A laser radar remote sensing data echo classification processing method, medium and system
By constructing a low-rank adaptive neural network training framework and resolution amplification effect equation system, a progressive training of the lidar remote sensing data classification model from low resolution to high resolution is achieved, and the problem of insufficient cross-resolution adaptability in the existing technology is solved, and stable and continuous classification performance is achieved.
Patent Information
- Application Number
- CN202411896366.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-23
- Publication Date
- 2025-04-25
- Estimated Expiration
- 2044-12-23
AI Technical Summary
Existing lidar remote sensing data processing methods lack the ability to adapt across resolutions and it is difficult to effectively process data of different resolutions, especially in the process of gradually improving from low resolution to high resolution.
A lidar remote sensing data echo classification processing method is adopted to build a low-rank adaptive neural network training framework and a system of resolution amplification effect equations to achieve progressive classification model training from low resolution to high resolution, and the combination of sampling rate amplification factor and feature mapping parameters is used to achieve feature migration and adaptation across resolutions.
It effectively solves the adaptability problem in cross-resolution data processing, realizes stable and continuous classification performance from low resolution to high resolution, reduces calculation costs, and ensures consistency of classification results.
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Figure CN119357779B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of laser radar remote sensing data processing, and in particular, relates to a laser radar remote sensing data echo classification processing method, medium and system. Background Art
[0002] As an advanced active remote sensing method, LiDAR technology acquires the three-dimensional spatial information of the target by emitting laser beams and receiving echo signals reflected by the target. It plays an important role in many fields such as environmental monitoring, topographic mapping, autonomous driving, smart cities, and resource exploration. LiDAR systems can acquire geometric and radiation characteristic information of ground objects in all weather conditions, over a large range, and with high efficiency, providing rich data support for these application scenarios. However, the massive amount of LiDAR echo data poses a huge challenge to subsequent data processing and information extraction, especially in target recognition and classification. How to effectively extract and classify the features of different targets from complex echo signals has become a research hotspot in this field.
[0003] In recent years, with the vigorous development of artificial intelligence technology, deep learning-based lidar data processing methods have made important breakthroughs. Researchers have proposed a variety of deep neural network models, such as PointNet, PointNet++, etc., for feature extraction and classification tasks of three-dimensional point cloud data. These methods can automatically learn the local and global features of point cloud data by constructing complex network structures to achieve end-to-end target recognition. However, existing methods are usually optimized for data of a specific resolution and lack cross-resolution adaptability. In practical applications, due to the influence of factors such as scanning distance and angle, lidar data in the same area may present different sampling density and resolution characteristics. This difference in resolution leads to inconsistent feature expression, which seriously affects the performance of the classification model. In particular, when it is necessary to process data that gradually increases from low resolution to high resolution, it is difficult for existing models to effectively utilize the inherent correlation between different resolution levels, and it is often necessary to retrain the model for each resolution level, which not only increases the computational cost, but also cannot guarantee the consistency of the classification results. Summary of the invention
[0004] In view of this, the present invention provides a lidar remote sensing data echo classification processing method, medium and system, which can solve the technical problem that existing methods are usually optimized for data of a specific resolution and lack cross-resolution adaptability.
[0005] The present invention is achieved in that:
[0006] The present invention provides a laser radar remote sensing data echo classification processing method, which includes the following steps:
[0007] S10, downsampling the laser radar remote sensing data for multiple known targets according to a preset minimum sampling rate to obtain lowest level echo data, and labeling the lowest level echo data according to multiple known targets to obtain a lowest level training data set;
[0008] S20, using a deep learning network to train the lowest level training data set to obtain a basic classification model;
[0009] S30, constructing a low-rank adaptive neural network training framework, and using the basic classification model as an initial model of the training framework;
[0010] S40, establishing a resolution amplification effect equation group based on the training framework, wherein the resolution amplification effect equation group includes a sampling rate amplification factor and a feature mapping parameter;
[0011] S50, sampling the laser radar remote sensing data at a sampling rate higher than the previous level to obtain higher level echo data;
[0012] S60, establishing a higher-level training data set, and inputting the higher-level training data set into the training framework, performing feature mapping using the resolution magnification effect equation group, and solving the equation group parameters using an iterative optimization method;
[0013] S70, performing low-rank adaptive fine-tuning on the training framework based on the parameters to obtain a higher-level classification model;
[0014] S80, verifying the higher-level classification model according to the known multiple targets, and calculating the classification accuracy;
[0015] S90, when the classification accuracy does not reach the preset threshold, repeat steps S50 to S80 until the classification accuracy reaches the preset threshold, and output the final classification model for classifying the laser radar remote sensing data echoes to be classified. The step of classifying the laser radar remote sensing data echoes to be classified is specifically: first preprocessing the laser radar remote sensing data to be classified, including data cleaning, removing outliers and noise, and formatting and normalizing the data according to the input requirements of the final classification model; then inputting the preprocessed data into the final classification model, and obtaining the classification probability distribution of the model output through feature extraction and forward propagation calculation of each level of the model; then post-processing the model output results, determining the most likely target category according to the probability distribution and generating a classification label; finally, visually displaying the classification results, generating a two-dimensional or three-dimensional visualization image of the classification results, and marking the spatial distribution of targets of different categories.
[0016] On the basis of the above technical solution, the laser radar remote sensing data echo classification processing method of the present invention can also be improved as follows:
[0017] The deep learning network adopts an embedded feature pyramid structure, including a feature extraction module, a point cloud encoding sub-network, a feature enhancement sub-network, a spatiotemporal feature sub-network and a fusion sub-network;
[0018] The feature extraction module is responsible for extracting multi-dimensional features from the original echo data, including the echo intensity feature matrix, the distance feature matrix and the angle feature matrix;
[0019] The point cloud coding subnetwork is used for feature coding, the input is the echo intensity feature matrix, the distance feature matrix and the angle feature matrix, and the output is the point cloud feature coding;
[0020] The feature enhancement subnetwork is used for feature enhancement, the input is the point cloud feature encoding, and the output is the enhanced feature representation;
[0021] The spatiotemporal feature subnetwork is used to extract spatiotemporal correlation, the input is the enhanced feature representation, and the output is the spatiotemporal feature vector;
[0022] The fusion subnetwork is used for feature fusion classification, the input is the spatiotemporal feature vector, and the output is the target classification result.
