Methods, systems and electronic devices for restoring the physical scale of three-dimensional solids

Abstract

This invention discloses a method and system for restoring the physical scale of a three-dimensional entity, comprising: acquiring a normalized point cloud; performing normalized sampling preprocessing through farthest point sampling to preserve the original absolute position distribution of the point cloud; inputting the normalized input point set into a scale-sensitive point cloud representation module, using three-dimensional coordinates and Euclidean distances from neighboring points to a reference point as enhanced inputs, and obtaining point-level local responses through aggregation using a shared multilayer perceptron; after cross-channel feature coupling, performing mean aggregation and extreme value aggregation on each scale channel and concatenating them to obtain a shape-level representation vector; performing Z-score normalization on the shape-level representation vector, and predicting scale parameters through a radial basis function kernel support vector regression model; performing inverse size mapping on the normalized point cloud based on the predicted scale parameters to restore the true physical size point cloud. This invention requires no external sensors or additional scale acquisition equipment, and can restore the true physical size of the target object with high precision using only the point cloud data itself.

Description

Technical Field

[0001] This invention relates to the field of 3D computer vision and point cloud processing technology, and in particular to a method, system and electronic device for physical scale recovery of 3D entities based on multi-scale point cloud feature learning. Background Technology

[0002] 3D computer vision technology has significant application value in fields such as obstacle avoidance for unmanned vehicles, low-altitude urban reconnaissance by drones, multimodal data fusion, and cross-platform 3D scene understanding. (Single-view) Figure 3 3D reconstruction is one of the core technologies, aiming to recover the three-dimensional geometry of a target object from a single or a few images. In practical engineering applications, 3D reconstruction pipelines typically apply normalization preprocessing to the output point cloud data, compressing point clouds of different categories and sizes into a standard reference space to ensure the numerical stability of network training. However, this preprocessing operation results in the true physical size information of the target object being implicitly included in the scale mapping parameters. The normalized point cloud obtained from the reconstruction cannot directly reflect the physical scale of the target entity in real space, making it difficult for the 3D reconstruction results to meet the needs of downstream engineering applications requiring precise measurements.

[0003] PointNet is one of the most widely used foundational deep learning frameworks in point cloud feature extraction. PointNet takes an unordered 3D point set as input, performs independent feature mapping on each point using a parameter-sharing multilayer perceptron, and then aggregates the high-dimensional feature vectors of all points into a fixed-length global feature vector through global max pooling. However, PointNet's max pooling mechanism only retains the extreme values ​​of each feature dimension, discarding the relative positional relationships and distance information between points in the point cloud; furthermore, its point-by-point independent processing mechanism cannot model spatial relationships between points, and the generated feature vectors are almost insensitive to the absolute scale of the input point cloud. Experiments show that when using the feature vectors extracted by PointNet for scale parameter prediction, the R²-score is only 0.553, and the RMSE is as high as 423.86, making the scale information extraction accuracy insufficient for the needs of entity size recovery.

[0004] PointNet++ is an improved point cloud deep learning framework based on PointNet. By introducing a hierarchical local region sampling and feature extraction mechanism, it enables the network to learn local geometric details at different scales. However, PointNet++ converts the coordinates of each point within a local region to local coordinates relative to the centroid in each ensemble abstraction layer. While this operation enhances invariance to translation transformations, it actively eliminates absolute scale information. Its multi-scale grouping strategy essentially involves extracting local features independently at the same centroid with different radii and then concatenating them; the point-to-point distance ratio between local regions at different scales is not explicitly encoded. Furthermore, both of these methods are designed for point cloud classification and semantic segmentation tasks. The networks tend to learn shape features that are discriminative of object categories, while suppressing scale changes as interference factors. This fundamentally deviates from the requirement of scale recovery tasks, which demand that feature vectors be highly sensitive to changes in physical scale. This results in structural limitations in scale parameter prediction tasks that are difficult to overcome through parameter adjustment.

[0005] Therefore, there is an urgent need for a technical solution for the physical scale restoration of three-dimensional entities that can solve the above problems. Summary of the Invention

[0006] The present invention aims to provide a method, system and electronic device for restoring the physical scale of a three-dimensional entity, so as to overcome the shortcomings of the prior art. The technical problem to be solved by the present invention is achieved through the following technical solutions.

[0007] According to a first aspect of this application, a method for restoring the physical scale of a three-dimensional entity is provided, the method comprising: S1: Obtain the normalized point cloud output by the 3D reconstruction pipeline, and perform normalized sampling preprocessing on the normalized point cloud by sampling the farthest point. The point cloud of arbitrary density is uniformly downsampled to a fixed number of points to obtain a normalized input point set. During the sampling process, no centroid translation, scale normalization or local coordinate system transformation is applied to the point cloud, so as to preserve the original absolute position distribution of the point cloud in the normalized space. S2: The normalized input point set is input into the scale-sensitive point cloud representation module to generate a shape-level representation vector. The scale-sensitive point cloud representation module sets up multiple parallel scale channels. For each scale channel, the neighborhood points are constructed with three-dimensional coordinates and the Euclidean distance from the neighborhood points to the reference point to construct an enhanced input. After mapping by a shared multilayer perceptron, element-wise max pooling aggregation is performed to obtain the point-level local response. At the same time, an independent original coordinate distribution response extraction branch is set up to perform global position mapping on the original three-dimensional coordinates of all points. The original coordinate distribution response and the point-level local response are coupled across channels through linear adaptation mapping for each scale channel. Mean aggregation and extreme value aggregation are performed on each scale channel respectively, and the two types of statistical results of each channel are concatenated to obtain the shape-level representation vector. S3: After performing Z-score normalization preprocessing on the shape-level representation vector, input it into the support vector regression model based on radial basis function kernel to predict the scale parameters corresponding to the normalized point cloud; S4: Based on the predicted scale parameters, multiply the coordinates of each point in the normalized point cloud in each coordinate axis direction by the predicted scale parameters of the corresponding axis, and perform inverse size mapping to obtain a three-dimensional point cloud that restores the true physical size.

[0008] Preferably, the multiple parallel scale channels include three channels, corresponding to neighborhood radii of 0.1, 0.3, and 0.5, respectively; the three channels capture local structures at three levels: fine-grained, medium-grained, and coarse-grained, respectively; the maximum number of neighborhood points for the fine-grained channel, medium-grained channel, and coarse-grained channel are 32, 64, and 128, respectively, and random downsampling is allowed when the number of neighborhood points exceeds the limit, and repeated sampling is allowed when the number of neighborhood points is insufficient.

