Small sample projection coordinate direct conversion method based on neural network classification determination and related equipment

Abstract

The invention provides a small sample projection coordinate direct conversion method based on neural network classification judgment and related equipment. The method comprises the following steps: acquiring projection coordinates under a first reference system to be converted; for the projection coordinates to be converted under the first reference system, obtaining the projection coordinates of the projection coordinates under the second reference system through polynomial fitting; inputting the projection coordinates in the first reference system and the projection coordinates, obtained by fitting, in the second reference system into a trained neural network model to judge whether the distance conversion error is within a preset distance error range, and outputting the distribution condition of the conversion errors in the horizontal and vertical directions and corresponding probability values; and if the distance conversion error is not in the preset distance error range, correcting the output probability value based on the Bayesian law and Monte Carlo simulation, and correcting the projection coordinate under the second reference system obtained by fitting based on the corrected probability value. According to the invention, the precision of single projection coordinate conversion in the statistical sense is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of coordinate conversion, and in particular, to a direct conversion method for small-sample projection coordinates based on neural network classification determination and related devices. Background Art

[0002] A Spatial Reference System or a Coordinate Reference System is a coordinate system used to accurately measure positions on the Earth's surface. In the field of geographic information science, spatial reference systems are divided into geographic coordinate systems and projection coordinate systems according to longitude and latitude coordinates and plane rectangular coordinates. For the conversion between two projection coordinate systems with known ellipsoid and projection parameters, an indirect conversion method can be adopted, that is, as Figure 1 shown: ① Inverse calculate the projection coordinates in the A spatial reference system to the geographic coordinate system under the A spatial reference system; ② Then convert to the geographic coordinate system under the B spatial reference system through a three-parameter or seven-parameter conversion method; ③ Then perform forward projection to the projection coordinate system under the B spatial reference system, and vice versa. For two projection coordinate systems with unknown ellipsoid or projection parameters, a direct conversion method is adopted, generally based on a known set of control points, and the direct conversion between the two projection coordinate systems is realized through a four-parameter conversion such as Helmert or through least squares fitting polynomial.

[0003] Neural networks have the advantage of determining the relationship between two coordinate systems without a known mathematical model. Therefore, neural networks are very suitable for the direct conversion of projection coordinates, and there are mainly three ideas: (1) Use the known control point coordinates as the training set to let the neural network learn the conversion relationship between the coordinates; (2) Build a specific neural network model to adapt to some special scenarios; (3) First, implement coordinate conversion through traditional methods, and then train an error model through a neural network to better improve the accuracy.

[0004] The above ideas essentially hope that the neural network model can establish the relationship between two projection coordinate systems through learning to achieve coordinate conversion, which can be regarded as a regression problem. However, since the regression problem is the observation and prediction of continuous values, usually more data is required to capture the complex relationship between the input and output. In practice, the number of control points in any country or region is limited. ① For such small-sample regression problems of neural network models, problems such as unstable models and poor generalization ability often occur; ② At the same time, due to the poor interpretability of neural network models themselves, for a batch of projection coordinate conversions, the statistical error can be reduced (such as the average value after conversion is reduced), but for a single projection coordinate conversion, it is impossible to know whether its conversion error is reduced or increased. Summary of the Invention

[0005] Generally speaking, neural networks have more advantages in solving classification problems than regression problems in small samples. To further improve the accuracy of direct projection coordinate conversion, considering the limited number of control points, the present invention converts the neural network learning of "the relationship between two projection coordinate systems" (regression problem) into two types of judgment problems for the neural network to determine whether "the distance error after projection coordinate conversion is within a certain threshold range" and "the possible distribution areas of the errors in the horizontal and vertical directions", and provides a method and related device for direct projection coordinate conversion of small samples based on neural network classification judgment.

[0006] In a first aspect, the present invention provides a method for direct projection coordinate conversion of small samples based on neural network classification judgment, including:

[0007] Obtain the projection coordinates in the first reference system to be converted;

[0008] For the projection coordinates in the first reference system to be converted, obtain their projection coordinates in the second reference system through polynomial fitting;

[0009] Input the projection coordinates in the first reference system and the projection coordinates in the second reference system obtained by fitting into the trained neural network model to determine whether the distance conversion error is within the preset distance error range and output the distribution of the conversion error in the horizontal direction and the corresponding probability value, as well as the distribution of the conversion error in the vertical direction and the corresponding probability value;

[0010] If the distance conversion error is not within the preset distance error range, then correct the output probability value based on Bayes' law and Monte Carlo simulation, and correct the projection coordinates in the second reference system obtained by fitting based on the corrected probability value.