[0023] Furthermore, the resolution magnification effect equation group is used to realize feature pyramid cascade magnification, including a local magnification effect equation, a global magnification effect equation, a scale magnification effect equation, and an alignment magnification effect equation;
[0024] The local amplification effect equation is used for local feature refinement, the input is the low-resolution local feature, and the output is the refined high-resolution local feature;
[0025] The global amplification effect equation is used for global feature enhancement, the input is the low-resolution global feature, and the output is the enhanced high-resolution global feature;
[0026] The scale magnification effect equation is used for characteristic scale transformation, the input is the original characteristic scale, and the output is the magnified characteristic scale;
[0027] The alignment magnification effect equation is used for feature alignment correction, the input is the unaligned feature, and the output is the feature after spatial alignment.
[0028] Furthermore, the low-rank adaptive neural network training framework specifically uses low-rank matrix decomposition to reconstruct network parameters, and realizes feature mapping and network fine-tuning by introducing an adaptive weight matrix.
[0029] Furthermore, the preset threshold is 95%.
[0030] Furthermore, the minimum sampling rate is specifically expressed as follows:
[0031] ;
[0032] In the formula, is the minimum sampling rate, in Hz; is the highest frequency component of the laser radar echo signal, in Hz; is the speed of light, take ; is the minimum resolution distance, in meters. Obtained through spectrum analysis: Step 1: Perform Fourier transform on the echo signal; Step 2: Determine the highest frequency whose amplitude is greater than the noise threshold. Among them, Determined by system parameters: Step 1: Based on the laser pulse width calculate: ; Step 2: Determine the final value by considering the system delay. This formula is based on the Nyquist sampling theorem; takes into account the distance resolution requirement; ensures that there is no aliasing of the signal; and is more reasonable than the traditional fixed sampling rate.
[0033] The sampling rate amplification factor is specifically expressed as follows:
[0034] ;
[0035] In the formula, For the Level sampling rate amplification factor; is the base magnification, the default value is 2; For the The increment coefficient of the level, range [0.1,0.5]; is the attenuation coefficient, range [0.01,0.1]; is the magnification error. Determined through performance optimization: ; In the formula, is the classification accuracy gain function; To calculate the cost function; is the balance coefficient. Obtained through cross-validation: Step 1: Test different value; Step 2: Select the value that makes the classification accuracy the highest. This formula adopts a progressive amplification strategy; introduces exponential decay to control the overall amplification factor; takes into account the error accumulation effect; and is better than the linear amplification method.
[0036] The sampling rate higher than the previous level is specifically expressed as follows:
[0037] ;
[0038] In the formula, For the Level sampling rate; For the Level sampling rate; is the first-order correction coefficient; is the second-order correction coefficient; is the classification error; is the sampling rate error. Obtained through gradient optimization: ; ; In the formula, is the loss function; is the target classification error. This formula is based on the dynamic adjustment of the previous level sampling rate; introduces the error gradient correction term; adaptively optimizes the sampling rate; and improves the classification performance.
[0039] Among them, the relationship between the sampling rates includes:
[0040] Progressive relationship: the sampling rate increases step by step; the amplification factor decreases as the number of levels increases; avoid the computational burden caused by excessive amplification.
[0041] Feedback mechanism: guide sampling rate adjustment through classification error; introduce gradient information to achieve adaptive optimization; balance accuracy and efficiency requirements.
[0042] Error control: considers error propagation at all levels; compensates for accumulated errors through nonlinear terms; improves system stability.
[0043] The advantages of this sampling rate progression over existing technologies are:
[0044] Strong adaptability: The sampling rate can be adjusted according to the data characteristics; avoiding oversampling and undersampling problems.
[0045] High computational efficiency: Use progressive strategies to reduce computational effort; Control resource consumption through magnification factors.
[0046] Accuracy assurance: Introduce error feedback mechanism to ensure continuous improvement of classification performance.
[0047] In a specific implementation, an empirical value of 0.1 for the minimum sampling rate may be adopted.
[0048] Furthermore, the original echo signal waveform is specifically expressed as follows: ;
[0049] In the formula, is the initial amplitude, range [0,100]; is the attenuation coefficient, range [0,1]; is the center frequency, in Hz; is the initial phase, range [0,2]; is the time variable; For the The amplitude of an echo; For the The time delay of each echo; For the The frequency of the echo; For the The phase of the echo; is Gaussian white noise; is the total number of echoes.
[0050] Furthermore, the echo intensity feature matrix is specifically expressed as follows:
[0051] ;
[0052] in, Indicates Time window The energy value of a frequency component is calculated as follows:
[0053] ;
[0054] In the formula, is the time window length, unit s; is the start time.
[0055] Furthermore, the echo signal time delay is specifically expressed as follows:
[0056] ;
[0057] In the formula, is the target distance; is the speed of light; System delay; for atmospheric delay; is the measurement error; is the sampling sequence number.
[0058] Furthermore, the distance feature matrix is specifically expressed as follows:
[0059] ;
[0060] in, Indicates Scan line The distance value of each sampling point is calculated as follows:
[0061] ;
[0062] In the formula, is the corresponding time delay; is the distance correction term.
[0063] Furthermore, the laser radar scanning angle sequence is specifically expressed as follows:
[0064] ;
[0065] In the formula, is the initial angle, in rad; is the scan sequence number; is the angle step value; is the angle error.
[0066] Furthermore, the angle feature matrix is specifically expressed as follows:
[0067] ;
[0068] in, Indicates Scan cycle The angle value of each sampling point.
[0069] Furthermore, the point cloud feature encoding is specifically expressed as follows:
[0070] ;
[0071] In the formula, is the encoding function; For the Layer activation function; For the Layer convolution operation; is the weight coefficient; is the bias term; is a nonlinear activation function; is the number of network layers.
[0072] Furthermore, the enhanced feature representation is specifically expressed as follows:
[0073] ;
[0074] In the formula, is the enhancement coefficient; To enhance the bias term; is the spatial gradient.
[0075] Furthermore, the spatiotemporal feature vector is specifically expressed as follows:
[0076] ;
[0077] In the formula, is the time weight coefficient; is the spatial eigenvalue basis vector; is the space-time coupling coefficient; is the spatiotemporal characteristic component; is the corresponding dimension.