[0009] Preferably, the shared multilayer perceptron layer structure and output dimensions of the three channels are as follows: the fine-grained channel has an input dimension of 4, which is mapped to the output dimension of 64 through an intermediate dimension of 32; the medium-grained channel has an input dimension of 4, which is mapped to the output dimension of 128 through an intermediate dimension of 64; the coarse-grained channel has an input dimension of 4, which is mapped to the output dimension of 256 through an intermediate dimension of 64; and the shape-level representation vector obtained by splicing the mean and extreme values ​​of each channel has a dimension of 896.

[0010] Preferably, the number of fixed points is 1024; the farthest point sampling selects the point farthest from the already sampled point set as the next sampling point each time, ensuring that the 1024 sampled points are evenly distributed in space and fully cover the overall geometric structure of the target.

[0011] Preferably, the scale parameter is represented in the form of a diagonal matrix, which includes independent scale parameters for the three coordinate directions of x-axis, y-axis and z-axis. For targets that need to distinguish the scale of each axis, three support vector regression instances are trained independently for the three directions of x-axis, y-axis and z-axis, and each outputs the scale parameter for the corresponding axis, which are then combined into a scale estimation matrix.

[0012] Preferably, the penalty parameter C of the support vector regression model is set to 1000, the insensitive band width is set to 0.1, and the kernel function bandwidth parameter is estimated using an adaptive method. The optimal hyperparameter configuration of the support vector regression model is determined by a grid search method. The search space covers three dimensions: kernel function type, penalty parameter, and insensitive band width, with a total of 18 hyperparameter combinations. Each combination is evaluated independently on a fixed-partition training set and test set.

[0013] Preferably, the training process of the support vector regression model includes: randomly dividing the dataset into a training set and a test set at a ratio of 80% / 20%; calculating the mean and standard deviation of each feature dimension only on the training set; performing Z-score standardization on the training set and the test set respectively to avoid data leakage; implementing support vector regression based on the Scikit-learn framework, using the sequence minimum optimization algorithm at the bottom layer, and enabling the shrinkage heuristic method to accelerate the optimization solution.

[0014] According to a second aspect of this application, a three-dimensional physical scale restoration system employing the above-described three-dimensional physical scale restoration method is provided, comprising: The preprocessing module is used to obtain a normalized point cloud. By sampling the farthest point, the normalized point cloud is downsampled to a fixed number of points to obtain a normalized input point set. During the sampling process, no centroid translation, scale normalization or local coordinate system transformation is applied to the point cloud, so as to preserve the original absolute position distribution of the point cloud in the normalized space. The scale-sensitive point cloud representation module is used to construct neighborhood point sets under corresponding neighborhood radii for the normalized input point set through multiple parallel scale channels. The neighborhood points are aggregated through a shared multilayer perceptron with 3D coordinates and Euclidean distance from the neighborhood points to the reference point as enhanced inputs to obtain point-level local responses. At the same time, global position mapping is performed on the original 3D coordinates of all points through independent branches, and the original coordinate distribution response is coupled with the local response through linear adaptation mapping. Mean convergence and extreme value convergence are performed on each scale channel, and the two types of statistical results of each channel are concatenated to generate a shape-level representation vector. The scale parameter regression module is used to perform Z-score normalization preprocessing on the shape-level representation vector and predict the scale parameter corresponding to the normalized point cloud through a support vector regression model based on radial basis function kernel. The point cloud size recovery module is used to perform inverse size mapping on each point in the normalized point cloud in each coordinate axis direction according to the predicted scale parameters, so as to obtain a three-dimensional point cloud that recovers the true physical size.

[0015] According to a third aspect of this application, an electronic device is provided, comprising: a memory and a processor; the memory stores a computer program, and the processor executes the computer program to implement the above-described three-dimensional physical scale restoration method.

[0016] According to a fourth aspect of this application, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the above-described method for restoring the physical scale of a three-dimensional entity.

[0017] The embodiments of the present invention have the following advantages: This invention does not require external ranging sensors, artificial scale references, or additional size acquisition devices. It can achieve high-precision recovery of the true physical size of the target entity based solely on point cloud data, which greatly reduces deployment costs and improves system integration flexibility. The scale-sensitive point cloud representation module proposed in this invention captures local structural changes simultaneously at three levels—fine-grained, medium-grained, and coarse-grained—through a multi-receptive field parallel modeling mechanism, so that scale information is no longer limited to a specific spatial level and effectively covers multi-scale structural changes. In the characterization process, this invention sets up an independent original coordinate distribution response extraction branch and directly performs global position mapping on the original three-dimensional coordinates of all points. This avoids the weakening of absolute scale cues during preprocessing and specifically makes up for the inherent defect of existing general methods that actively eliminate absolute scale information. This invention explicitly introduces the Euclidean distance from a neighboring point to a reference point into the enhanced input, enabling point-level representation to directly perceive the local point distance structure, and allowing targets of different physical sizes to produce distinguishable distance response distributions within the same normalized scale channel. This invention employs a support vector regression model based on radial basis function kernels, which can effectively capture the nonlinear relationship between feature vectors and scale parameters in a high-dimensional feature space. On the test set, it achieves a prediction accuracy of R²-score of 0.838 and RMSE of 144.229, which is significantly better than the baseline scheme that uses PointNet features as input. This invention maintains stable prediction accuracy for multiple types of targets with different shapes and scales. It can effectively distinguish targets with identical bounding boxes in the normalized coordinate system but different actual physical dimensions, thus effectively improving the availability and reliability of 3D reconstruction results in engineering application scenarios such as obstacle avoidance of unmanned vehicles, reconnaissance of drones, and multimodal data fusion. Attached Figure Description

[0018] Figure 1 This is a flowchart of the steps of a three-dimensional solid physical scale restoration method according to the present invention; Figure 2 This is a system architecture diagram of a three-dimensional physical scale restoration system according to the present invention; Figure 3 This is a schematic diagram of the structure of an electronic device according to the present invention; Figure 4 This is a schematic diagram of the structure of a computer-readable storage medium according to the present invention. Detailed Implementation

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] It should be noted that the above detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0021] Example 1: A 3D Entity Physical Scale Reconstruction Method Based on Multi-Scale Point Cloud Feature Learning This embodiment discloses a method for physical scale recovery of 3D entities based on multi-scale point cloud feature learning, applicable to single-view applications. Figure 3 After the 3D reconstruction pipeline is completed, the normalized point cloud is used to restore its true physical dimensions. This method has a linear pipeline structure, consisting of a preprocessing module, a scale-sensitive point cloud representation module, and a scale parameter regression module connected in series. The modules exchange information through shape-level feature vectors, exhibiting good module decoupling.