[0011] Further, the training process of the neural network model includes:

[0012] Obtain a set of control points and divide them into a training set and a test set. For any point in the training set, use the projection coordinates of this point in the first reference system and the projection coordinates of this point in the second reference system obtained by polynomial fitting as the input of the preset neural network, and use whether the distance conversion error is within the preset distance error range and the distribution of the conversion errors in the horizontal and vertical directions as the output of the preset neural network to optimize the parameters of the neural network.

[0013] Further, using whether the distance conversion error is within the preset distance error range and the distribution of the conversion errors in the horizontal and vertical directions as the output of the preset neural network specifically includes:

[0014] Use the first parameter to represent whether the distance conversion error is within the preset distance error range, use the second parameter, the third parameter, and the fourth parameter to comprehensively represent whether the conversion error in the horizontal direction is within the preset horizontal error range, and use the fifth parameter, the sixth parameter, and the seventh parameter to comprehensively represent whether the conversion error in the vertical direction is within the preset vertical error range.

[0015] Furthermore, regard whether the distance conversion error is within the preset distance error range and the distribution of the conversion errors in the horizontal and vertical directions as the output of a preset neural network, specifically including:

[0016] Use the first parameter to represent whether the distance conversion error is within the preset distance error range, use the second parameter to represent whether the conversion error in the horizontal direction is negative or positive, use the third parameter to represent whether the conversion error in the vertical direction is negative or positive, and use the fourth parameter, the fifth parameter, and the sixth parameter to comprehensively represent the distribution of the slope or the difference between the absolute values of the conversion errors in the horizontal and vertical directions.

[0017] Furthermore, if the distance conversion error is not within the preset distance error range, then correct the output probability value based on Bayes' law and Monte Carlo simulation, and correct the projected coordinates in the second reference system obtained by fitting based on the corrected probability value, specifically including:

[0018] If the distance conversion error is not within the preset distance error range, but the conversion errors in the horizontal and vertical directions are both within their respective preset error ranges, then do not correct the projected coordinates in the second reference system;

[0019] If the distance conversion error is not within the preset distance error range, and one of the conversion errors in the horizontal and vertical directions is within the corresponding preset error range and the other is not within the corresponding preset error range, then only correct the probability value corresponding to the conversion error that is not within the corresponding preset error range;

[0020] If the distance conversion error is not within the preset distance error range, and the conversion errors in the horizontal and vertical directions are both not within their respective preset error ranges, then correct the probability values corresponding to the conversion errors in both directions;

[0021] Correspondingly, correcting the projected coordinates in the second reference system obtained by fitting based on the corrected probability value includes: judging whether the corrected probability value is greater than a preset first probability threshold. If so, adjust the corresponding conversion error by N times of L. If not but greater than the second probability threshold, then adjust the corresponding conversion error by N times of ; where L represents the preset distance error threshold; the first probability threshold is greater than the second probability threshold, and N is a positive number less than or equal to 1.

[0022] Furthermore, the neural network adopts a backpropagation neural network.

[0023] In a second aspect, the present invention provides a small-sample projection coordinate direct conversion device based on neural network classification determination, including:

[0024] An acquisition module, configured to acquire the projection coordinates in a first reference system to be converted;

[0025] A coordinate conversion module, configured to, for the projection coordinates in the first reference system to be converted, obtain the projection coordinates in a second reference system thereof through polynomial fitting;

[0026] An error judgment module, configured to input the projection coordinates in the first reference system and the projection coordinates in the second reference system obtained by fitting into a trained neural network model, so as to judge whether the distance conversion error is within a preset distance error range, and output the distribution of the conversion error in the horizontal direction and the corresponding probability value, as well as the distribution of the conversion error in the vertical direction and the corresponding probability value;

[0027] A coordinate correction module, configured to, when the distance conversion error is not within the preset distance error range, correct the output probability value based on Bayes' law and Monte Carlo simulation, and correct the projection coordinates in the second reference system obtained by fitting based on the corrected probability value.

