Three-dimensional point cloud classification segmentation method based on geometric perception fitting convolution

Abstract

The invention relates to the technical field of three-dimensional point cloud data processing, and discloses a three-dimensional point cloud classification segmentation method based on geometric perception fitting convolution, and the method comprises the following specific steps: S1, selecting a public data set, reading point cloud coordinates, labels and RGB information, dividing a point cloud into a plurality of local fields, and extracting the initial features of the point cloud; s2, a bidirectional geometric normalization pooling module is adopted, and non-uniform point cloud density and feature difference are relieved through forward and reverse two-dimensional normalization and adaptive aggregation; s3, designing a fitting convolution module based on Taylor expansion, enhancing geometric expression ability and structural robustness of the features, processing the features by the module, constructing a segmentation model, and extracting feature representation fusing local geometry and global context; and S4, classifying and segmenting the point cloud data based on the output features generated by the network model, so that a local geometric structure and a neighborhood change rule can be more fully described while the calculation efficiency is maintained, and a more accurate three-dimensional point cloud classification and segmentation result is realized.

Description

A 3D point cloud classification and segmentation method based on geometric perception fitting convolution. Technical Field

[0001] This invention relates to the field of 3D point cloud data processing technology, specifically a 3D point cloud classification and segmentation method based on geometric perception fitting convolution. Background Technology

[0002] With the rapid development of high-precision sensors such as LiDAR and Kinect, 3D point clouds have become the core data format for representing the real world. After acquiring scene point clouds through sensors, it is necessary to rely on 3D point cloud classification and segmentation technology to achieve a deep understanding of the 3D scene, thereby supporting accurate object recognition and scene analysis. This technology has been widely used in fields such as autonomous driving, mobile robots, industrial control, augmented reality, and medical image analysis. Especially in complex industrial scenarios, equipment structures are diverse, spatially distributed, and point cloud density is uneven, often accompanied by occlusion and noise. Accurate point cloud analysis is crucial for equipment identification and safety inspection. Therefore, it is urgent to deepen the research of related technologies to improve its application efficiency in complex environments.

[0003] In recent years, deep learning-based 3D point cloud classification and segmentation methods have become a research hotspot, mainly divided into three categories: projection-based, voxel-based, and point-based methods. Among them, projection-based methods, while utilizing mature image convolutional networks, are prone to losing 3D geometric structure and depth information during the projection process, leading to a decrease in segmentation accuracy under complex spatial relationships. Voxel-based methods, by voxelizing the point cloud and applying 3D convolution, can preserve spatial structure, but are usually accompanied by high computational overhead and memory consumption. Moreover, the choice of voxel resolution has a direct impact on detail representation and computational efficiency, making it difficult to adapt to large-scale or high-precision scenarios. Point-based methods directly process the original point cloud, avoiding the loss of structural information, and can be further divided into two categories: convolution-based and Transformer-based. The former has strong performance in extracting local features of the point cloud through convolution operations; the latter, with the help of attention mechanisms, can better capture global contextual information, but is usually weaker in processing local details and structural fitting, and has higher computational complexity.

[0004] Existing methods generally suffer from common defects, especially when dealing with complex point clouds. These problems include extremely uneven point cloud density distribution (e.g., denser near points and sparser far points), low feature discrimination between devices with similar structures, loss of local geometric information due to noise and occlusion, and difficulty in adapting to irregular point cloud distributions using traditional convolution. These issues result in insufficient classification and segmentation accuracy and poor robustness, making it difficult to meet the requirements of high-precision applications. Summary of the Invention

[0005] The purpose of this invention is to provide a 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, a 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution is provided, comprising the following steps: S1, selecting a public dataset, reading the point cloud coordinates, labels, and RGB information, dividing the point cloud into multiple local neighborhoods, and extracting the initial features of the point cloud; S2, using a bidirectional geometrically normalized pooling module to process the initial features obtained in S1, alleviating the uneven density and feature differences in the spatial distribution of the point cloud; S3, processing the normalized features obtained in S2 based on the fitting convolution module, constructing a 3D point cloud classification and segmentation model, extracting feature representations that fuse local geometry and global context, performing low-order and high-order decomposition and fitting of local neighborhood features based on the Taylor expansion idea, and constructing a network model framework, determining the input and output features of the backbone network; S4, based on the output features generated by the network model in S3, using an optimizer to optimize the parameters, and using the overall accuracy as the evaluation index, classifying and segmenting the point cloud data.

