.

[0115] The experimental environment configuration is as follows: Hardware: Intel Core i9-10920X@3.50GHz CPU, 48GB RAM, NVIDIA GeForce RTX 3090 GPU (24GB VRAM); Software: MATLAB R2023a.

[0116] 4.1 Data Acquisition

[0117] Given the characteristics of bamboo and wooden slips artifacts, such as thin-walled structures, large fracture curvature, and complex surface carvings, this dataset utilizes an industrial-grade structured light scanner (accuracy <0.05mm) for multi-view point cloud acquisition. The scanning range covers the entire surface of the bamboo and wooden slips, with an angle range of θ∈[0°,360°] and an angle interval of Δθ=15°. Figure 4 As shown in the image. Simultaneously, a high-resolution full-frame camera (60 megapixels) was used to synchronously acquire the surface texture and fine features of the bamboo slip fragments, thus constructing a cross-modal geometry-texture joint dataset. The final acquired data is shown in the image. Figure 5 As shown.

[0118] 4.2 Ablation Experiment

[0119] To verify the impact of constraint optimization strategies on the accuracy of the proposed registration model, this embodiment designed and conducted corresponding ablation experiments. The registration model improves registration accuracy and robustness by introducing three optimization strategies: point cloud normal vector features, a feature reference mechanism based on the texture gradient of the bamboo slips, and the application of the generalized T-Student kernel function. This embodiment uses the control variable method to remove individual optimization strategies to evaluate the contribution of each strategy to the overall registration effect, thereby clarifying the relative impact of each strategy on the final registration result.

[0120] To quantify the registration accuracy, the experiment generated a fixed point set by rotating the movable point set by 30 degrees around the z-axis, and set a predefined rotation matrix R. set With translation vector During point cloud registration, the actual registration rotation matrix R obtained by the algorithm is recorded. get ′ and translation vector and The standard error was calculated based on this to measure the registration accuracy. The experimental results are shown in Table 1.

[0121] Table 1 Ablation Experiment Results

[0122]

[0123] Experimental results show that, when applying various optimization strategies, the feature reference mechanism based on the texture gradient of bamboo slips achieves the highest registration accuracy, highlighting the crucial role of semantic information in point cloud registration. Unlike local geometric descriptors such as normal vectors, which may be unstable in regions with complex curvature or degraded surfaces, texture gradient features, derived from RGB-D data, can encode the continuity and directionality of ink marks and lacquer lines. These semantic cues provide stronger constraints for correspondence matching, especially when geometric features are insufficient to uniquely determine spatial relationships.

[0124] The performance differences become even more pronounced when different optimization modules are used in combination. For example, the registration performance is better than using either strategy alone when point cloud normal features are used in conjunction with the generalized T-Student kernel function. This is because normal vectors can effectively describe local surface orientation, while the T-Student kernel function has heavy-tailed characteristics, which can suppress the influence of noise and outliers. The combination of the two not only achieves accurate local geometric modeling but also improves the robustness of global optimization, making it particularly suitable for real-world situations with scanning noise, surface scratches, or incomplete data.

[0125] Optimal results are achieved when all three modules—Normal Vector Statistics (NV), Texture Gradient Consistency (TG), and Generalized T-Student Kernel Function (GT-SK)—are fully integrated. In this case, the registration process benefits from multimodal feature guidance: geometry, surface texture orientation, and noise modeling complement each other. Texture feature references enhance the reliability of matching point estimation, normal constraints stabilize local structural alignment, and the kernel-based error model effectively mitigates noise interference. This multi-layered synergy achieves an optimal trade-off between registration accuracy and robustness, making it particularly suitable for the urgent need for high-fidelity reconstruction of bamboo and wooden slips in practical cultural heritage digitization tasks.

[0126] 4.3 Rotation Experiment

[0127] To verify the registration capability of the proposed algorithm in this embodiment when handling point sets with large initial rotational attitudes, a rotation simulation experiment was designed. Four sets of point cloud datasets were selected for testing and compared with baseline algorithms. The experiment generated a fixed point set by applying a preset rotation to the movable point set, and then used rotation errors (ε) to calculate the fixed point set. R Translation error The registration accuracy is evaluated using metrics. The registration results are as follows: Figure 6 , Figure 7 , Figure 8 As shown in Table 2.