[0028] In a third aspect, the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, the method described in the first aspect is implemented.

[0029] In a fourth aspect, the present invention provides a non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the method described in the first aspect is implemented.

[0030] The beneficial effects of the present invention are as follows:

[0031] (1) Under the condition of limited number of control points, the present invention makes full use of the advantage of the neural network in determination under small-sample conditions, and converts the coordinate conversion problem (essentially a regression problem) into a classification problem. At the same time, aiming at the situation that the determination conclusions may be contradictory or supportive to each other, an error correction strategy of a "two-stage determination probability correction model" is designed, which significantly reduces the error rate, ensures that the error is optimized both from a single data and a statistical sense, and the training of the model is very simple and fast, without consuming a large amount of time and computing resources. After the parameters of the method of the present invention are modified according to experience, it can not only be applied to the direct conversion of projection coordinates, but also to other problems of plane coordinate conversion.

[0032] (2) By conducting comparative experiments on traditional polynomial fitting, traditional neural network methods, and the method of the present invention, the results show that the method of the present invention not only improves the accuracy in the statistical sense of projection coordinate conversion, but also significantly reduces the error rate in coordinate conversion and improves the accuracy of single projection coordinate conversion due to enhancing the interpretability in neural network coordinate conversion. Description of the Drawings

[0033] Figure 1 Conversion between projection coordinates in different reference systems;

[0034] Figure 2 One of the schematic flowcharts of the small-sample projection coordinate direct conversion method based on neural network classification determination provided by the embodiment of the present invention;

[0035] Figure 3 Another schematic flowchart of the small-sample projection coordinate direct conversion method based on neural network classification determination provided by the embodiment of the present invention;

[0036] Figure 4 A schematic diagram of the training process of a neural network model provided by the embodiment of the present invention;

[0037] Figure 5 The error correction strategy of the two-stage determination probability correction model provided by the embodiment of the present invention;

[0038] Figure 6 The comparison result after error correction between the method of the present invention and the existing coordinate conversion method provided by the embodiment of the present invention;

[0039] Figure 7 The comparison result of the error rate after error correction between the method of the present invention and the existing coordinate conversion method provided by the embodiment of the present invention;

[0040] Figure 8 The structural schematic diagram of the small-sample projection coordinate direct conversion device based on neural network classification determination provided by the embodiment of the present invention;

[0041] Figure 9 The structural block diagram of an electronic device provided by the embodiment of the present invention. Detailed Embodiments

[0042] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0043] The current neural network model is applied to the direct conversion of projection coordinates, mainly by training with control point data to establish the connection between two coordinate systems. However, in practice, the number of control points in a country or region is limited. ① For such small-sample regression problems of neural network models, problems such as unstable models and poor generalization ability often occur; ② At the same time, due to the poor interpretability of neural network models themselves, for a batch of projection coordinate conversions, the error can be reduced statistically (such as the reduction of the average value after conversion), but for a single projection coordinate conversion, it is impossible to know whether its conversion error is reduced or increased.

[0044] To solve the above problems, on the premise of admitting the establishment of the Second Law of Geography (Spatial Heterogeneity), the present invention believes that there is a certain connection between the error caused by any direct projection coordinate conversion method and the spatial distribution. On this basis, the present invention abandons the neural network's direct learning of the connection between two projection coordinate systems, but instead learns the connection between "whether the error is within a certain threshold range" and "spatial distribution", thus converting the regression problem of "establishing the connection between two projection coordinate systems" into two types of determination problems, and in view of the possible contradictory or supportive situations in the determination conclusions, an error correction strategy of "two-stage determination probability correction model" is designed to correct the error.

[0045] To better understand the technical solution of the present invention, the technical problems to be solved by the present invention are defined as follows:

[0046] Suppose there is a known set C of n control points, that is, the projection coordinates of n control points in two reference systems are known, which are respectively represented as follows:

[0047] (1) The projection coordinates of n control points in the A reference system are (x A1 , y A1 ), (x A2 , y A2 ), …… (x An , y An );

[0048] (2) The projection coordinates of n control points in the B reference system are (x B1 , y B1 ), (x B2 , y B2 ), …… (x Bn , y Bn );

[0049] For any unknown point k, the projection coordinate in the A reference system is known as Solve for the projection coordinate of k in the B reference system to make it as close as possible to the true value.