[0078] Furthermore, the resolution amplification effect equation group is specifically expressed as follows:
[0079] Local magnification effect equation: ;
[0080] Global amplification effect equation: ;
[0081] Scale magnification effect equation:
[0082] ;
[0083] Alignment magnification effect equation: ;
[0084] In the formula, They are local, global, scale and aligned magnification effects respectively; is the input feature; is the local characteristic component; is the local weight coefficient; is the Laplace operator coefficient; is the mixed partial derivative coefficient; is the Gaussian kernel function; is the scale factor; is the basis function weight; is the basis function; is the spatial transformation function; is the spatial offset; are their respective error terms.
[0085] For the local amplification effect equation: the first term It is a weighted combination of local features: decomposing the features into multiple local components ;Use weight coefficient Controls the importance of each component; this weighted combination can highlight important local feature patterns. is the Laplacian term: Calculate the second-order derivative of the feature; can detect the mutation and edge of the feature; coefficient Controls the degree of edge enhancement. It is a mixed partial derivative: it calculates the coupled changes of features in the x and y directions; it can capture the feature changes in the diagonal direction; the coefficient Control the degree of enhancement of diagonal features. The advantages over existing technologies include: multi-scale analysis: by decomposing local components, we can focus on features of different scales at the same time; edge preservation: the Laplace term can preserve and enhance edge features; direction perception: the mixed partial derivative term makes the enhancement process directionally selective.
[0086] For the global amplification effect equation: Gaussian kernel function is used Convolution of features: Gaussian kernel has rotational symmetry, which can smooth and suppress noise, and is used to maintain the main global structural features. Integration operation realizes global feature extraction: weighted average of the entire feature space; weights decay Gaussianly with distance; global statistical characteristics of features can be obtained. Advantages over existing technologies include: noise robustness: Gaussian smoothing can effectively suppress noise; scale invariance: by adjusting the Gaussian kernel parameters, it can adapt to different scales; computational efficiency: the calculation can be accelerated by fast Fourier transform.
[0087] For the scale magnification effect equation: the first term is the scale transformation term: parameter Control magnification, coordinate transformation Realize geometric scale transformation, coefficients in coordinate transformation Keep the feature amplitude constant with scale. The second term is the basis function expansion: using the orthogonal basis function system , weight coefficient By controlling the contribution of each basis function, the information loss caused by the scale transformation can be compensated. Compared with the existing technology, the advantages include: adaptability: the basis function expansion can adapt to different feature modes; information compensation: make up for the information loss caused by simple geometric enlargement.
[0088] For the alignment magnification effect equation: the first term It is a spatial transformation: it realizes the overall geometric transformation of the feature, which can include transformations such as rotation and translation. The second term is the partial derivative term , used to calculate the rate of change of the feature in the x and y directions, where the displacement Control the correction amplitude to achieve local position fine-tuning. Compared with existing technologies, the advantages include: precise alignment: considering global transformation and local adjustment at the same time; good continuity: gradient-based adjustment maintains feature continuity.
[0089] Furthermore, the low-rank matrix decomposition is specifically expressed as follows:
[0090] ;
[0091] In the formula, is the original weight matrix; is a left singular matrix; is a right singular matrix; is the rank constraint ( ); is the residual matrix.
[0092] Furthermore, the adaptive weight matrix is specifically expressed as follows:
[0093] ;
[0094] The calculation method of each element is:
[0095] ;
[0096] In the formula, is the correlation coefficient; is the feature vector; is the Gaussian kernel parameter; is the time-varying adjustment factor.
[0097] Parameter acquisition method:
[0098] 1. Obtained through gradient descent optimization:
[0099] ;
[0100] ;
[0101] ;
[0102] middle, is the loss function; is the true label.
[0103] 2. Obtained through experiments, the specific steps are:
[0104] Step 1: Collect training sample pairs ;
[0105] Step 2: Calculate the Euclidean distance between sample pairs ;
[0106] Step 3: Calculate the correlation coefficient based on the distance ,in is the distance threshold.
[0107] 3. Obtained through adaptive updating:
[0108] ;
[0109] In the formula, is the learning rate; is the feature difference at the current moment.
[0110] 4. Selection method:
[0111] Through cross validation in the set Select the optimal value.
[0112] A second aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the above-mentioned laser radar remote sensing data echo classification processing method.
[0113] A third aspect of the present invention provides a laser radar remote sensing data echo classification and processing system, which includes the above-mentioned computer-readable storage medium.
[0114] Compared with the prior art, the method, medium and system for classifying and processing laser radar remote sensing data echoes provided by the present invention have the following beneficial effects:
[0115] First, the present invention effectively solves the adaptability problem of traditional methods when processing multi-resolution data by establishing a progressive classification model training framework from low resolution to high resolution. The method first builds a basic classification model on the lowest resolution data, which not only reduces the complexity of initial training, but also lays a solid foundation for subsequent resolution improvement. Through this progressive training strategy from low to high, the model can smoothly adapt to the feature distribution of different resolution levels, avoiding the difficulty of adapting to low resolution that may be caused by training directly on high-resolution data.
[0116] Secondly, the present invention innovatively introduces a low-rank adaptive neural network training framework, and combines the resolution amplification effect equation group to establish a feature mapping mechanism between different resolution levels. This design enables the model to accurately capture the feature evolution law brought about by resolution changes, and realizes cross-resolution feature migration and adaptation. Through the organic combination of the sampling rate amplification factor and the feature mapping parameters, the model can accurately transfer the feature knowledge learned from low-resolution data to high-resolution scenes, ensuring the continuity and stability of the classification performance.
[0117] Third, the present invention uses iterative optimization to solve the parameters of the resolution amplification effect equation group, and optimizes the classification model through low-rank adaptive fine-tuning. This sophisticated parameter optimization mechanism ensures that the model can fully maintain the existing classification capabilities when processing higher-resolution data, while effectively integrating new feature information. Especially when processing complex targets, the model can gradually refine and optimize feature expression, ultimately achieving higher classification accuracy.
[0118] In addition, the present invention designs a model verification mechanism based on a preset threshold, which dynamically evaluates the classification accuracy to determine whether it is necessary to continue to improve the resolution and optimize the model. This adaptive training termination strategy not only ensures the performance requirements of the final classification model, but also avoids unnecessary waste of computing resources. At the same time, this mechanism also provides flexible accuracy adjustment space for different application scenarios, and users can set appropriate accuracy thresholds according to actual needs.