[0022] To facilitate the characterization of the size mapping relationship of point clouds before and after normalization, this invention introduces a scale parameter to represent the size transformation law of the target point cloud in three coordinate directions. The scale parameter is represented in diagonal matrix form, containing scale components in the x-axis, y-axis, and z-axis directions, denoted as λ. x λᵧ and λz. When the three components are equal, it indicates that the point cloud undergoes a proportional scaling transformation in three-dimensional space; when the three are not all equal, it indicates that the point cloud corresponds to different dimensional scaling relationships in different directions.

[0023] Normalization essentially involves using a scale mapping matrix to compress or recalibrate the original point cloud coordinates along the axes, thereby bringing the point cloud into a unified scale reference space. After this processing, the geometric features of the point cloud are preserved, but its original true physical size information is implicit in the scale parameters. The goal of this invention is to predict these scale parameters from the normalized point cloud, and then restore the normalized point cloud to its true physical size space through inverse scale mapping.

[0024] like Figure 1 As shown in the figure, the 3D entity physical scale recovery method based on multi-scale point cloud feature learning in this embodiment includes the following steps: S1: Obtain the normalized point cloud output by the 3D reconstruction pipeline, and perform normalized sampling preprocessing on the normalized point cloud by sampling the farthest point. The point cloud of arbitrary density is uniformly downsampled to a fixed number of points to obtain a normalized input point set. During the sampling process, no centroid translation, scale normalization or local coordinate system transformation is applied to the point cloud, so as to preserve the original absolute position distribution of the point cloud in the normalized space. In this step, since the reconstructed point cloud density varies for different targets, in order to ensure the consistency of the input size of the subsequent scale-sensitive point cloud representation module, this step performs farthest point sampling (FPS) on the input normalized point cloud, uniformly downsampling the point cloud of arbitrary density to a fixed number of points 1024, to obtain the normalized input point set P, where each point pᵢ (i=1,2,...,1024) contains three-dimensional coordinates (aᵢ, bᵢ, cᵢ).

[0025] The specific process of farthest point sampling is as follows: Initialize the sampling point set to an empty set and randomly select an initial point; in each subsequent iteration, calculate the distance from all unsampled points to the nearest point in the current sampled point set, and select the point with the largest distance to add to the sampling set, until the number of samples reaches 1024. This sampling strategy ensures that the 1024 sampled points are evenly distributed in space, fully covering the overall geometry of the target and avoiding over-representation of local dense areas.

[0026] The most critical constraint in this step is that no additional centroid translation, scale normalization, or local coordinate system transformation is applied to the point cloud. The point cloud coordinates are directly inherited from the normalized reconstruction result, preserving their original absolute positional distribution in the normalized space. This constraint is a fundamental prerequisite for the subsequent scale-sensitive representation to successfully capture scale cues—if scale compression or coordinate centering is applied again at this stage, the scale-related spatial distribution information remaining in the normalized point cloud will be further destroyed, causing subsequent scale parameter predictions to fail.

[0027] This step introduces a scale parameter to characterize the size transformation of the target point cloud in three coordinate directions. The scale parameter is represented in matrix form as a scale mapping matrix:

[0028]

[0029] in, , and These represent the target point cloud in axis, Shaft and Scale parameters along the axial direction. When When all three are equal, it indicates that the point cloud undergoes a proportional scaling transformation in 3D space; when not all three are equal, it indicates that the point cloud corresponds to different size scaling relationships in different directions. Through the above definition, the scale parameter is no longer used as a single numerical quantity, but as a set of structured parameters describing the mapping relationship of point cloud size, which is used for subsequent normalization modeling and real size restoration.

[0030] Specifically: Mathematical representation of the point cloud normalization process: Let the original target point cloud be denoted as:

[0031] in, This indicates the number of points contained in the point cloud. Indicates the first The three-dimensional coordinates of a point in real physical space.

[0032] For the original point cloud After applying normalization, we obtain the normalized point cloud:

[0033] The normalization process can be represented as:

[0034] It can also be written in the form of quantities:

[0035] The above process shows that the normalization operation essentially uses a scale mapping matrix to compress or recalibrate the original point cloud coordinates along the axis, thereby bringing the point cloud into a unified scale reference space. After this processing, the geometric features of the point cloud are preserved, but its original true physical size information is implicit in the scale parameters.

[0036] The relationship for obtaining the scale parameter: As can be seen from the above normalization process, the scale parameter essentially reflects the mapping relationship between the original point cloud and the normalized point cloud in each coordinate direction. Therefore, for any point... and its corresponding normalization point The component expressions for the scale parameter can be obtained as follows:

[0037]

[0038] In actual training and inference processes, this invention does not directly rely on point-by-point analytical solution of the above parameters. Instead, it extracts scale-sensitive representations from the normalized point cloud through the constructed scale parameter regression module and outputs the scale parameter estimation results of the corresponding target point cloud:

[0039] in, This represents the scale parameter estimation matrix output by the model. , , These are the estimated values ​​for the corresponding three axes. This method allows for the explicit recovery of the true scale information that was compressed and hidden during normalization, providing a parameter basis for subsequent reconstruction of the true-size point cloud.

[0040] Point cloud true size recovery based on scale parameters: for any normalized point cloud After obtaining its corresponding scale parameter estimation matrix Then, the true size restoration operation can be performed. Set the normalization point. The restored coordinates are The recovery process is represented as follows:

[0041]

[0042] When expanded, it can be written as:

[0043] This yields the restored point cloud with the true dimensions:

[0044] in, This indicates that the coordinates of each point in the target point cloud, after being restored by the scale parameters, correspond to the true physical size space of the target entity. Therefore, this invention achieves the restoration of the normalized point cloud to a point cloud with the true physical size by first estimating the scale parameters and then applying an inverse size mapping, thereby completing the size registration process of the target entity. This process does not require the introduction of additional external ranging devices or size references; the true size restoration can be completed solely based on the point cloud data itself.