[0050] To solve the above problems, as Figure 2 shown, an exemplary embodiment of the present invention provides a small sample projection coordinate direct conversion method based on neural network classification determination, including the following steps:

[0051] S101: Obtain the projection coordinates in the first reference system to be converted;

[0052] S102: For the projection coordinates in the first reference system to be converted, obtain their projection coordinates in the second reference system through polynomial fitting;

[0053] Specifically, due to the different selected reference ellipsoids and projection methods, different coordinate systems will be formed. The first reference system and the second reference system in the present invention represent coordinate systems under different reference ellipsoids, such as the 1954 Beijing Coordinate System, the 1980 Xi'an Coordinate System, the 2000 National Coordinate System, and the WGS-84 Coordinate System. If the geographic coordinates in the first reference system are known, the geographic coordinates can be converted into the projection coordinates in the first reference system by using GIS software or an online coordinate system conversion tool. It should be noted that the projection coordinates in the two reference systems in the exemplary embodiments of the present invention adopt the same projection method.

[0054] In practical applications, the direct conversion method of projection coordinates between two reference systems through polynomial fitting includes, but is not limited to, 2D Helmert transformation (four parameters), affine transformation six-parameter method, and quadratic polynomial, etc.

[0055] (1) 2D Helmert transformation. It mainly includes: Coordinate system A is transformed into coordinate system B through translation, scaling, and rotation. The 2D Helmert transformation formula is as follows, where T x , T y belongs to the translation variable, s is the scaling variable, and θ is the rotation angle.

[0056]

[0057] (2) Affine transformation six-parameter method. Coordinate system A and coordinate system B are not orthogonal, and the scale factors in the X and Y directions may also be different. The affine transformation six-parameter method conversion formula is as follows, where T x , T y belongs to the translation variable, S x , S y are the scale variables in the X and Y directions respectively, θ is the rotation angle, and β is the non-orthogonal intersection angle between the two coordinate systems.

[0058]

[0059] (3) Quadratic polynomial transformation. Affine transformation can be regarded as a linear polynomial transformation. The general formula for polynomial transformation is as follows.

[0060]

[0061] In practical applications, the power degree of the polynomial should not be too high. Generally, it is considered that the power degree of the polynomial is preferably no higher than 3.

[0062] The parameters of the above three transformation methods are all obtained by the least squares method for the known control points to solve the parameters.

[0063] S103: Input the projection coordinates in the first reference system and the fitted projection coordinates in the second reference system into the trained neural network model to determine whether the distance conversion error is within the preset distance error range, and output the distribution of the conversion error in the horizontal direction and the corresponding probability value, as well as the distribution of the conversion error in the vertical direction and the corresponding probability value;

[0064] Specifically, the neural network can be a traditional machine learning network, such as a BP neural network, or a neural network based on deep learning, such as a convolutional neural network, a recurrent neural network, etc. It should be noted that compared with other network types, in practical applications, the BP neural network is preferred for the neural network model of the present invention.

[0065] S104: If the distance conversion error is not within the preset distance error range, then correct the output probability value based on Bayes' law and Monte Carlo simulation, and correct the fitted projection coordinates in the second reference system based on the corrected probability value.

[0066] For example, as Figure 3 shown, for the projection coordinates to be solved for conversion in the A reference system First, obtain the projection coordinates in the B reference system by the method of polynomial fitting Then, through the already trained neural network model, it is possible to determine that the conclusions may be contradictory or mutually supportive; use the error correction strategy of the pre-designed "two-stage determination probability correction model" to correct the projection coordinates in the B reference system obtained by the method of polynomial fitting Further correction.

[0067] The small-sample projection coordinate direct conversion method based on neural network classification and determination provided by the embodiments of the present invention converts the neural network learning of "the relationship between two projection coordinate systems" (a regression problem) into two determination problems of the neural network determining "whether the distance error after projection coordinate conversion is within a certain threshold range" and "the possible distribution areas of the errors in the horizontal and vertical directions" under the condition of limited number of control points. In view of the possible contradictory or supporting situations in the determination conclusions, an error correction strategy of "two-stage determination probability correction model" is designed, which not only improves the accuracy of projection coordinate conversion in the statistical sense, but also greatly reduces the error rate in coordinate conversion and improves the accuracy of single projection coordinate conversion due to enhancing the interpretability in neural network coordinate conversion.