[0007] Furthermore, in step S1, the point cloud is sampled from the original point cloud using the farthest point sampling algorithm (FPS); then, the K-nearest neighbor (KNN) algorithm is used to determine the grouping points of each sampled point and form a local region set, and the lightweight PointNet is used to extract features from the local region.

[0008] Furthermore, the bidirectional geometric normalization pooling module in step S2 includes forward geometric normalization, reverse geometric normalization, and adaptive pooling. Forward geometric normalization uses the features of the sampling points to normalize the features of the grouping points; reverse geometric normalization normalizes the features of the sampling points according to the features of the grouping points; affine transformation is performed on the above normalization results, and adaptive pooling is used to adaptively aggregate the local features to ensure that the sorting is not distorted, and a structured region feature vector that retains the underlying geometric attributes is output.

[0009] Further, in step S3, within the neighborhood of the center point of the sampling point, the neighborhood features are structurally expanded and approximated based on the local geometric changes; the feature vector of the structured region is transformed by a linear mapping function to obtain a low-order convolution of the local region, which is used to describe the structural parts that change smoothly within the neighborhood and are not easily affected by noise; a high-order convolution is constructed to learn precise detailed features from the relative features of the center point and neighboring points, and the low-order convolution and the high-order convolution are fused to obtain the final representation of the fitted convolution.

[0010] Further, after obtaining the high-order and low-order convolutions in step S3, the network model framework is constructed in two steps: First, a fitting convolution module is constructed: This module is based on Taylor expansion, with the Taylor expansion order selected from 2 to 8 based on the local geometric complexity of the point cloud. It performs low-order and high-order decomposition and fitting of local neighborhood features. Second, a network model is constructed: This model includes an MLP layer and four cascaded feature extraction modules. Each feature extraction module includes a sequentially connected bidirectional normalized pooling module and a fitting convolution module. Adjacent feature extraction modules pass features through residual connections. Then, through three feature propagation modules, the multi-level features extracted in the feature extraction stage are gradually restored to the resolution of the original point cloud and fused with the features of the corresponding level through skip connections, thereby achieving an effective combination of high and low resolution information.

[0011] Furthermore, in the process of constructing higher-order convolution, the construction method of higher-order convolution is as follows: First, the geometric information between sampling points and grouping points is explicitly introduced to obtain sensitive detail features in local geometric changes. The sensitive detail features and the neighborhood deviation between sampling points and groups caused by grouping are fitted to obtain the fitting function. The fitting function is then aggregated through an aggregation function to obtain the higher-order convolution.

[0012] Furthermore, the output features generated by the network model were trained using the PyTorch framework. The training process used labeled smooth cross-entropy as the loss function, AdamW as the optimizer, with an initial learning rate of 0.01, a weight decay coefficient of 1, and a batch size of 32.

[0013] Furthermore, the overall accuracy rate is used as the core objective indicator in the evaluation process to measure the model's overall ability to distinguish test samples. In the classification task, the prediction results of the samples can correspond to four situations: actually being a positive class and being judged as a positive class, actually being a negative class and being judged as a negative class, actually being a negative class but being misclassified as a positive class, and actually being a positive class but being misclassified as a negative class. The percentage of the overall accuracy rate is calculated based on the ratio of the correct values ​​in the above four situations to the total.