[0045] S2: The normalized input point set is input into the scale-sensitive point cloud representation module to generate a shape-level representation vector. The scale-sensitive point cloud representation module sets up multiple parallel scale channels. For each scale channel, the neighborhood points are constructed with three-dimensional coordinates and the Euclidean distance from the neighborhood points to the reference point to construct an enhanced input. After mapping by a shared multilayer perceptron, element-wise max pooling aggregation is performed to obtain the point-level local response. At the same time, an independent original coordinate distribution response extraction branch is set up to perform global position mapping on the original three-dimensional coordinates of all points. The original coordinate distribution response and the point-level local response are coupled across channels through linear adaptation mapping for each scale channel. Mean aggregation and extreme value aggregation are performed on each scale channel respectively, and the two types of statistical results of each channel are concatenated to obtain the shape-level representation vector. In this step, the scale-sensitive point cloud representation module is one of the core innovations of this invention. Its design differs fundamentally from general point cloud networks such as PointNet and PointNet++: general networks tend to eliminate scale variations to improve the generalization ability of shape classification, while this module regards scale variations as a key source of information that needs to be explicitly captured and enhanced in its representation. Specifically, this module adopts a hierarchical receptive field parallel modeling mechanism, generating a shape-level representation vector with both shape description and scale sensitivity capabilities through four sub-steps: parallel construction of multiple receptive field neighborhoods, construction of local scale responses, extraction of original coordinate distribution responses, and cross-channel feature coupling. Specifically, it includes:

[0046] 1. Parallel Construction of Multiple Receptive Field Neighborhoods: This module sets up three parallel scale channels, corresponding to neighborhood radii of 0.1, 0.3, and 0.5 (in normalized coordinate units), respectively. For each reference point pᵢ in the input point set, in the s-th scale channel (s=1,2,3), all points whose Euclidean distance does not exceed the corresponding neighborhood radius are included in the neighborhood point set of that scale channel. The three channels capture local structures at three levels: fine-grained (details such as weapon attachments and sensors), medium-grained (components such as vehicle outlines and wing structures), and coarse-grained (overall building spans, overall armored vehicle outlines, etc.). The maximum number of neighborhood points for each channel is set to 32, 64, and 128, respectively. Random downsampling is allowed when the number exceeds the limit, and repeated sampling is allowed when the number is insufficient. Wherein: Let the input point cloud be denoted as:

[0047]

[0048] in, Indicates the number of points. Indicates the first The coordinates of each point in a 3D coordinate system. The module input uses point cloud coordinates without additional scale normalization, that is, it directly preserves the original spatial positional relationships to ensure that the coordinate distribution features related to the real scale can be included in the subsequent representation process.

[0049] When constructing a multi-receptive field neighborhood, the module is set to have a total of [number] settings. The number of parallel scale channels, the first Each channel corresponds to a neighborhood scale parameter. For any point In the Construct its neighborhood point set at each scale:

[0050]

[0051] in, Indicates As a reference point, in the first Local neighborhoods obtained at different spatial scales. Different channels are selected for different scales. This allows for the perception of local structural changes at multiple levels, including fine-grained, medium-grained, and coarse-grained.

[0052] 2. Construction of Local Scale Response: The construction of the local scale response is a key design feature that distinguishes this module from existing methods. In the s-th scale channel, a 4-dimensional augmented input is constructed for each point pⱼ in the neighborhood, containing the three-dimensional coordinates of the neighborhood points ( And the Euclidean distance from the neighboring point to the reference point. Unlike PointNet++, which only uses relative coordinates as local input, this module explicitly introduces the Euclidean distance from neighboring points to the reference point as a fourth-dimensional feature. This design directly endows the network with the ability to perceive local point spacing, enabling targets of different physical sizes to produce different distance response distributions within the same normalized scale channel, thereby forming a distinguishable scale difference encoding at the feature level.

[0053] For each reference point, all augmented inputs in the neighborhood are mapped through a shared multilayer perceptron and then aggregated using element-wise max pooling to obtain the point-level local response. The layer structure and output dimensions of the three-channel multilayer perceptron are as follows: fine-grained channel input dimension 4 is mapped to output dimension 64 via intermediate dimension 32; medium-grained channel input dimension 4 is mapped to output dimension 128 via intermediate dimension 64; coarse-grained channel input dimension 4 is mapped to output dimension 256 via intermediate dimension 64. Specifically:

[0054] To strengthen the expression of distance relationships within the neighborhood, the first... Neighboring points in each scale channel Construct the following enhanced input:

[0055] in,

[0056] Let represent the Euclidean distance between the neighboring points and the reference point. Therefore, the ... The point-level local response corresponding to each scale channel is defined as:

[0057]

[0058] in, Indicates the first The combined operator of the shared mapping network and local aggregation process used in each scale channel. The meaning of this formula is that, within each scale channel, not only are the coordinate values ​​of the points used, but the distances from neighboring points to the reference point are also explicitly introduced into the input, so that the point-level representation can directly perceive the local point distance structure, rather than learning it indirectly from subsequent networks.

[0059] 3. Original Coordinate Distribution Response Extraction: Parallel to local response, this module sets up an independent branch for original coordinate distribution response extraction. It directly performs global position mapping on the original 3D coordinates of all points to obtain the global absolute position response gᵢ for each point. This branch does not rely on any local center point, directly using absolute coordinates as input, ensuring that the overall distribution range of the point set in the original normalized space—i.e., the spatial span information closely related to the real scale—is fully preserved and mapped to a high-dimensional representation. This branch is specifically designed to address the inherent limitation of PointNet++, which uses relative coordinates as input and actively eliminates absolute scale information. The global position mapping is implemented using a multilayer perceptron, with an output dimension of 128 dimensions. Specifically:

[0060] The absolute position response is constructed as follows:

[0061] in, This represents a shared network that performs mapping on the original 3D coordinates. Because this branch directly uses absolute coordinate inputs instead of performing relativistic transformations with reference to a central point, the overall distribution range of the point set in the original space is preserved and participates in subsequent fusion as part of the scale-sensitive information.

[0062] 4. Cross-channel feature coupling: Considering the different dimensions of local responses in channels of different scales, the global position response is also considered. Introduce a linear adaptation mapping for the s-th channel. Map the 128-dimensional global position response to the local response dimension of the s-th channel. The same dimension is then added element-wise to the point-level local response of that channel to obtain the fused point-level representation. This additive fusion operation enables the final representation of each point to carry two complementary types of information: "the local point spacing structure perceived within the current scale channel" and "the absolute position distribution in the original space," thus possessing both shape description capability and scale sensitivity capability.