[0068] In one embodiment, as Figure 4 shown, for the above neural network model, the embodiments of the present invention also provide a training method for the neural network model, which specifically includes the following steps:

[0069] Obtain a control point set and divide it into a training set and a test set. For any point in the training set, use the projection coordinate of the point in the first reference system and the projection coordinate obtained by polynomial fitting in the second reference system as the input of the preset neural network, and use whether the distance conversion error is within the preset distance error range and the distribution of the conversion errors in the horizontal and vertical directions as the output of the preset neural network to optimize the parameters of the neural network. Figure 4 Among them, (x ′ B1 ,y ′ B1 ),(x ′ B2 ,y ′ B2 ),……(x ′ Bn ,y ′ Bn ) represents the projection coordinate calculated by the method of polynomial fitting of the projection coordinate in the A reference system and converted to the B reference system.

[0070] Specifically, for the training of the neural network, the input is defined as the projection coordinate of any point i in the control point set in the A reference system and the projection coordinate in the B reference system calculated by polynomial fitting, that is, {x Ai ,y Ai ,x ′ Bi ,y ′ Bi}, i ∈ C. Its purpose is to enable the neural network to know the spatial distribution of the control points in the A and B reference frames. It should be noted that in order to adapt to the requirements of the neural network (such as the BP neural network) for input, it is necessary to normalize the input coordinates.

[0071] In the embodiments of the present invention, the output of the neural network essentially needs to solve two types of determinations. The first type of determination is whether the distance error is greater than a certain tolerance (the tolerance is assumed to be L); the second type of determination is which direction mainly causes the distance error (horizontal, vertical, or both directions).

[0072] For the first type of determination, it is relatively simple. It only needs to determine whether Δdist is greater than L, and the output parameter is R1:

[0073]

[0074] For the second type of determination, there are at least two ideas: (1) First, determine the positive and negative of the horizontal and vertical directions, and then determine the main error direction through the slope or the difference between the absolute values of the two directions. The following formula:

[0075]

[0076] Among them, Δx and Δy are the conversion errors in the horizontal and vertical directions, C is a constant, and R2 to R6 are the parameters output by the neural network.

[0077] (2) is to directly determine the distribution range of the error according to the horizontal and vertical directions.

[0078]

[0079] Among them, Δx and Δy are the conversion errors in the horizontal and vertical directions, L x , L y is a constant, R2 to R7 are the output parameters of the neural network.

[0080] It should be noted that when the error in the horizontal or vertical direction is small, if the neural network model adopts the first idea, it is easy to make mistakes in the determination of the positive and negative directions of the error, which will significantly increase the risk of increasing the error in the next error revision. If the positive and negative determination of the horizontal or vertical direction becomes a three-point determination close to 0, far greater than 0, and far less than 0, the number of output parameters will increase from 6 to 10, increasing the complexity of the learning objective. This problem is especially prominent for small samples. Therefore, in the setting of the output parameters, it is recommended to choose the second idea as more appropriate. In addition, the output target value must be normalized.

[0081] The small-sample projection coordinate direct conversion method based on neural network classification determination provided by the embodiments of the present invention has a very simple and fast training of the neural network model, without consuming a large amount of time and computing resources.

[0082] In one embodiment, as Figure 5 shown, this embodiment also provides a "two-stage determination probability correction model". Different from the neural network model for independent classification problems, the two types of problems determined by the neural network model provided by the present invention: (1) distance error distribution determination and (2) horizontal and vertical direction error distribution determination, are inherently closely related. There will be situations where the conclusions of the two types of determinations are contradictory or supportive (partially supportive) of each other. How to calibrate the output probability value based on the logical relationship between the two types of determinations on the basis of the probability value of the existing determination conclusion output by the neural network is the key problem to be solved by the "two-stage determination probability correction model" established by the embodiments of the present invention, so as to provide a basic basis for formulating corresponding error correction strategies.

[0083] The correction model in this embodiment follows the following basic assumptions: (1) The errors in the horizontal and vertical directions follow a certain specific probability distribution, and this distribution can be determined by statistical methods such as descriptive statistics and hypothesis testing; (2) The output value of the model for classification is regarded as the probability value belonging to a certain class.