[0014] This invention offers the following advantages over existing technologies: 1. By employing a bidirectional geometric normalization pooling module, this invention utilizes a dual normalization design—forward calibration of group point features and backward calibration of sample point features—combined with local and global mean / standard deviation calculations and learnable affine transformations. This effectively alleviates the feature shift problem caused by density differences in the spatial distribution of point clouds. Compared to traditional single-direction normalization methods, this module can simultaneously balance the feature distribution of sample points and group points, outputting structured feature vectors that retain underlying geometric attributes. This lays a stable foundation for subsequent feature extraction, ensuring consistent feature representation capabilities in both sparse and dense regions. 2. The fitting convolution module is based on Taylor expansion. By dynamically selecting the 2nd to 4th order expansion, it achieves low-order and high-order decomposition of local neighborhood features. Low-order features capture a smooth and noise-resistant overall structure, while high-order features accurately fit neighborhood deviations using a custom fitting function, effectively extracting sensitive details in geometric changes. This overcomes the limitation of traditional convolution, which can only capture local features. The limitations of smooth features are significantly overcome, enhancing the model's ability to distinguish complex geometric structures, fine-grained components, and regions with similar shapes, thus greatly improving the accuracy of classification and segmentation. 3. The feature extraction module of the dry network includes a bidirectional geometric normalization pooling module to alleviate the problem of uneven distribution of spatial features in point clouds, laying a stable foundation for subsequent feature extraction. Combined with the fitting convolution module, low-order and high-order decomposition and fitting of neighborhood features are performed to enhance the geometric expressiveness and structural robustness of features, achieving more accurate 3D point cloud classification and segmentation results. 4. Through the stability guarantee of bidirectional normalization, the geometric perception enhancement of Taylor expansion, and the collaborative optimization of the network architecture, the model has stronger noise resistance and environmental adaptability, showing excellent performance in synthetic datasets, real-world datasets, and industrial scenarios. It can handle both standard scenarios of synthetic data and complex situations such as background interference, random disturbances, and dense equipment distribution in real-world scenarios, solving the shortcomings of traditional methods in terms of insufficient robustness in complex scenarios. Attached Figure Description

[0015] Figure 1 is a flowchart of the three-dimensional point cloud classification and segmentation method of the present invention; Figure 2 is a schematic diagram of the bidirectional geometric normalized pooling module of the present invention; Figure 3 is a schematic diagram of the geometric perception fitting convolution module of the present invention; Figure 4 is a schematic diagram of the three-dimensional point cloud classification and segmentation network framework of the present invention; Figure 5 is a schematic diagram of the component segmentation results of point cloud data of the present invention. Detailed Implementation

[0016] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0017] In one implementation, as shown in Figures 1-5, a 3D point cloud classification and segmentation method based on geometric perception fitting convolution is specifically described in Figure 1. The method includes the following steps: S1, point cloud data preprocessing and initial feature extraction - select a public dataset, read the point cloud coordinates, labels and RGB information, divide the point cloud into multiple local areas, and extract the initial features of the point cloud.

[0018] S11. Set the original point cloud as input. Where N represents the number of points in the point cloud, and each point in the point cloud X... All contain 3D coordinate information and RGB feature information. The farthest point sampling algorithm (FPS) is used to select G sampling points from the original point cloud. The number of sampling points G is 1 / 4 to 3 / 4 of the number of points N in the original point cloud. Preferably, in this embodiment, G = N / 4, to control the computational load while ensuring feature representativeness; S12, for each sampling point... The K-Nearest Neighbors (KNN) algorithm is used to find K grouping points to form a local region set. Where K ranges from 16 to 64, and in this embodiment, K=32 is preferred to balance local feature coverage and computational efficiency; S13, using a lightweight PointNet, features are extracted from each local region through a shared multilayer perceptron (MLP), and max pooling is used to obtain local features. In this embodiment, the shared MLP of the lightweight PointNet contains 3 convolutional layers, with feature dimensions of 64→128→256 respectively. The kernel size is 1×1, and the activation function is ReLU, the mathematical expression of which is as follows: ;in, For the i-th local region The feature representation; D is the feature dimension; For local neighborhood The j-th point in the cloud; then point cloud grouping and feature extraction yielded G local features. .