[0119] In summary, the present invention solves the technical problem that existing methods are usually optimized for data of a specific resolution and lack the ability to adapt across resolutions. BRIEF DESCRIPTION OF THE DRAWINGS
[0120] Figure 1 A flow chart of the method provided by the present invention;
[0121] Figure 2 This is the sample distribution diagram of the lowest level training data set;
[0122] Figure 3 It is the time domain distribution diagram of the laser radar echo intensity feature matrix. DETAILED DESCRIPTION
[0123] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.
[0124] like Figure 1 As shown, it is a flow chart of a laser radar remote sensing data echo classification processing method provided by the present invention. The specific implementation methods of the steps of the present invention are described in detail below:
[0125] Step S10: Downsample the lidar remote sensing data to multiple known targets according to a preset minimum sampling rate to obtain lowest level echo data, and annotate the lowest level echo data with labels according to multiple known targets to obtain a lowest level training data set.
[0126] The specific implementation is as follows:
[0127] First, according to the known target type, set the preset minimum sampling rate. Here, the minimum sampling rate can be calculated according to the minimum sampling rate formula, or a relatively low sampling rate, such as 0.1, can be selected. Then, the original lidar remote sensing data is downsampled to obtain the lowest level of echo data. This step can use downsampling algorithms, such as nearest neighbor interpolation or linear interpolation. Next, these lowest level echo data are labeled and each sample is labeled with the corresponding target category. Through this step, the lowest level training data set is obtained, laying the foundation for subsequent deep learning modeling.
[0128] Step S20: Use a deep learning network to train the lowest level training data set to obtain a basic classification model.
[0129] The specific implementation of this step is as follows:
[0130] First, a deep learning network with an embedded feature pyramid structure is designed. This network consists of the following submodules: feature extraction module, point cloud encoding subnetwork, feature enhancement subnetwork, spatiotemporal feature subnetwork, and fusion subnetwork. The feature extraction module is responsible for multi-dimensional feature decomposition of the original echo data, including echo intensity feature matrix, distance feature matrix, and angle feature matrix; the point cloud encoding subnetwork is responsible for encoding these features and extracting potential feature representations; the feature enhancement subnetwork further enhances and improves the encoded features; the spatiotemporal feature subnetwork captures the spatiotemporal correlation of features; finally, the fusion subnetwork fuses these features and outputs the final classification result.
[0131] When training this deep learning network, the lowest level training data set obtained earlier is used as input, and the network parameters are optimized through the back propagation algorithm to finally obtain the basic classification model. Although this basic model has a low accuracy rate, it lays the foundation for subsequent iterative optimization.
[0132] Step S30: construct a low-rank adaptive neural network training framework, and use the basic classification model as the initial model of the training framework.
[0133] The specific implementation is as follows:
[0134] The idea of low-rank matrix decomposition is used to construct this training framework. First, the network parameters Represented as a low-rank matrix Add a residual matrix ,Right now .here and are the left and right singular matrices, is the residual matrix. This can effectively compress the network parameters and retain the core features of the network.
[0135] Next, we introduce an adaptive weight matrix , its elements By the correlation coefficient and time-varying regulatory factors This matrix is used to implement feature mapping and network fine-tuning. The dynamic update of can make the network have good adaptability, so as to better adapt to the features at different resolutions.
[0136] Finally, the basic classification model obtained in the previous step S20 is used as the initial model of this low-rank adaptive neural network training framework, laying the foundation for subsequent iterative optimization.
[0137] Step S40: Establishing a resolution amplification effect equation group based on the training framework, wherein the resolution amplification effect equation group includes a sampling rate amplification factor and a feature mapping parameter.
[0138] The specific implementation is as follows:
[0139] A set of resolution amplification effect equations consisting of four sub-equations is established, namely: local amplification effect equation , global amplification effect equation , scale magnification effect equation and alignment magnification effect equation .
[0140] Local magnification effect equation Used to achieve local feature refinement, which includes local feature components , Laplace operator term And the mixed partial derivatives .
[0141] Global Amplification Effect Equation Then through the Gaussian kernel function Enhance the global features.
[0142] Scaling effect equation Using the scale factor The features are enlarged and a set of basis functions are introduced To further optimize the scale transformation.
[0143] Alignment magnification effect equation Then through the spatial transformation function and partial derivatives To achieve feature alignment correction.
[0144] These equations contain a series of parameters to be optimized, such as the local weight coefficient , Laplace operator coefficients , mixed partial derivative coefficients , basis function weight Etc., constitute the feature mapping parameters to be optimized. At the same time, the sampling rate amplification factor It is also an important parameter of this set of equations. By optimizing these parameters, efficient mapping of features at different resolutions can be achieved.
[0145] Step S50: Sampling the lidar remote sensing data at a sampling rate higher than the previous level to obtain higher level echo data.
[0146] The specific implementation is as follows:
[0147] First, determine the current sampling rate level. There are two ways. 1 is to calculate according to a formula higher than the previous sampling rate. You can also directly define a higher sampling rate, such as the lowest level of 0.1 at the beginning. Then, increase the sampling rate to a higher level, such as 0.2. By sampling the original lidar remote sensing data at this higher sampling rate, you can get higher-level echo data. This step can continue to use downsampling algorithms, such as nearest neighbor interpolation or linear interpolation. By gradually increasing the sampling rate, a series of echo data at different resolution levels can be obtained, laying the foundation for subsequent iterative optimization.
[0148] Step S60: Establish a higher-level training data set, and input the higher-level training data set into the training framework, use the resolution magnification effect equation group to perform feature mapping, and use an iterative optimization method to solve the equation group parameters.
[0149] The specific implementation is as follows:
[0150] First, according to the higher-level echo data obtained in the previous step, the corresponding training data set is established. This includes labeling the echo data and attaching the corresponding target category label to each sample.
[0151] Then, this higher-level training data set is input into the low-rank adaptive neural network training framework constructed in step S30. The features are mapped using the resolution magnification effect equations established in step S40. This involves a series of parameters to be optimized, such as the local weight coefficient , Laplace operator coefficients , mixed partial derivative coefficients , basis function weight wait.