[0084] To better understand the solution of the present invention, the problem of the correction model in this embodiment is described as follows: Given the following two conditions: (1) The distance error determination is named as class A event. When Δdist > L, it is considered that event A occurs, and the output probability value is P(A) = R1. When Δdist ≤ L, it means that event A does not occur, and the probability value is (2) The horizontal and vertical direction error determination is named as class B event, which can be further divided into B h event (horizontal) and B v event (vertical). Corresponding to different horizontal and vertical direction distribution ranges, the output probability values are as follows:

[0085]

[0086] Problem solving: When the probability value R1 of the occurrence of class A event, and and the probability values R2, R4, R5, and R7 corresponding to the occurrence of the event are how much, the error needs to be corrected; how to correct it.

[0087] The basic process of the two-stage determination probability correction model provided by the embodiments of the present invention is as Figure 5 shown:

[0088] (1) The input of the correction model is the determination result of the neural network model: {R1, R2, R3, R4, R5, R6, R7} and the known error sample distributions in the horizontal and vertical directions; when the error sample distributions in the horizontal and vertical directions are unknown, they can be determined by statistical methods such as descriptive statistics and hypothesis testing;

[0089] (2) In the first stage, a preliminary screening is carried out. If the distance error is within the threshold range, that is, under the conditions of {Δdist > L | P(A) > 0.5}, the second-stage determination can be carried out; otherwise, the projected coordinates calculated by the original polynomial fitting are retained, the error is not corrected, and the process ends;

[0090] (3) Enter the second-stage determination. For the error distributions in the horizontal and vertical directions (a three-classification problem), the category with the maximum probability value is taken as the prediction result. When the second-stage determination and the first-stage determination are contradictory (the first case in Table 1), the error is not corrected, and the process ends;

[0091] Table 1 The relationship between the two types of determinations in the second stage and their processing strategies

[0092]

[0093] (4) When there is one-way support or two-way support for the two types of determinations (the second to sixth cases in Table 1), the probability value of the second type of determination is corrected according to Bayes' law and the Monte Carlo model.

[0094] (4.1) Taking the second case in Table 1 as an example, the derivation of the probability value correction in the case of one-way support is illustrated.

[0095] It is known that the observed Probability value of the event occurrence And it is known that event A occurs, which is one-way support for this event. Solve

[0096] According to Bayes' formula:

[0097]

[0098] Among them,

[0099] It is known that, that is The probability value R1 of observing event A occurring under the condition that occurs; however is unknown. One method is to assume that the probability of observing event A occurring is unbiased, that is, 50%. But a better method is that the error distributions in the horizontal and vertical directions are known, and the probability value can be solved through Monte Carlo simulation.

[0100] (4.2) Taking the 6th case in Table 1 as an example, the derivation of the probability value correction in the case of bidirectional support is illustrated.

[0101] It is known that event B is observed (i.e., the errors in both the horizontal and vertical directions exceed the threshold), and the probability value is P(B). It is also known that event A occurs, which is a one-way support for this event. Solve for P(B|A) under the condition that event A occurs.

[0102] P(B) is the joint probability that the errors in the horizontal and vertical directions exceed the threshold, that is

[0103]

[0104] Similarly, according to Bayes' formula:

[0105]

[0106] Among them,

[0107] P(A|B) is known, that is, the probability value R1 of observing event A under the condition that B occurs; is also unknown, and the probability value can be solved through Monte Carlo simulation.

[0108] In one embodiment, based on the magnitude of the probability value solved according to the "two-stage decision probability correction model" in the above embodiment, this embodiment provides two correction strategies, namely radical and conservative, which specifically include: making an N-fold adjustment of L or for the errors in the horizontal, vertical, or both directions based on the corrected probability value. The adjustment method is specifically shown in Table 2. Among them, Θ is the first probability threshold, which is set to 70% here; the second probability threshold is set to 50%. N is set to 1.

[0109] Table 2 Radical or conservative correction strategies based on the probability value solved according to the "two-stage decision probability correction model"

[0110]

[0111] To verify the effectiveness of the solution of the present invention, the present invention also provides the following experimental data.