[0019] S2. Bidirectional Geometric Normalization Pooling Feature Processing: The initial features obtained in S1 are processed using a bidirectional geometric normalization pooling module to alleviate the uneven density and feature differences in the spatial distribution of the point cloud. The bidirectional geometric normalization pooling module includes a forward normalization unit, a reverse normalization unit, and an adaptive pooling unit, as shown in Figure 2. The specific implementation process is as follows: S21. Forward Geometric Normalization Unit: Based on the sampling points... Features to normalize grouping points The features; as a preferred embodiment of step S21, it specifically includes the following steps: S211, firstly calculate the mean based on the sampling points. and standard deviation It can be represented from both local and global perspectives: ; Where K is the number of grouping points and G is the number of sampling points; the mean and standard deviation are calculated along the feature channel dimension D and are statistically analyzed on the local neighborhood point dimension K and the global sampling point dimension G respectively, so as to simultaneously characterize the feature distribution within the neighborhood and the overall feature scale across the neighborhood.

[0020] S212, to Apply learnable affine transformations to normalize the features of the grouped points: ;in, It is the scaling factor. These are offset coefficients, and they are all learnable parameters; It represents the Hadamardi (or Hadama) stack; It is an extremely small number that maintains numerical stability.

[0021] S22, Reverse geometric normalization unit based on grouping points Features to normalize sampling points The features of step S22 are as follows. As a preferred embodiment of step S22, the specific steps include: S221, firstly calculating the mean of the grouping points. and standard deviation The calculation formula is as follows: ; Similar to forward normalization, the calculation is performed on the feature channel dimension D. and The calculation is represented from both local and global perspectives, thereby achieving normalization constraints at both local and global scales.

[0022] S222, to Apply learnable affine transformations to normalize the features of the sampling points: ;in, It is the scaling factor. These are offset coefficients, and they are all learnable parameters; It represents the Hadamardi (or Hadama) stack; It is an extremely small number that maintains numerical stability. Affine transformation, while preserving the local features of the point cloud, also captures the rigid transformation of the features; S23, in order to maintain the sorting without deformation, adaptive pooling aggregation is performed on the local features. The aggregation process is to perform adaptive pooling aggregation on the features after forward and backward normalization, and output a structured local region feature vector that preserves the underlying geometric attributes. The specific formula is: ;in, The output feature of the i-th local region pooling is a structured feature vector obtained by performing SoftMax adaptive weighting on the K neighborhood features in the region. This weighting process is determined only by the features in the neighborhood and is independent of the order of the neighborhood points, thus ensuring the order invariance of the pooling operation. It serves as the input feature for the subsequent fitting convolution module.

[0023] S3. Fitted Convolution Feature Extraction and Network Model Construction - Based on the fitted convolution module, the normalized features obtained in S2 are processed to construct a 3D point cloud classification and segmentation model, extracting feature representations that fuse local geometry and global context. This module is based on the Taylor expansion idea, performing low-order and high-order decomposition and fitting of local neighborhood features, thereby enhancing the geometric expressiveness and structural robustness of the features. Specifically, it includes the following steps: S31. Feature Processing of the Fitted Convolution Module: Within the neighborhood of the center point, based on local geometric changes, the neighborhood features are structurally expanded to approximate the overall change trend of the neighborhood. The approximate form is as follows: ; where the coefficient It characterizes higher-order geometric changes in local structures. In actual implementation, when the Taylor expansion order n is too low, it can only depict linear changes in local areas and is difficult to effectively characterize higher-order geometric features such as curvature changes and boundary bends. When the expansion order is too high, the computational complexity increases significantly, and higher-order terms are more sensitive to noise, which can easily lead to unstable feature fitting. Therefore, this invention limits the number n to the range of 2–4 as the preferred range.

[0024] S32. By transforming the central features through a linear mapping function, low-order convolutions of local regions are obtained, which are used to describe the structural parts that change smoothly in the neighborhood and are not easily affected by noise. ;in, This represents a learnable linear mapping function; S33: Construct a low-order convolution to learn the geometric information of the local neighborhood; S34: Construct a high-order convolution to learn precise detailed features from the relative features of the center point and neighboring points.