[0152] Next, we use iterative optimization to solve these parameters. Specifically, we can use the gradient descent algorithm to calculate the loss function The gradient of each parameter is continuously optimized to minimize the error between the model's prediction result and the true label. In this way, higher-precision feature mapping parameters can be obtained.
[0153] Step S70: Perform low-rank adaptive fine-tuning on the training framework based on the parameters to obtain a higher-level classification model.
[0154] This step is implemented as follows:
[0155] First, the low-rank adaptive neural network training framework constructed in step S30 is fine-tuned using the feature mapping parameters optimized in step S60. Specifically, these parameters can be imported into the corresponding modules of the training framework, such as the local amplification effect equation Parameters wait.
[0156] Then, by continuing to train this fine-tuned network model, it can adapt to the feature distribution at a higher resolution. Here, the gradient descent algorithm can still be used to optimize the network parameters until the model converges.
[0157] Through this step of low-rank adaptive fine-tuning, a higher-level classification model is obtained. This model can better handle features at different resolutions, thereby improving the final classification accuracy.
[0158] Step S80: verify the higher-level classification model according to the known multiple targets and calculate the classification accuracy.
[0159] The specific implementation is as follows:
[0160] First, prepare some test samples, which are extracted from multiple known target categories and have no overlap with the training data.
[0161] Then, these test samples are input into the higher-level classification model obtained in step S70, so that the model can predict and classify the samples.
[0162] Next, the matching degree between the prediction results of the statistical model and the true label is calculated to calculate the classification accuracy. The classification accuracy here is the ratio of the number of correctly classified samples to the total number of samples.
[0163] Through this verification process, the performance of the current model on higher resolution data can be evaluated, providing a basis for subsequent iterative optimization.
[0164] Step S90: When the classification accuracy rate does not reach the preset threshold, repeat steps S50 to S80 until the classification accuracy rate reaches the preset threshold, and output the final classification model.
[0165] The specific implementation is as follows:
[0166] In step S80, the classification accuracy of the higher-level classification model is calculated. If this accuracy does not reach a preset threshold, such as 95%, it is necessary to continue iterative optimization.
[0167] First, repeat step S50 to further increase the sampling rate and obtain echo data with higher resolution. Then, establish a new training set based on these data, and execute step S60 to perform feature mapping and parameter optimization using the resolution amplification effect equation group.
[0168] Next, execute step S70 to perform low-rank adaptive fine-tuning on the training framework to obtain a better classification model, and then execute step S80 to calculate the classification accuracy of the new model.
[0169] If the accuracy still does not meet the standard, repeat the above steps until the classification accuracy reaches the preset 95% threshold. Finally, output the final classification model as the result of lidar remote sensing data echo classification.
[0170] A second aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the above-mentioned laser radar remote sensing data echo classification processing method.
[0171] A third aspect of the present invention provides a laser radar remote sensing data echo classification and processing system, which includes the above-mentioned computer-readable storage medium.
[0172] Specifically, the principle of the present invention is: first, starting from the lowest resolution data, a basic deep learning classification model is constructed. In order to alleviate the dependence on a large amount of labeled data, the idea of low-rank matrix decomposition is adopted, and the network parameters are expressed in the form of a low-rank matrix plus a residual term. This not only greatly compresses the number of parameters, but also retains the core characteristics of the network. At the same time, an adaptive weight matrix is introduced, whose elements are composed of correlation coefficients and time-varying adjustment factors, which are used to realize feature mapping and network fine-tuning. By dynamically updating this weight matrix, the network has good adaptive ability and can better adapt to the feature distribution at different resolutions.
[0173] Next, a set of equations for resolution magnification effect was established, including multiple sub-equations such as local magnification, global enhancement, scale transformation and spatial alignment. These equations introduce a series of parameters to be optimized, such as local weight coefficients, operator coefficients, basis function weights, etc. By iteratively optimizing these parameters, efficient mapping of features with different resolutions can be achieved. Specifically, the local magnification equation can refine local features, the global enhancement equation can enhance global information, the scale transformation equation can adapt to different feature scales, and the alignment equation can correct the spatial position deviation of the feature.
[0174] In the iterative optimization process, we start with low-resolution data and use a small number of labeled samples to train the basic model. Then, we gradually increase the sampling rate to obtain higher-resolution echo data and establish a new training set. These data are input into the low-rank adaptive training framework, and the resolution magnification equation group is used for feature mapping and parameter optimization. By repeating this process, we can obtain a high-precision classification model that can adapt to high-resolution data.
[0175] This progressive feature learning and model iteration optimization strategy can effectively solve the problems in the existing technology. First, it greatly reduces the demand for labeled data. Through low-rank compression and adaptive mechanisms, a small number of samples can be fully utilized for model training. Secondly, the resolution amplification equation group can achieve efficient mapping of features, so that the model has good adaptability and can adapt to data features at different resolutions. Finally, the design of the embedded feature pyramid network can extract multi-dimensional refined features from the original echo data, providing strong support for complex target recognition tasks.
[0176] A specific embodiment 1 of the method of the present invention is provided below: Step S10: downsample the lidar remote sensing data to multiple known targets according to a preset minimum sampling rate to obtain lowest level echo data, and annotate the lowest level echo data with labels based on multiple known targets to obtain a lowest level training data set.
[0177] The specific implementation is as follows:
[0178] First, set the default minimum sampling rate ,For example For the original lidar remote sensing data (in is the number of sampling points, is the sampling dimension), the downsampling algorithm can be used to perform downsampling processing to obtain the lowest level echo data . Here, the nearest neighbor interpolation method or linear interpolation method can be used for downsampling.
[0179] Next, according to the known target category Label each sample with a corresponding category label (in represents the target category set). This gives us the lowest level training data set , laying the foundation for subsequent deep learning modeling.
[0180] Step S20: Use a deep learning network to train the lowest level training data set to obtain a basic classification model.
[0181] The specific implementation of this step is as follows:
[0182] A deep learning network with an embedded feature pyramid structure is designed, which contains the following submodules:
[0183] 1. Feature extraction module: This module is responsible for the original echo data Perform multi-dimensional feature decomposition, including echo intensity feature matrix , distance feature matrix and the angle characteristic matrix .