[0128] The comparison results shown in Table 2 clearly demonstrate that existing point cloud registration algorithms have significant limitations in handling bamboo and wooden slip reconstruction tasks. Traditional methods such as ICP, Picky-ICP, Robust-ICP, MCC-ICP, and HSV-ICP all exhibit varying degrees of sensitivity to initial rotation and noise. These algorithms primarily rely on geometric proximity, with their core mechanism based on minimizing point-to-point Euclidean distance. Therefore, they are prone to getting trapped in local optima when faced with large rotational deviations or structural incompleteness. Furthermore, these methods experience a significant drop in registration performance when dealing with fine-grained texture features, ink marks, or lacquer line continuity on the surface of bamboo and wooden slip fragments. Even enhanced variants such as MCC-ICP and HSV-ICP, which introduce additional constraints or color information, still suffer from insufficient registration accuracy due to their inability to semantically parse the directionality of texture gradients or robustly suppress heavy-tailed noise.

[0129] Table 2 Registration error in rotation experiment

[0130]

[0131] In contrast, while deep learning-based algorithms such as PCRNet, RPM-Net, and DeepGMR perform well in conventional rigid registration tasks, they also face adaptation challenges in the specific domain of bamboo and wooden slips. These models are mostly trained on regular geometries in synthetic or real-world scenarios, with clear structures but lacking complex curvature and degradation features. In contrast, bamboo and wooden slip fragments possess unique characteristics such as high local curvature, non-rigid aging (e.g., oxidation, fracture erosion), and texture-guided semantic cues, which are often difficult for models trained on general datasets to accurately capture. Therefore, these methods often suffer from convergence instability or inability to maintain surface orientation consistency in bamboo and wooden slip tasks, which is crucial for subsequent text analysis and cultural information reconstruction.

[0132] In contrast, the proposed method achieves significantly lower registration errors on all test datasets, and its superior performance can be attributed to three core innovations. First, the fusion of texture gradient feature reference mechanisms enables the algorithm to utilize the semantic continuity reflecting the direction of ink marks to provide key constraints for the splicing of bamboo and wooden slips. Second, the use of normal vector statistical encoding enhances local geometric robustness, particularly excelling in high curvature and data-missing regions. Third, the introduction of a generalized T-Student kernel function to construct an optimization model possesses the ability to suppress heavy-tailed noise, effectively avoiding the interference of outliers on the registration results. The synergistic effect of these three aspects enables the method to achieve an excellent balance between accuracy and robustness, meeting the stringent requirements for high-fidelity registration in cultural heritage restoration tasks such as the surface reconstruction of bamboo and wooden slips.

[0133] 4.4 Noise Experiment

[0134] In real-world applications, cultural heritage preservation tasks inevitably involve noise and outliers. Therefore, point cloud registration algorithms for bamboo and wooden slip reconstruction must possess strong noise resistance. To verify the robustness of the proposed algorithm under noise interference, this study designed a noise simulation experiment. By introducing random Gaussian color noise (with the standard deviation of the Gaussian function set to 0.01) into the point cloud data, the noise level of the point set is enhanced, with the rotation error (ε) being considered. R Translation error This is a quantitative indicator of registration accuracy. The experimental results are shown in Table 3.

[0135] Table 3 Registration error in noise experiment

[0136]

[0137] Compared to rotational simulation experiments, the registration error of all algorithms generally increased in noise simulation experiments due to the influence of Gaussian color noise. Traditional ICP-based methods (such as Standard ICP, Picky-ICP, and Robust-ICP) are mostly built on a rigid least-squares registration framework, lacking the ability to effectively distinguish between noise, outliers, and valid matching points. After introducing Gaussian noise, these algorithms often misclassify noisy points as valid corresponding points, leading to error accumulation and registration drift. Even with the point-pair filtering mechanism introduced in Robust-ICP, registration misalignment is still difficult to avoid when facing high-density noise interference.

[0138] Correntropy-ICP employs the Maximum Information Potential (MCC) criterion to enhance outlier suppression, but its noise tolerance is limited in areas with strong texture degradation or blurred boundaries, making it difficult to maintain a stable residual distribution and ultimately leading to a significant increase in rotational error. While Color-ICP has a theoretical advantage in improving matching accuracy under clean conditions by leveraging color information, its color channels are highly susceptible to interference in noisy environments, and the method lacks a modeling mechanism for color noise distribution, thus proving ineffective under Gaussian color noise.

[0139] Meanwhile, although learning-based methods such as PCRNet, RPM-Net, and DeepGMR can model global features and perform well in noise-free environments, their generalization ability is insufficient when dealing with data such as bamboo and wooden slips. On the one hand, these models are usually trained on geometrically regular datasets with clear textures, while bamboo and wooden slip fragments exhibit complex features such as ink degradation, material breakage, and surface contamination. On the other hand, the registration strategies of these algorithms mostly rely on global pose estimation, which is extremely sensitive to large-scale noise, leading to a significant decrease in registration and matching accuracy.