[0025] As shown in Figure 3, the preferred embodiment of step S23 specifically includes the following steps: S331, Explicitly introducing the geometric information of sampling points and grouping points is beneficial for fitting the relative spatial distribution relationship between convolution learning points, significantly enhancing the ability to fit the shape of the convolutional perception point cloud. The interaction between sampling points and grouping points is expressed as: ;in, Neighborhood weights; For learnable mappings; and S332. Fit the neighborhood deviation to obtain sensitive detail features in local geometric changes. The specific fitting function is defined as follows: Here, parameter s is used to adjust the linear response strength between the center point features and the neighborhood features, and parameter p is used to control the sensitivity of the fitting function to nonlinear geometric biases. During model initialization, parameters s and p are initialized to 1, and the fitting function degenerates into an affine basis function, which is beneficial for stable model training. During training, the parameters are adaptively updated through backpropagation, and their value range is preferably constrained to... , This is to avoid numerical divergence in the higher-order fitting process and to ensure that higher-order features respond effectively to local geometric changes.

[0026] S333. Aggregate the fitted function using an aggregation function to obtain a higher-order convolution. : ;in, S34 is the max pooling function; S35, the low-order convolution obtained in S32 is fused with the high-order convolution obtained in S33 to obtain the final representation of the fitted convolution: S35. Design the network model, i.e., the network framework of the backbone network, and determine the input and output of the backbone network, as shown in Figure 4. The backbone network of the 3D point cloud classification and segmentation model consists of one input MLP layer, four cascaded feature extraction modules, and three feature propagation modules. S351. The input MLP layer contains two convolutional sub-layers, and the activation function is ReLU. In this embodiment, the 256-dimensional initial features output from S1 are linearly mapped to 64-dimensional features through convolution operations. S352. The four feature extraction modules are cascaded sequentially. Each feature extraction module contains a sequentially connected bidirectional geometric normalized pooling module and a fitting convolution module. Adjacent feature extraction modules transfer features through residual connections. When the input and output feature dimensions are different... In this process, dimensionality matching is adjusted using 1×1 convolution. In this embodiment, the output feature dimensions of the first three feature extraction modules are 128, 256, and 512, respectively, and the fourth feature extraction module outputs 1024-dimensional global features. In S353, all three feature propagation modules use deconvolution to restore resolution. In this embodiment, the deconvolution kernel size is 3×3, and the stride is 2. After each restoration, the feature dimension is consistent with the output dimension of the corresponding layer's feature extraction module. The three feature propagation modules sequentially restore the 1024-dimensional, 512-dimensional, and 256-dimensional features obtained in the feature extraction stage to the resolution of the original point cloud, and fuse them with the features of the corresponding layer through skip connections to achieve an effective combination of high and low resolution information.

[0027] S4. Based on the output features generated by the network model, classify and segment the point cloud data; S41. In this implementation, training is completed under the PyTorch framework. The training process uses labeled smooth cross-entropy as the loss function, AdamW as the optimizer, with an initial learning rate of 0.01, a weight decay coefficient of 1, and a batch size of 32; S42. Overall accuracy (OA) is used as the core objective indicator in the evaluation process to measure the model's overall ability to discriminate test samples; its calculation formula is: Wherein, TP is the number of samples that are actually positive and are judged as positive, TN is the number of samples that are actually negative and are judged as negative, FP is the number of samples that are actually negative but are misjudged as positive, and FN is the number of samples that are actually positive but are misjudged as negative.