[0063] Global position response Introducing the first Linear adaptation mapping for each channel The fused point-level representation is defined as follows:

[0064] 5. Statistical Convergence and Shape-Level Representation Generation: For each scale channel, the fused representation zᵢˢ of all points is subjected to mean convergence and extreme value convergence respectively, yielding the overall statistical response and salient response of that channel. Mean convergence preserves the global statistical distribution characteristics, while extreme value convergence captures the most significant geometric response of each channel; the two are complementary. Further, the two types of statistical results for each scale channel are concatenated in channel order to obtain the shape-level representation vector r output by the module. Specifically, the dimensions after mean convergence and extreme value convergence for the three channels are 64×2=128, 128×2=256, and 256×2=512 dimensions respectively, and the total dimension of the concatenated shape-level representation vector is 896 dimensions. Where:

[0065] For each scale channel, the fused representation of all points is... Perform mean aggregation and extreme value aggregation separately:

[0066]

[0067] in, Indicates the first The overall statistical response of each scale channel This represents the significant response of the corresponding channel. Furthermore, the two types of statistical results from each scale channel are concatenated to obtain the shape-level representation vector of the module output:

[0068]

[0069] in, This is the shape-level representation vector output by the scale-sensitive point cloud representation module. This vector comprehensively carries multi-scale local geometric information, original coordinate distribution information, and point distance relationship clues, and serves as the input basis for the subsequent scale parameter regression module.

[0070] Taking a typical comparative scenario in reconnaissance missions as an example: small unmanned vehicles (approximately 0.3m in real-world scale) and large armored vehicles (approximately 7m in real-world scale) have similar bounding box sizes after normalization, but within fine-grained channels, the former's neighborhood midpoint spacing is significantly larger. The former is generally very small (highly dense point cloud in normalized space), while the latter is relatively large; within the coarse-grained channel, the former's neighborhood almost covers the entire target point cloud, while the latter's neighborhood only covers local structures. These differences are encoded into an 896-dimensional representation vector through explicitly introduced distance features and a multi-scale parallel mechanism, forming an effective distinguishing representation of the two types of targets at their true scale.

[0071] This module uses multiple scale channels to process the same set of input points in parallel, rather than performing unified modeling within a single spatial range. By establishing responses for local regions under different receptive fields, the module can simultaneously capture the compact structure at the level of detail, the spatial unfolding at the level of components, and the geometric span at the level of the whole. This allows scale information to be no longer limited to a specific spatial level, but to enter the final representation result in a parallel manner.

[0072] This module does not apply additional local normalization, centroid translation, or scale unification operations to the input point set during the representation stage. Instead, it directly constructs the global position response based on the original coordinates. In this way, the absolute position distribution and overall spatial span of the point cloud can be fully transferred to the representation layer, avoiding the weakening of absolute scale cues during preprocessing.

[0073] S3: After performing Z-score normalization preprocessing on the shape-level representation vector, input it into the support vector regression model based on radial basis function kernel to predict the scale parameters corresponding to the normalized point cloud; The shape-level representation vector *r* is input into the scale parameter regression module. Before being input into the support vector regression model, Z-score standardization preprocessing must be performed: for each dimension *j* of the feature vector, subtract the mean μⱼ of the corresponding dimension on the training set, and then divide by the standard deviation of the corresponding dimension. This yields standardized feature vectors. The standardized parameters are computed only on the training set and are directly loaded during inference to avoid data leakage and ensure that each feature dimension contributes equally to the support vector regression optimization process.

[0074] The shape-level feature vector output by the scale-sensitive point cloud representation module Before inputting an SVR model, it needs to undergo standardization preprocessing. The standardization operation is defined as follows:

[0075]

[0076] in For the first The mean of each feature dimension on the training set This represents the corresponding standard deviation. After standardization, the mean of each feature dimension is 0 and the variance is 1, eliminating the interference of differences in magnitude between different feature dimensions on the SVR optimization process.

[0077] It is worth noting that the mean used for standardization and standard deviation It is computed only on the training set and applied directly to the test samples during the testing phase to avoid data leakage.

[0078] The standardized feature vectors are used as input to train a support vector regression model based on radial basis function kernels. The basic idea of ​​support vector regression is to first map the input representation vectors to a high-dimensional feature space (achieved through radial basis function kernels), and then construct the optimal regression function in this space to make the prediction results approximate the true scale parameters as closely as possible, while maintaining the model's generalization ability through structural risk control. Compared with general deep fully connected regression heads, this method is more suitable for handling high-dimensional representation regression problems with medium-sized samples, especially applicable to technical scenarios with high input dimensionality, continuous target variables, and significant nonlinear mapping relationships.

[0079] The hyperparameters of the support vector regression model are determined by a systematic grid search method. This module uses the grid search method to systematically traverse and optimize the key hyperparameters.

[0080] The three hyperparameters that have the most significant impact on SVR performance were selected as the search objects: kernel type, penalty parameter, and so on. ) and insensitive band width ( The remaining hyperparameters (such as degree, coef0, tol, etc.) remain fixed to control the size of the search space. The candidate values ​​for each parameter are set as follows:

[0081]

[0082] The above parameter space constitutes A number of hyperparameter combinations were used, and each combination was trained and evaluated on a fixed training and testing set (80% training, 20% testing), with the corresponding results recorded. -Score, RMSE, and EVS metrics.

[0083] After a systematic review, the evaluation results for each hyperparameter combination are summarized below. For a linear kernel, when... , At this time, the optimal result under this kernel function is obtained. -score is 0.724, RMSE is 188.335; for RBF cores, when , At this time, the globally optimal result is achieved. The score is 0.838, the RMSE is 144.229, and the EVS is 0.855, which is significantly better than the best results of the linear kernel.

[0084] The reason why the RBF kernel is superior to the linear kernel is that the mapping relationship between shape-level eigenvectors and scaling factors has significant nonlinear characteristics. The linear kernel cannot effectively capture this nonlinear structure, while the RBF kernel can establish nonlinear partitions in infinite-dimensional RKHS through Gaussian radial basis mapping, and has stronger nonlinear expression capabilities. The larger penalty parameter setting indicates that, in this task, appropriately reducing the model's tolerance for training errors and strengthening the fit to training samples helps improve prediction accuracy, which is consistent with the characteristics of strong regularity of scale information and relatively low noise level in the dataset. The smaller insensitivity band width setting ensures that the model is highly sensitive to changes in the scale factor value, which helps to capture subtle scale differences.