[0140] In contrast, the proposed method maintains high registration accuracy even under strong noise conditions, thanks to the following two key innovations: First, the introduction of texture gradient direction consistency constraints enhances the semantic reliability of point pair matching and effectively mitigates the impact of noise on direction estimation; Second, the embedding of the generalized T-Student kernel function in the core optimization function, whose heavy-tailed distribution characteristics can dynamically suppress the interference of high residual point pairs, thereby effectively solving the common convergence instability problem of the least squares framework under non-uniform noise.

[0141] 5. Overview

[0142] In summary, this embodiment proposes a data registration and stitching method for fragmented bamboo and wooden slips based on the generalized T-Student kernel function. This method achieves high-precision reconstruction of fragmented bamboo and wooden slips under complex damage conditions by fusing geometric features, texture gradient information, and the generalized T-Student kernel function. The main conclusions are as follows: Multimodal feature collaboration: Joint optimization of geometric normal vectors and texture gradients effectively reduces registration errors on fracture surfaces. Enhanced noise robustness: The adaptive weighting mechanism based on the generalized T-Student kernel function effectively distinguishes between interior points, noise (Gaussian noise standard deviation σ = 0.1 mm), and outliers, suppressing the interference of asymmetric noise on registration accuracy. Stronger rotation robustness: In rotation simulation experiments, this method exhibits higher tolerance to initial attitude deviations (±180°), verifying its effectiveness in combining geometric features and hard constraints of texture gradient direction compared to other advanced methods.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described with reference to preferred embodiments, those skilled in the art should understand that various changes in form and detail can be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function, characterized in that, Obtain the data of the bamboo and wooden slip fragments to be spliced, which includes point cloud data and texture image data of the bamboo and wooden slip fragments; use the data of the bamboo and wooden slip fragments to be spliced ​​as the input of the point cloud splicing model of the bamboo and wooden slip fragments, and output the splicing result of the data of the bamboo and wooden slip fragments to be spliced. The bamboo and wooden slip fragment point cloud stitching model includes a geometric feature extraction module, a texture feature extraction module, and a joint optimization registration module. The model transmits the input bamboo and wooden slip fragment data to the geometric feature extraction module and the texture feature extraction module, respectively. The geometric feature extraction module extracts the local normal vectors of the point cloud data and constructs a multi-scale geometric descriptor that integrates the region connectivity graph convolution to generate geometric labels. The texture feature extraction module extracts and calculates the texture gradient vector of the texture image data and generates a binary orientation mask. Then, the joint optimization registration module combines the outputs of the geometric and texture feature extraction modules to construct a multimodal error function that combines geometric and texture errors. The multimodal error function is weighted using a generalized T-Student kernel function, and the weighted multimodal error function is iterated to obtain the stitching result of the bamboo and wooden slip stitching data as the output.

2. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 1, characterized in that, The specific processing steps of the geometric feature extraction module in the bamboo and wooden slip fragment point cloud splicing model include the following steps: First, the point cloud data of the bamboo and wooden slips used as input... Each point cloud sampling point x i A k-nearest neighbor search is performed to obtain the local neighborhood point set, where N represents the number of point cloud sampling points contained in the point cloud data X of the bamboo and wooden slips. Then, the local normal vector is obtained by minimizing the sum of squared distances from the neighborhood points to the tangent plane. Finally, graph convolution is used to construct a connected graph of the region. Specifically, the set of point cloud sampling points in the point cloud data X of the bamboo and wooden slips fragments is constructed as a vertex set. The set of Euclidean distances between point cloud sampling points is used to construct an edge set ε, which is then used in the multi-scale regional connectivity graph. The graph convolution operation is used to extract multi-scale geometric descriptors, s = 1, 2, ..., S, where S is the total number of graph convolution layers. Finally, the multi-scale geometric descriptors are concatenated and classified by a multilayer perceptron to output geometric labels.

3. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 2, characterized in that, The objective function of the local normal vector is: subject to||n i ||2=1; In the formula, n i This represents the i-th point cloud sampling point x in the point cloud data X of the bamboo and wooden slips fragments. i The corresponding local normal vector; Represents the sampling point x in the point cloud i The local neighborhood point set; Representation of neighborhood point set The center of mass.

4. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 2, characterized in that, The processing procedure for the multi-scale geometric descriptor is expressed as follows: In the formula, f represents the multi-scale geometric descriptor of the graph convolution at layer s; j W represents the point cloud coordinates of point j. (s) With b (s) Let represent the weights and bias parameters of the graph convolution at layer s, respectively. This represents the edge weight between point i and point j. Let represent the local neighborhood point set of point i in the graph convolution of the s-th layer; σ represents the activation function.

5. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 1, characterized in that, The specific processing steps of the texture feature extraction module in the bamboo and wooden slip fragment point cloud stitching model include the following steps: First, the point cloud data of the bamboo and wooden slip fragments, which are used as input, are mapped to obtain the corresponding texture image data. Then, the horizontal and vertical gradients of the texture image are calculated using a Sobel convolution kernel to generate a texture gradient vector. Next, the gradient direction is calculated using an inverse tangent function, and the gradient direction is quantized into K discrete directions, thereby generating a binary direction mask for each discrete direction.

6. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 5, characterized in that, The horizontal and vertical gradients of the texture image, and the generated texture gradient vector, are represented as follows: G x (x i )=I(x i )*S x ,G y (x i )=I(x i )*S y ; In the formula, I(x) i ) represents the i-th point cloud sampling point x in the point cloud data X of the bamboo and wooden slip fragments. i Corresponding texture image; S x and S y Both represent Sobel convolution kernels; G x (x i ) and G y (x i ) represent the sampling points x in the point cloud, respectively. i Gradient along the horizontal and vertical directions in the texture image; g(x) i ) represents the sampling point x in the point cloud. i The texture gradient vector.

7. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 6, characterized in that, The gradient direction is represented as: In the formula, θ(x) i ) represents the sampling point x in the point cloud. i The gradient direction; ∈ represents a preset positive constant; The binary direction mask generated for each discrete direction is represented as follows: In the formula, M k (x i ) represents the sampling point x in the point cloud. i Directional mask; θ k This represents the central angle of the k-th discrete direction. Δ represents the directional tolerance.

8. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 1, characterized in that, The specific processing steps of the joint optimization registration module in the bamboo and wooden slip fragment point cloud stitching model include the following steps: S1. Obtain the source point cloud and target point cloud to be registered from the point cloud data of the bamboo and wooden slips, and perform downsampling, noise reduction and coordinate normalization preprocessing. S2. For each point in the preprocessed source point cloud, based on the similarity between the multi-scale geometric descriptor and the geometric label, candidate point pairs are matched in the target point cloud through nearest point search. S3. Based on the texture gradient vector of the candidate point pair and the corresponding binary orientation mask, calculate the texture gradient orientation difference of the candidate point pair, and filter out candidate point pairs that are greater than a preset angle threshold. S4. Construct a multimodal error function that includes geometric error, label error, and texture error, and perform weighted processing based on the multimodal error function using the generalized T-Student kernel function; with the goal of optimizing the multimodal error function weighted by the generalized T-Student kernel function, use the optimization algorithm to calculate the rotation matrix and translation vector, and update the source point cloud based on the calculated rotation matrix and translation vector; S5. Determine whether the weighted average registration error between the updated source point cloud and the target point cloud is less than a preset threshold. If it is, proceed to step S7. If not satisfied, proceed to step S6; S6. Return to step S2 and continue iterative optimization based on the updated source point cloud; S7. The optimization process converges, the iteration ends, and the final rotation matrix and translation vector, as well as the registered point cloud data, are output.

9. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 8, characterized in that, In step S4, the multimodal error function, which includes geometric error, label error, and texture error, is expressed as follows: size T R=I,det(R)=1,c(i)∈{1,2,…,N y },d(i)∈{1,2,…,N y }, In the formula, E represents the multimodal error function; Indicates geometric error; Indicates labeling error; Represents texture error; R and t represent the rotation matrix and translation vector, respectively; x i Let y represent the i-th point in the source point cloud. c(i) Indicates the relationship between x and the target point cloud. i Corresponding candidate points; and These represent the two points in the CIELAB color space; w1 and w2 both represent weighting coefficients; g(x i ) and g(y d(i) )) represent the source point x i At the target point y c(i) The image gradient vector at that location; This represents the angle between two gradient vectors; Represents a binary indicator function; c(i) and d(i) both represent indices in the target point cloud; N y Represents the target point cloud number; θ th This indicates the preset threshold angle.

10. The method for registering and splicing fragmented bamboo and wooden slips based on the generalized T-Student kernel function according to claim 9, characterized in that, In step S5, the objective function of the generalized T-Student kernel-weighted multimodal error function is expressed as: size T R=I,det(R)=1,c(i)∈{1,2,…,N y },d(i)∈{1,2,…,N y }, In the formula, E' represents the multimodal error function weighted by the generalized T-Student kernel function.

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