[0028] To evaluate the performance of the method of this invention in point cloud classification tasks, experiments were conducted on the synthetic point cloud dataset ModelNet40 and the real-world scene point cloud dataset ScanObjectNN, and comparisons were made with various other methods. The ModelNet40 dataset consists of approximately 12K synthetic 3D CAD models, covering 40 object categories. The ScanObjectNN dataset contains approximately 15K point cloud samples from 15 categories, all composed of real scan data obtained from complex background environments, and is divided into three variants: OBJ_BG, OBJ_ONLY, and PB_T50_RS. Among them, OBJ_BG retains the background interference in the original scene; OBJ_ONLY removes the background and retains only the target point cloud; PB_T50_RS introduces random translation, rotation, scaling, and other perturbations while retaining background noise. On this dataset, the number of input point clouds is set to 2048. The experimental results are shown in Table 1, which lists the classification results of the method of this invention on ModelNet40 and ScanObjectNN.

[0029] Table 1

[0030] As shown in Table 1, Params(M) represents the number of parameters and FLOPs(G) represents the model complexity (computational cost). It can be seen that this method achieves a classification accuracy of 94.2% on the ModelNet40 dataset, surpassing other existing methods, and significantly reduces the number of parameters and floating-point operations. On the ScanObjectNN dataset OBJ_ONLY subset, it achieves a classification accuracy of 87.83%, demonstrating excellent classification performance. This fully validates the effectiveness of the proposed geometric normalized pooling module and fitting convolution module in this implementation.

[0031] Using this method, component segmentation experiments were conducted on the ShapeNetPart dataset. ShapeNetPart includes approximately 16K synthetic 3D object models, spanning 16 categories and 50 labeled components. During the experiment, N=2048 points were used as input. Figure 5 shows a comparison between the original point cloud's true labels and the prediction results processed by the method of this invention. The segmentation results show that this method can obtain segmentation results that are highly consistent with the true labels on complex structural boundaries, fine-grained components, and regions with similar shapes, fully demonstrating the effectiveness of this method in 3D point cloud segmentation tasks.

[0032] To deeply analyze the role and contribution of each component in the proposed method, this implementation designed a comprehensive ablation experiment. The effectiveness of the proposed two modules—the bidirectional geometric normalized pooling module and the fitting convolution module—as well as the Taylor series number *n* and the number of grouping points *k*, was verified through ablation analysis. The performance differences with and without these modules, along with the number of experimental variables, were compared to evaluate their role and contribution to classification accuracy. Tables 2, 3, and 4 show the results of the effectiveness verification for each module. Table 3 shows the impact of the Taylor series size, and Table 4 shows the impact of the number of grouping points *k* on classification accuracy.

[0033] Table 2. Labels: Bidirectional Geometric Normalized Pooling Fitting Convolution ModelNet40 P (M) F (G) 1 2 3 √×√×√√ 83.6% 93.8% 94.2% 4.8 97.4 77.6 32.1 43.6 53.78 Table 3 n 1 2 3 4 5 6 OA (%) 92.8 93.9 94.2 93.7 92.6 90.3 Table 4k48163264128OA (%) 92.6 93.1 93.3 94.2 93.6 93.4 As shown in Table 2, P(M) represents the number of parameters and F(G) represents the model complexity (computational cost). The ablation experiment results show that the complete model achieves optimal performance while maintaining a low number of parameters and computational complexity, reaching a classification accuracy of 94.2% on the ModelNet40 dataset, which verifies the rationality and effectiveness of the collaborative design of each module.

[0034] As shown in Table 3, different Taylor expansion orders have a significant impact on model performance. When the expansion order is low, the model can only characterize linear or approximately linear changes in local regions and has limited ability to express complex geometric details. The model performance reaches its optimum when n=3. As the order continues to increase, the higher-order terms become more sensitive to noise, leading to a decrease in classification accuracy.

[0035] As shown in Table 4, when the number of neighborhood points k is small, the local neighborhood coverage is insufficient, and the geometric information is not fully represented. As k increases, the model can capture more complete local structural information, achieving optimal classification performance when k=32.