[0085] In determining the optimal hyperparameter combination (kernel=rbf, , After that, complete the training of the SVR model by following these steps: Dataset partitioning: The complete dataset is randomly divided into a training set and a test set at a ratio of 80% / 20%. The training set is used for model parameter learning, and the test set is used for final performance evaluation. The two sets are strictly non-overlapping.

[0086] Feature standardization parameter estimation: Calculate the mean of each feature dimension on the training set. with standard deviation The feature vectors of the training set are standardized to obtain the standardized feature matrix of the training set. .

[0087] SVR model solution: using the standardized training set feature matrix With the corresponding scaling factor label vector Using this as input, the optimal Lagrange multipliers are obtained by solving the SVR dual optimization problem. With bias term This module determines the set of support vectors and completes model training. It is implemented based on the SVR algorithm in the Scikit-learn framework, and uses the Sequential Minimal Optimization (SMO) algorithm at the underlying level, which has high solution efficiency.

[0088] Model performance evaluation: The standardized parameters estimated on the training set are used to standardize the feature vectors of the test set. The standardized feature vectors of the test set are then input into the trained SVR model to generate predicted scaling factor values. and with real labels Compare, calculate Evaluation metrics include score, RMSE, and EVS.

[0089] Scale parameter prediction and point cloud size recovery: During the inference phase, for a given normalized point cloud, the workflow of the scale factor regression module is as follows: The first step is to input the normalized point cloud into the scale-sensitive point cloud representation module 3 to generate shape-level feature vectors. .

[0090] The second step is to use the standardized parameters estimated during the training phase to... Standardization process is performed to obtain .

[0091] The third step is to Input the trained SVR model and calculate the predicted values ​​of the scaling parameters using the following prediction function:

[0092] The summation is performed only on the support vector set SV. For the first The standardized feature vectors of the support vectors.

[0093] The fourth step is to utilize the predicted scale parameters. (corresponding scaling matrix) Applying an inverse transform to the normalized point cloud restores it to its true physical scale:

[0094] Complete the restoration of normalized point clouds to point clouds of true physical size.

[0095] This module introduces - The insensitive band mechanism is naturally robust to "relative outliers" arising from large scale spans between different categories of objects in the training data. When the difference between the true value and the model prediction of the scaling factor of a training sample is large... When the gap is within the specified range, the sample does not incur any loss and does not become a support vector; only when the gap exceeds the specified range will the sample become a support vector. Only when the time is right will it affect the model parameters. This mechanism effectively avoids excessive interference from a few extreme-scale samples (such as the scale comparison between point clouds of super-large buildings and point clouds of small weapons and equipment) on the overall regression parameters, ensuring the balance of the model's prediction performance across the entire scale range.

[0096] Penalty parameters It controls the trade-off between model complexity and training error: The larger the value, the more strictly the model penalizes the training error, and the more it tends to fit the training samples precisely, but this may lead to overfitting. The smaller the value, the stronger the model's fault tolerance and the better its generalization ability, but it may underfit. This module determines the optimal value through grid search. Given the data scale and feature dimensionality of this task, a larger penalty parameter helps the model fully utilize the distribution pattern of scaling factors in the high-dimensional feature space. While maintaining a strong fitting ability, it avoids overfitting through the implicit regularization effect of the RBF kernel function, thus achieving a good balance between training accuracy and generalization ability.

[0097] Engineering Implementation Based on the Scikit-learn Framework: This module is implemented using the Python Scikit-learn (Sklearn) framework. This framework is built upon scientific computing libraries such as NumPy and SciPy, providing an efficient and stable SVR implementation (using the LIBSVM library at the underlying level). Specific hyperparameter settings are shown in the table below:

[0098]

[0099] Where gamma is set to auto, that is ( (where is the feature dimension), which is a common adaptive strategy to avoid over-concentration or over-diffusion of the RBF kernel when the feature dimension is high. Setting the shrinking parameter to True enables the shrinking heuristic in the SMO algorithm, which accelerates the optimization solution by excluding samples that are obviously unlikely to become support vectors during the iteration process, and has a significant computational speedup effect on large-scale datasets.

[0100] S4: Based on the predicted scale parameters, multiply the coordinates of each point in the normalized point cloud in each coordinate axis direction by the predicted scale parameters of the corresponding axis, and perform inverse size mapping to obtain a three-dimensional point cloud that restores the true physical size.

[0101] After obtaining the scale estimation matrix, an inverse size mapping is applied to each point of the input normalized point cloud: the coordinates of each point in the x-axis direction are multiplied by the predicted x-axis scale parameter, the coordinates in the y-axis direction are multiplied by the predicted y-axis scale parameter, and the coordinates in the z-axis direction are multiplied by the predicted z-axis scale parameter. This yields the restored true physical size point cloud, where the coordinates of each point re-correspond to the three-dimensional position of the target entity in real physical space, and the dimension is restored to meters (m). The computational complexity of this operation is linearly related to the number of input points. For a typical 1024-point point cloud, the execution time is on the order of microseconds, and its impact on the processing latency of real-time systems is negligible.

[0102] Taking common target categories in reconnaissance missions as an example: four types of targets (small unmanned vehicles, military transport vehicles, large armored vehicles, and low-altitude fixed-wing UAVs) have the same bounding box size in the normalized coordinate system (0.80×0.50×0.30). Targets with high shape similarity are difficult to reliably distinguish based on shape features alone. However, this invention clarifies the differences in the actual physical size of each target by restoring scale parameters, providing a measurable basis for distinction for downstream systems.

[0103] Example 2: Application of UAVs in urban low-altitude reconnaissance scenarios This embodiment illustrates the specific application of the present invention in urban low-altitude reconnaissance and target identification scenarios using unmanned aerial vehicles (UAVs). When performing urban low-altitude reconnaissance missions, the UAV is equipped with a single-view optical camera to continuously acquire images of ground targets, and then transmits these images through a single-view camera. Figure 3 The 3D reconstruction network transforms an image into a 3D point cloud representation of the target. Since monocular cameras lack a direct scale reference, the reconstruction pipeline applies normalization preprocessing to the output point cloud, compressing point clouds of different categories and sizes into a unified reference space, with the true physical size information implicitly contained in the scale mapping parameters.