[0184] Echo intensity feature matrix (in , is the number of frequency domain components) can be calculated by the original echo signal The instantaneous power spectral density To obtain, among which satisfy:
[0185] ;
[0186] Distance feature matrix (in is the number of sampling points) can be calculated based on the time delay of the echo signal Calculated .
[0187] Angle feature matrix The angle sequence can be scanned by laser radar get .
[0188] 2. Point cloud encoding subnetwork: This network receives , and As input, use the encoding function
[0189] Extract point cloud feature encoding .
[0190] 3. Feature Enhancer Network: This network receives As input, using the enhancement function Generating enhanced feature representation .
[0191] 4. Spatiotemporal feature sub-network: This network receives As input, the spatiotemporal feature extraction function Extracting spatiotemporal correlation features .
[0192] 5. Fusion sub-network: This network receives As input, the final classification result is output.
[0193] When training this deep learning network, use the lowest level training dataset obtained earlier As input, the network parameters are optimized through the back propagation algorithm, and finally the basic classification model is obtained. Although the accuracy of this basic model is low, it lays the foundation for subsequent iterative optimization.
[0194] Step S30: construct a low-rank adaptive neural network training framework, and use the basic classification model as the initial model of the training framework.
[0195] The specific implementation is as follows:
[0196] The idea of low-rank matrix decomposition is used to construct this training framework. First, the network parameters Represented as a low-rank matrix Add a residual matrix ,Right now ,in is the left and right singular matrix, is a rank constraint ( ), is the residual matrix. This can effectively compress the network parameters and retain the core features.
[0197] Next, we introduce an adaptive weight matrix , its elements By the correlation coefficient and time-varying regulatory factors composition:
[0198] ;
[0199] This matrix is used to implement feature mapping and network fine-tuning. The dynamic update of can make the network have good adaptability, so as to better adapt to the features at different resolutions.
[0200] Finally, the basic classification model obtained in the previous step S20 is used as the initial model of this low-rank adaptive neural network training framework, laying the foundation for subsequent iterative optimization.
[0201] Step S40: Establishing a resolution amplification effect equation group based on the training framework, wherein the resolution amplification effect equation group includes a sampling rate amplification factor and a feature mapping parameter.
[0202] The specific implementation is as follows:
[0203] A set of equations for the resolution amplification effect is established, which includes four sub-equations:
[0204] Local magnification effect equation:
[0205] ;
[0206] in, is the local characteristic component, is the local weight coefficient, are the Laplace operator coefficients, is the mixed partial derivative coefficient, is the error term.
[0207] Global amplification effect equation:
[0208] ;
[0209] in, is the Gaussian kernel function, is the error term.
[0210] Scale magnification effect equation:
[0211] ;
[0212] in, is the scale factor, is the basis function weight, is the basis function, is the error term.
[0213] Alignment magnification effect equation:
[0214] ;
[0215] in, is the spatial transformation function, is the spatial offset, is the error term.
[0216] These equations contain a series of parameters to be optimized, such as the local weight coefficient , Laplace operator coefficients , mixed partial derivative coefficients , basis function weight Etc., constitute the feature mapping parameters to be optimized. At the same time, the sampling rate amplification factor It is also an important parameter of this set of equations. By optimizing these parameters, efficient mapping of features at different resolutions can be achieved.
[0217] Step S50: Sampling the lidar remote sensing data at a sampling rate higher than the previous level to obtain higher level echo data.
[0218] The specific implementation is as follows:
[0219] First determine the current sampling rate level , for example, the initial level is the lowest Then, increase the sampling rate to a higher level ,For example . For the original lidar remote sensing data To perform this higher sampling rate Sampling processing to obtain higher level echo data This step can continue to use downsampling algorithms, such as nearest neighbor interpolation or linear interpolation. By gradually increasing the sampling rate, a series of echo data with different resolution levels can be obtained, laying the foundation for subsequent iterative optimization.
[0220] Step S60: Establish a higher-level training data set, and input the higher-level training data set into the training framework, use the resolution magnification effect equation group to perform feature mapping, and use an iterative optimization method to solve the equation group parameters.
[0221] The specific implementation is as follows:
[0222] First, based on the higher-level echo data obtained in the previous step , establish the corresponding training data set This includes labeling the echo data and giving each sample a corresponding target category label. .
[0223] Then, this higher level training dataset Input into the low-rank adaptive neural network training framework constructed in step S30. Use the resolution magnification effect equations established in step S40 to map the features. This involves a series of parameters to be optimized, such as the local weight coefficient , Laplace operator coefficients , mixed partial derivative coefficients , basis function weight wait.
[0224] Next, we use iterative optimization to solve these parameters. Specifically, we can use the gradient descent algorithm to calculate the loss function The gradient of each parameter , and continuously optimize the parameter values to minimize the error between the model's prediction results and the true labels. In this way, higher-precision feature mapping parameters can be obtained.
[0225] Step S70: Perform low-rank adaptive fine-tuning on the training framework based on the parameters to obtain a higher-level classification model.
[0226] This step is implemented as follows:
[0227] First, the feature mapping parameters optimized in step S60, such as the local weight coefficient , Laplace operator coefficients , mixed partial derivative coefficients , basis function weight etc., fine-tune the low-rank adaptive neural network training framework constructed in step S30. Specifically, these parameters can be imported into the corresponding modules of the training framework, such as the local amplification effect equation wait.
[0228] Then, by continuing to train this fine-tuned network model, it can adapt to the feature distribution at a higher resolution. Here, the gradient descent algorithm can still be used to optimize the network parameters until the model converges.
[0229] Through this step of low-rank adaptive fine-tuning, a higher-level classification model is obtained. This model can better handle features at different resolutions, thereby improving the final classification accuracy.
[0230] Step S80: verify the higher-level classification model according to the known multiple targets and calculate the classification accuracy.
[0231] The specific implementation is as follows:
[0232] First, prepare some test samples, which are extracted from multiple known target categories and have no overlap with the training data.
[0233] Then, these test samples are input into the higher-level classification model obtained in step S70, so that the model can predict and classify the samples.
[0234] Next, the matching degree between the prediction results of the statistical model and the true label is calculated to calculate the classification accuracy. ; Through this verification process, the performance of the current model on higher resolution data can be evaluated, providing a basis for subsequent iterative optimization.
[0235] Step S90: When the classification accuracy rate does not reach the preset threshold, repeat steps S50 to S80 until the classification accuracy rate reaches the preset threshold, and output the final classification model.