[0036] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution, characterized in that: Includes the following steps: S1. Select a public dataset, read the point cloud coordinates, labels and RGB information, divide the point cloud into multiple local areas, and extract the initial features of the point cloud; S2. The initial features obtained in S1 are processed using a bidirectional geometric normalized pooling module to alleviate the uneven density and feature differences in the spatial distribution of point clouds. S3. The normalized features obtained in S2 are processed using a fitting convolution module to construct a 3D point cloud classification and segmentation model. Feature representations that integrate local geometry and global context are extracted. Based on the Taylor expansion idea, low-order and high-order decomposition and fitting of local neighborhood features are performed, and a network model framework is constructed to determine the input and output features of the backbone network. S4. Based on the output features generated by the network model in S3, an optimizer is used to optimize the parameters, and the point cloud data is classified and segmented using the overall accuracy as the evaluation index.

2. The 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution according to claim 1, characterized in that: In step S1, the point cloud is sampled using the farthest point sampling algorithm (FPS); then, the K-nearest neighbor (KNN) algorithm is used to determine the grouping points of each sampled point and form a local region set. The lightweight PointNet is used to extract features from the local region.

3. The 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution according to claim 2, characterized in that: In step S2, the bidirectional geometric normalization pooling module includes forward geometric normalization, reverse geometric normalization, and adaptive pooling. Forward geometric normalization uses the features of the sampling points to normalize the features of the grouping points; reverse geometric normalization normalizes the features of the sampling points based on the features of the grouping points. The normalized results are subjected to affine transformation, and adaptive pooling is used to adaptively aggregate local features to ensure that the sorting is not distorted, and a structured region feature vector that retains the underlying geometric properties is output.

4. The 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution according to claim 3, characterized in that: In step S3, within the neighborhood of the center point of the sampling point, the neighborhood features are structurally expanded and approximated based on the local geometric changes. The feature vector of the structured region is transformed by a linear mapping function to obtain a low-order convolution of the local region, which is used to describe the structural parts that are smoothly changing within the neighborhood and are not easily affected by noise. A high-order convolution is constructed to learn precise detailed features from the relative features of the center point and neighboring points. The low-order convolution and the high-order convolution are fused to obtain the final representation of the fitted convolution.

5. The 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution according to claim 4, characterized in that: After obtaining the high-order and low-order convolutions in step S3, the network model framework is constructed in two steps: First, a fitting convolution module is constructed. This module is based on Taylor expansion, with the Taylor expansion order selected from 2 to 8 based on the local geometric complexity of the point cloud. It performs low-order and high-order decomposition and fitting of local neighborhood features. Second, a network model is constructed. This model includes an MLP layer and four cascaded feature extraction modules. Each feature extraction module includes a sequentially connected bidirectional normalized pooling module and a fitting convolution module. Adjacent feature extraction modules pass features through residual connections. Then, through three feature propagation modules, the multi-level features extracted in the feature extraction stage are gradually restored to the resolution of the original point cloud and fused with the features of the corresponding level through skip connections, thereby achieving an effective combination of high and low resolution information.

6. The 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution according to claim 5, characterized in that: In the process of constructing a higher-order convolution, the construction method is as follows: First, the geometric information between the sampling point and the grouping point is explicitly introduced to obtain the sensitive details in the local geometric changes. The sensitive details and the neighborhood deviation between the sampling point and the group caused by the grouping are fitted to obtain the fitting function. The fitting function is then aggregated by the aggregation function to obtain the higher-order convolution.

7. The 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution according to claim 1, characterized in that: The output features generated by the network model were trained in the PyTorch framework. The training process used labeled smooth cross-entropy as the loss function, AdamW as the optimizer, with an initial learning rate of 0.01, a weight decay coefficient of 1, and a batch size of 32.

8. The 3D point cloud classification and segmentation method based on geometrically perceptual fitting convolution according to claim 1, characterized in that: The overall accuracy rate is used as the core objective indicator in the evaluation process to measure the model's overall ability to distinguish test samples. In classification tasks, the prediction results of samples can correspond to four situations: actually positive and judged as positive, actually negative and judged as negative, actually negative but misclassified as positive, and actually positive but misclassified as negative. The percentage of the overall accuracy rate is calculated based on the ratio of the correct values ​​in the above four situations to the total.

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