[0104] In this embodiment, the military target augmentation dataset upon which this invention relies covers nine categories, including military transport vehicles, aircraft, drones, buildings, and weaponry, comprising 523 detailed 3D models. Divided into 80% and 20% categories, the training set contains approximately 418 samples. The scale range between different target categories in the dataset (from small weapons and equipment to large buildings) covers the target scale range commonly encountered in urban low-altitude reconnaissance missions, ensuring the applicability of the model in actual deployment scenarios.

[0105] The system receives normalized reconstructed point clouds as input, each containing between 1024 and 4096 points. First, it undergoes sampling and normalization of the farthest point to 1024 points in step S1 of Example 1. Then, it sequentially passes through the scale-sensitive point cloud characterization module in step S2 and the scale parameter regression module in step S3 to predict the target's scale parameters in the x, y, and z axes. Finally, the true physical size point cloud is recovered through inverse size mapping in step S4. The system ultimately outputs a three-dimensional point cloud with the recovered true physical size and the corresponding scale parameter estimation matrix, where the scale parameters are in meters (m). This output can be directly interfaced with the downstream analysis module of the reconnaissance system, providing measurable physical size data for tasks such as strike radius calculation, flight path avoidance, and multi-target spatial relationship analysis.

[0106] This embodiment achieves a prediction accuracy of 0.838 R²-score, 144.229 mm RMSE, and 0.855 on the test set, which is significantly better than the baseline scheme with PointNet features as input (R²-score of 0.553 and RMSE of 423.86 mm). This verifies that the present invention has good size estimation capability for various types of targets in actual reconnaissance scenarios.

[0107] Example 3: Application of Multimodal 3D Data Fusion Analysis Scenarios This embodiment illustrates the application of the present invention in multimodal 3D data fusion analysis scenarios. In fields such as smart city construction, digital preservation of cultural relics, and quality inspection of industrial parts, it is often necessary to fuse and analyze 3D point cloud data acquired from different data acquisition platforms (such as monocular cameras, binocular cameras, LiDAR, structured light scanners, etc.) or at different times. Because different acquisition platforms and processing workflows use different normalization methods for point clouds, the point clouds from each data source are often in different scale reference frames before fusion. Direct fusion will lead to scale inconsistencies, resulting in severe geometric distortion in the fusion results.

[0108] For multiple point cloud data sources from different acquisition platforms or processing workflows, this invention predicts the corresponding scale parameters for each point cloud and uniformly restores all point clouds to the real physical scale space. Through this operation, heterogeneous point cloud data originally under different scale reference systems are mapped to a unified physical scale benchmark, providing a consistent scale premise for subsequent cross-source data fusion. In applications requiring cross-period 3D change detection of the same target or scene (such as building deformation monitoring, cultural relic weathering assessment, etc.), this invention restores the size of point clouds acquired and reconstructed at different times, ensuring that point cloud data from different time points are analyzed for differences under a unified physical scale reference system. This allows for accurate differentiation between the target's actual physical changes and scale differences introduced by data processing, avoiding misjudging normalization errors as actual target deformation.

[0109] This invention can achieve high-precision size reconstruction using only point cloud data without any external sensors or additional scale references. It also has good cross-class generalization ability and can maintain stable prediction accuracy for multiple types of targets with different shapes and scale characteristics. It is especially suitable for multimodal fusion analysis application scenarios that require processing a large amount of heterogeneous 3D data.

[0110] Example 4: Device Example like Figure 2 As shown, the three-dimensional physical scale restoration system in this embodiment includes: The preprocessing module is used to obtain a normalized point cloud. By sampling the farthest point, the normalized point cloud is downsampled to a fixed number of points to obtain a normalized input point set. During the sampling process, no centroid translation, scale normalization or local coordinate system transformation is applied to the point cloud, so as to preserve the original absolute position distribution of the point cloud in the normalized space. The scale-sensitive point cloud representation module is used to construct neighborhood point sets under corresponding neighborhood radii for the normalized input point set through multiple parallel scale channels. The neighborhood points are aggregated through a shared multilayer perceptron with 3D coordinates and Euclidean distance from the neighborhood points to the reference point as enhanced inputs to obtain point-level local responses. At the same time, global position mapping is performed on the original 3D coordinates of all points through independent branches, and the original coordinate distribution response is coupled with the local response through linear adaptation mapping. Mean convergence and extreme value convergence are performed on each scale channel, and the two types of statistical results of each channel are concatenated to generate a shape-level representation vector. The scale parameter regression module is used to perform Z-score normalization preprocessing on the shape-level representation vector and predict the scale parameter corresponding to the normalized point cloud through a support vector regression model based on radial basis function kernel. The point cloud size recovery module is used to perform inverse size mapping on each point in the normalized point cloud in each coordinate axis direction according to the predicted scale parameters, so as to obtain a three-dimensional point cloud that recovers the true physical size.

[0111] Example 5: Electronic Device Example Reference Figure 3 This embodiment discloses an electronic device, including a processor, a memory, a communication interface, and a system bus. The processor executes a computer program stored in the memory to implement the three-dimensional entity physical scale restoration method based on multi-scale point cloud feature learning as described in any of embodiments one to three above. The memory stores the computer program, as well as the parameter file of the support vector regression model (including the support vector set, corresponding Lagrange multipliers, and bias terms) and feature standardization parameters (mean and standard deviation of each dimension). The communication interface interacts with external devices or systems, receiving input normalized point cloud data and outputting the restored true physical size point cloud. The system bus connects the processor, memory, and communication interface to enable data transmission between the components.

[0112] Example 6: Computer-readable storage medium Reference Figure 4Furthermore, a computer-readable storage medium is provided, on which a computer program is stored. When executed by a processor, the computer program implements the three-dimensional entity physical scale recovery method based on multi-scale point cloud feature learning as described in any one of embodiments one to three above. The computer-readable storage medium may be a non-volatile storage medium, including but not limited to disk storage, optical storage, flash memory, etc.

[0113] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0114] It should be noted that the terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that the embodiments of this application described herein can be implemented in sequences other than those illustrated or described herein.

[0115] Furthermore, the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or apparatus.

[0116] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways, such as rotated 90 degrees or in other orientations, and the spatial relative descriptions used herein will be interpreted accordingly.

[0117] In the detailed description above, reference has been made to the accompanying drawings, which form part of this document. In the drawings, similar symbols typically identify similar parts unless the context otherwise indicates otherwise. The illustrated embodiments described in the detailed specification, drawings, and claims are not intended to be limiting. Other embodiments may be used and other changes may be made without departing from the spirit or scope of the subject matter presented herein.