[0236] The specific implementation is as follows:
[0237] In step S80, the classification accuracy of the higher-level classification model is calculated. If the accuracy does not reach the preset threshold (For example ), then it is necessary to continue iterative optimization.
[0238] First, repeat step S50 to further increase the sampling rate. , obtain higher resolution echo data Then, a new training set is created based on this data. , and execute step S60, using the resolution magnification effect equation group to perform feature mapping and parameter optimization.
[0239] Next, execute step S70 to perform low-rank adaptive fine-tuning on the training framework to obtain a better classification model. Then execute step S80 to calculate the classification accuracy of the new model. .
[0240] if If the target is still not met, repeat the above steps until the classification accuracy reaches the preset target. The final classification model is output as the result of the classification of the laser radar remote sensing data echo. The final model obtained is used to classify the laser radar remote sensing data echo to be classified. The steps of classifying the laser radar remote sensing data echo to be classified are as follows: the laser radar remote sensing data to be classified is first preprocessed, including data cleaning, removal of outliers and noise, and data formatting and normalization according to the input requirements of the final classification model; then the preprocessed data is input into the final classification model, and the classification probability distribution of the model output is obtained through feature extraction and forward propagation calculation of each level of the model; then the model output result is post-processed, and the most likely target category is determined according to the probability distribution and a classification label is generated; finally, the classification result is visualized, and a two-dimensional or three-dimensional visualization image of the classification result is generated, and the spatial distribution of targets of different categories is marked.
[0241] It should be noted that the variables mentioned in the specific implementation of the present invention are shown in Table 1 below:
[0242] Table 1 Variable explanation table
[0243]
[0244] In order to further better understand and implement the present invention, the following is an example 2 of a specific application scenario of the present invention: a certain unit collected a large amount of laser radar echo data when conducting regional environmental monitoring. In order to effectively classify these data, the researchers decided to adopt the laser radar remote sensing data echo classification processing method based on low-rank adaptive neural network proposed in the present invention. The specific implementation process is as follows:
[0245] Step 1: Data Preprocessing
[0246] The researchers first downsampled the original lidar echo data to obtain the lowest level echo data set. Since they knew the main environmental target categories in the area, including trees, buildings, and ground, they manually annotated these lowest level echo data to form the initial training data set.
[0247] Specifically, the lidar echo data in this area has a total of 1 million sampling points. After downsampling, a minimum level echo data set of 100,000 sampling points was obtained. Based on these data, the researchers manually observed and identified three main environmental target categories: trees, buildings, and ground. Table 2 shows the situation of these minimum level training data.
[0248] Table 2 The lowest level training data set
[0249] category Sample size Sample proportion Trees 3000 30% building 4000 40% ground 3000 30% total 10000 100%
[0250] like Figure 2 As shown, the sample distribution of the lowest level training data set is shown, including the number and proportion of samples in each category.
[0251] Step 2: Feature extraction network construction
[0252] After completing the construction of the initial training data set, the researchers began to build a feature extraction network. A deep learning network with an embedded feature pyramid structure was designed, which includes the following key modules:
[0253] 1. Feature extraction module: This module is responsible for extracting multidimensional features from the original echo data, including the echo intensity feature matrix, distance feature matrix and angle feature matrix.
[0254] The echo intensity feature matrix can be calculated by the original echo signal The instantaneous power spectral density To obtain, among which satisfy:
[0255] ;
[0256] The distance characteristic matrix can be calculated based on the time delay of the echo signal. Calculated .
[0257] The angle feature matrix can be obtained by scanning the angle sequence of the laser radar get .
[0258] like Figure 3 As shown, the time domain distribution of the lidar echo intensity feature matrix is displayed, showing the attenuation characteristics of the echo signal over time.
[0259] 2. Point cloud encoding subnetwork: This network receives the echo intensity feature matrix , distance feature matrix and the angle characteristic matrix As input, use the encoding function Extract point cloud feature encoding .
[0260] 3. Feature Enhancer Network: This network receives As input, using the enhancement function Generating enhanced feature representation .
[0261] 4. Spatiotemporal feature sub-network: This network receives As input, the spatiotemporal feature extraction function Extracting spatiotemporal correlation features .
[0262] 5. Fusion sub-network: This network receives As input, the final classification result is output.
[0263] The design of this deep learning network fully considers the characteristics of lidar echo data and can extract multi-dimensional refined features from the raw data, providing strong support for subsequent classification and recognition tasks.
[0264] Step 3: Low-rank adaptive training framework construction
[0265] After constructing the feature extraction network, the researchers began to build a low-rank adaptive neural network training framework. First, the network parameters Represented as a low-rank matrix Add a residual matrix ,Right now This can effectively compress network parameters and retain core features.
[0266] At the same time, the researchers introduced an adaptive weight matrix , its elements By the correlation coefficient and time-varying regulatory factors composition:
[0267] ;
[0268] This matrix is used to implement feature mapping and network fine-tuning, and is dynamically updated , which can make the network have good adaptive ability.
[0269] Finally, the researchers used the previously trained initial feature extraction network as the basic model of this low-rank adaptive training framework, laying the foundation for subsequent iterative optimization.
[0270] Step 4: Constructing the equation group for resolution amplification effect
[0271] Based on the low-rank adaptive training framework, the researchers further constructed a set of equations for the resolution amplification effect, including the following four sub-equations:
[0272] Local magnification effect equation:
[0273] ;
[0274] Global amplification effect equation:
[0275] ;
[0276] Scale magnification effect equation:
[0277] ;
[0278] Alignment magnification effect equation:
[0279] ;
[0280] These equations contain a series of parameters to be optimized, such as the local weight coefficient , Laplace operator coefficients , mixed partial derivative coefficients , basis function weight Etc. By iteratively optimizing these parameters, efficient mapping of features with different resolutions can be achieved.
[0281] Step 5: Model training and iterative optimization
[0282] With the above feature extraction network and resolution amplification effect equations, researchers began model training and iterative optimization. The specific steps are as follows:
[0283] 1. First, use the lowest level training data set obtained in step 1 ,The initial feature extraction network model was trained through the back propagation algorithm.
[0284] 2. Then, this initial model is used as the basis of the low-rank adaptive training framework to start iterative optimization. In each round of iteration, the researchers will:
[0285] a. Increase the sampling rate, obtain higher resolution echo data, and build a new training set ;
[0286] b. Use the resolution magnification effect equation group to map the features and optimize the parameters in each equation, such as wait;
[0287] c. Import the optimized parameters into the low-rank adaptive training framework and continue training the network model.
[0288] 3. By repeating the above steps until the classification accuracy of the model on the validation set reaches more than 95%, the researchers obtained the final high-precision classification model.
[0289] Throughout the optimization process, the researchers used the gradient descent algorithm to update the parameters. The specific formula is as follows:
[0290] ;
[0291] ;
[0292] ;
[0293] in, is the loss function, is the true label. At the same time, the correlation coefficient Through experimental methods, time-varying regulatory factors Then an adaptive update strategy is adopted:
[0294] ;
[0295] This way, we can make full use of a small amount of labeled data and adapt to feature changes at different resolutions, ultimately obtaining a high-precision classification model.
[0296] Step 6: Model validation and application
[0297] After completing model training and iterative optimization, the researchers verified the final classification model. First, they prepared a batch of test samples that had never been trained, covering three target categories: trees, buildings, and ground, with a total of 5,000 samples. These test samples were input into the trained model, and the matching degree between the predicted results and the true labels was statistically calculated. The classification accuracy was calculated to be 96.8%, far exceeding the preset 95% threshold.
[0298] With this high-precision classification model, researchers can apply it to actual lidar remote sensing data analysis. In a regional environmental monitoring, lidar echo data from 1 million sampling points were collected. After preprocessing and feature extraction, these data were input into the trained classification model, and the distribution of environmental targets in the entire region was quickly obtained, providing reliable basic data support for subsequent environmental analysis and early warning.
[0299] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.
Claims
1. A laser radar remote sensing data echo classification processing method, characterized in that: The following steps are involved: S10, downsampling the laser radar remote sensing data for multiple known targets according to a preset minimum sampling rate to obtain lowest level echo data, and labeling the lowest level echo data according to the multiple known targets to obtain a lowest level training data set; S20, using a deep learning network to train the lowest level training data set to obtain a basic classification model; S30, constructing a low-rank adaptive neural network training framework, and using the basic classification model as an initial model of the training framework; S40, establishing a resolution magnification effect equation group based on the training framework, wherein the resolution magnification effect equation group includes a sampling rate magnification factor and a feature mapping parameter; S50, sampling the laser radar remote sensing data at a sampling rate higher than the previous level to obtain higher level echo data; S60, establishing a higher-level training data set, and inputting the higher-level training data set into the training framework, performing feature mapping using the resolution magnification effect equation group, and solving the equation group parameters using an iterative optimization method; S70, performing low-rank adaptive fine-tuning on the training framework based on the parameters to obtain a higher-level classification model; S80, verifying the higher-level classification model according to the known multiple targets, and calculating the classification accuracy; S90, when the classification accuracy rate does not reach the preset threshold, repeating steps S50 to S80 until the classification accuracy rate reaches the preset threshold, and outputting a final classification model for classifying the laser radar remote sensing data echoes to be classified; The resolution magnification effect equation group is used to realize feature pyramid cascade magnification, including a local magnification effect equation, a global magnification effect equation, a scale magnification effect equation, and an alignment magnification effect equation; The local amplification effect equation is used for local feature refinement, the input is the low-resolution local feature, and the output is the refined high-resolution local feature; The global amplification effect equation is used for global feature enhancement, the input is the low-resolution global feature, and the output is the enhanced high-resolution global feature; The scale magnification effect equation is used for characteristic scale transformation, the input is the original characteristic scale, and the output is the magnified characteristic scale; The alignment magnification effect equation is used for feature alignment correction, the input is the unaligned feature, and the output is the feature after spatial alignment.
2. A laser radar remote sensing data echo classification processing method according to claim 1, characterized in that: The deep learning network adopts an embedded feature pyramid structure, including a feature extraction module, a point cloud encoding sub-network, a feature enhancement sub-network, a spatiotemporal feature sub-network and a fusion sub-network; The feature extraction module is responsible for extracting multi-dimensional features from the original echo data, including the echo intensity feature matrix, the distance feature matrix and the angle feature matrix; The point cloud coding subnetwork is used for feature coding, the input is the echo intensity feature matrix, the distance feature matrix and the angle feature matrix, and the output is the point cloud feature coding; The feature enhancement subnetwork is used for feature enhancement, the input is the point cloud feature encoding, and the output is the enhanced feature representation; The spatiotemporal feature subnetwork is used to extract spatiotemporal correlation, the input is the enhanced feature representation, and the output is the spatiotemporal feature vector; The fusion subnetwork is used for feature fusion classification, the input is the spatiotemporal feature vector, and the output is the target classification result.
3. A laser radar remote sensing data echo classification processing method according to claim 2, characterized in that: The low-rank adaptive neural network training framework specifically uses low-rank matrix decomposition to reconstruct network parameters, and realizes feature mapping and network fine-tuning by introducing an adaptive weight matrix.
4. A laser radar remote sensing data echo classification processing method according to claim 3, characterized in that: The preset threshold is 95%.
5. The laser radar remote sensing data echo classification processing method according to claim 4, characterized in that: The minimum sampling rate is specifically expressed as follows: ; In the formula, is the minimum sampling rate, in Hz; is the highest frequency component of the laser radar echo signal, in Hz; is the speed of light, take ; is the minimum resolution distance, in meters.
6. A laser radar remote sensing data echo classification processing method according to claim 5, characterized in that: The sampling rate amplification factor is specifically expressed as follows: ; In the formula, For the Level sampling rate amplification factor; is the base magnification, the default value is 2; For the The increment coefficient of the level, range [0.1,0.5]; is the attenuation coefficient, range [0.01,0.1]; To magnify the error.
7. A laser radar remote sensing data echo classification processing method according to claim 6, characterized in that: The sampling rate higher than the previous level is specifically expressed as follows: ; In the formula, For the Level sampling rate; For the Level sampling rate; is the first-order correction coefficient; is the second-order correction coefficient; is the classification error; is the sampling rate error.
8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the laser radar remote sensing data echo classification processing method described in any one of claims 1-7.
9. A laser radar remote sensing data echo classification processing system, characterized in that: Contains the computer-readable storage medium of claim 8.
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