[0118] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for restoring the physical scale of a three-dimensional entity, characterized in that, The method includes: S1: Obtain the normalized point cloud output by the 3D reconstruction pipeline, and perform normalized sampling preprocessing on the normalized point cloud by sampling the farthest point. The point cloud of arbitrary density is uniformly downsampled to a fixed number of points to obtain a normalized input point set. During the sampling process, no centroid translation, scale normalization or local coordinate system transformation is applied to the point cloud, so as to preserve the original absolute position distribution of the point cloud in the normalized space. S2: The normalized input point set is input into the scale-sensitive point cloud representation module to generate a shape-level representation vector. The scale-sensitive point cloud representation module sets up multiple parallel scale channels. For each scale channel, the neighborhood points are constructed with three-dimensional coordinates and the Euclidean distance from the neighborhood points to the reference point to construct an enhanced input. After mapping by a shared multilayer perceptron, element-wise max pooling aggregation is performed to obtain the point-level local response. At the same time, an independent original coordinate distribution response extraction branch is set up to perform global position mapping on the original three-dimensional coordinates of all points. The original coordinate distribution response and the point-level local response are coupled across channels through linear adaptation mapping for each scale channel. Mean aggregation and extreme value aggregation are performed on each scale channel respectively, and the two types of statistical results of each channel are concatenated to obtain the shape-level representation vector. S3: After performing Z-score normalization preprocessing on the shape-level representation vector, input it into the support vector regression model based on radial basis function kernel to predict the scale parameters corresponding to the normalized point cloud; S4: Based on the predicted scale parameters, multiply the coordinates of each point in the normalized point cloud in each coordinate axis direction by the predicted scale parameters of the corresponding axis, and perform inverse size mapping to obtain a three-dimensional point cloud that restores the true physical size.

2. The method for restoring the physical scale of a three-dimensional entity according to claim 1, characterized in that, The multiple parallel scale channels include three channels, corresponding to neighborhood radii of 0.1, 0.3, and 0.5, respectively; the three channels capture local structures at three levels: fine-grained, medium-grained, and coarse-grained, respectively; the maximum number of neighborhood points for the fine-grained, medium-grained, and coarse-grained channels is 32, 64, and 128, respectively, and random downsampling is allowed when the number of neighborhood points exceeds the limit, and repeated sampling is allowed when the number of neighborhood points is insufficient.

3. The method for restoring the physical scale of a three-dimensional entity according to claim 2, characterized in that, The shared multilayer perceptron layer structure and output dimensions for the three channels are as follows: the fine-grained channel has an input dimension of 4, which is mapped to an output dimension of 64 via an intermediate dimension of 32; the medium-grained channel has an input dimension of 4, which is mapped to an output dimension of 128 via an intermediate dimension of 64; and the coarse-grained channel has an input dimension of 4, which is mapped to an output dimension of 256 via an intermediate dimension of 64. The shape-level representation vector obtained by concatenating the mean and extreme values ​​of each channel has a dimension of 896.

4. The method for restoring the physical scale of a three-dimensional entity according to claim 1, characterized in that, The fixed number of points is 1024; the farthest point sampling selects the point farthest from the already sampled point set as the next sampling point each time, ensuring that the 1024 sampled points are evenly distributed in space and fully cover the overall geometric structure of the target.

5. The method for restoring the physical scale of a three-dimensional entity according to claim 1, characterized in that, The scale parameters are represented in the form of a diagonal matrix, which includes independent scale parameters for the three coordinate directions of x-axis, y-axis and z-axis. For targets that need to distinguish the scale of each axis, three support vector regression instances are trained independently for the three axes of x-axis, y-axis and z-axis, and each outputs the scale parameters for the corresponding axis, which are then combined into a scale estimation matrix.

6. The method for restoring the physical scale of a three-dimensional entity according to claim 1, characterized in that, The penalty parameter C of the support vector regression model is set to 1000, the insensitive band width is set to 0.1, and the kernel function bandwidth parameter is estimated using an adaptive method. The optimal hyperparameter configuration of the support vector regression model is determined by a grid search method. The search space covers three dimensions: kernel function type, penalty parameter, and insensitive band width, with a total of 18 hyperparameter combinations. Each combination is evaluated independently on a fixed-partition training set and test set.

7. The method for restoring the physical scale of a three-dimensional entity according to claim 1, characterized in that, The training process of the support vector regression model includes: randomly dividing the dataset into training and test sets at a ratio of 80% / 20%; calculating the mean and standard deviation of each feature dimension only on the training set; performing Z-score standardization on the training and test sets respectively to avoid data leakage; implementing support vector regression based on the Scikit-learn framework, using the sequence minimum optimization algorithm at the bottom layer, and enabling the shrinkage heuristic method to accelerate the optimization solution.

8. A three-dimensional solid physical scale restoration system employing the three-dimensional solid physical scale restoration method according to any one of claims 1 to 7, characterized in that, include: The preprocessing module is used to obtain a normalized point cloud. By sampling the farthest point, the normalized point cloud is downsampled to a fixed number of points to obtain a normalized input point set. During the sampling process, no centroid translation, scale normalization or local coordinate system transformation is applied to the point cloud, so as to preserve the original absolute position distribution of the point cloud in the normalized space. The scale-sensitive point cloud representation module is used to construct neighborhood point sets under corresponding neighborhood radii for the normalized input point set through multiple parallel scale channels. The neighborhood points are aggregated through a shared multilayer perceptron with 3D coordinates and Euclidean distance from the neighborhood points to the reference point as enhanced inputs to obtain point-level local responses. At the same time, global position mapping is performed on the original 3D coordinates of all points through independent branches, and the original coordinate distribution response is coupled with the local response through linear adaptation mapping. Mean convergence and extreme value convergence are performed on each scale channel, and the two types of statistical results of each channel are concatenated to generate a shape-level representation vector. The scale parameter regression module is used to perform Z-score normalization preprocessing on the shape-level representation vector and predict the scale parameter corresponding to the normalized point cloud through a support vector regression model based on radial basis function kernel. The point cloud size recovery module is used to perform inverse size mapping on each point in the normalized point cloud in each coordinate axis direction according to the predicted scale parameters, so as to obtain a three-dimensional point cloud that recovers the true physical size.

9. An electronic device, characterized in that, include: A memory and a processor; the memory stores a computer program, and the processor executes the computer program to implement the three-dimensional physical scale restoration method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the three-dimensional physical scale restoration method as described in any one of claims 1 to 7.

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