[0112] (1) Experimental process

[0113] (1) Projection coordinate conversion of known control points based on polynomials

[0114] 438 control points in a certain area were selected in this experiment. In the selection of polynomial fitting, the method with the smallest solution error of the control points in this area - the six-parameter affine transformation method was chosen. At the same time, the horizontal and vertical errors of the control points passed the Kolmogorov-Smirnov statistical test, and the horizontal error follows a normal distribution of N(0.13, 0.55 2 ), and the vertical error follows a normal distribution of N(-0.05, 0.5 2 ).

[0115] (2) Training of the neural network model for judging the projection coordinate conversion error of small samples

[0116] Given the projection coordinates in reference systems A and B, 6 groups of training sets (control point sets) and test sets (solution point combinations) were randomly generated in a ratio of 19:1. The neural network selected the error backpropagation neural network (Back Propagation Neural Network, abbreviated as BP neural network). For the 6 groups of training sets, repeated training was carried out. After practical optimization, finally, the input layer of the BP neural network has 4 input nodes, 20 nodes in the middle hidden layer, and 7 nodes in the output layer, and 200 times of repeated training were carried out.

[0117] (3) Error correction strategy of the "two-stage judgment probability correction model"

[0118] Since the error distributions of the two groups of samples are known, samples of horizontal and vertical errors of 1,000,000 were randomly generated, and the unknown conditional variables solved by Monte Carlo simulation are as follows:

[0119]

[0120] According to formula (5) and formula (7), the probability values output by the neural network model are corrected. From the detection results, the "two-stage judgment probability correction model" can effectively correct the probability values output by the neural network model according to the logical relationship between the two types of judgments (Table 3).

[0121] Table 3 Successful example of probability value correction of the "two-stage judgment probability correction model"

[0122]

[0123] (2) Experimental results

[0124] (1) After the error correction of the 6 groups of test sets by the method of the present invention, such as Figure 6As shown, it shows that the result is better than the general polynomial fitting method. Except for the No. 3 test set, the final average error solved by the method of the present invention is the same as that of the traditional neural network model method ("Li Dajun, Zou Shilin, Liu Yingzi, etc. Projection Transformation Method Based on Neural Network [J]. Bulletin of Surveying and Mapping, 2003, (03): 24 - 26 + 30"), and others are all better than the traditional neural network method;

[0125] (2) Compared with the traditional neural network model method, the neural network method of the present invention will significantly reduce the error rate (see Table 4 and Figure 7 ), which can ensure that the error values of the vast majority of corrected coordinates are smaller, and significantly enhance the reliability of direct coordinate conversion. Figure 7 As shown, except for the No. 5 test set, the error rate of the method of the present invention is slightly higher than that of the traditional neural network method, and others are all significantly better than the traditional neural network method.

[0126] Table 4 Comparison of errors after improvement between the traditional neural network method and the neural network method of the present invention (No. 4 test set)

[0127]

[0128] Through comparative experiments of the traditional polynomial fitting, the traditional neural network method and the method of the present invention, the results show that the method of the present invention not only improves the accuracy of projection coordinate conversion in the statistical sense, but also significantly reduces the error rate in coordinate conversion and improves the accuracy of single - projection coordinate conversion due to enhancing the interpretability in neural network coordinate conversion.

[0129] Based on the same inventive concept, the embodiment of the present invention also provides a small - sample projection coordinate direct conversion device based on neural network classification determination, including: an acquisition module, a coordinate conversion module, an error judgment module, and a coordinate correction module.

[0130] The acquisition module is used to acquire the projection coordinates in the first reference system to be converted. The coordinate conversion module is used to obtain the projection coordinates in the second reference system for the projection coordinates in the first reference system to be converted through polynomial fitting. The error judgment module is used to input the projection coordinates in the first reference system and the projection coordinates in the second reference system obtained by fitting into the trained neural network model to judge whether the distance conversion error is within the preset distance error range and output the distribution of the conversion error in the horizontal direction and the corresponding probability value, as well as the distribution of the conversion error in the vertical direction and the corresponding probability value. The coordinate correction module is used to, when the distance conversion error is not within the preset distance error range, correct the output probability value based on Bayes' law and Monte Carlo simulation, and correct the projection coordinates in the second reference system obtained by fitting based on the corrected probability value.

[0131] It should be noted that the device for correcting the direct conversion error of projection coordinates based on a neural network provided in the embodiments of the present invention is for implementing the method. For its specific functions, reference may be made to the above-mentioned method embodiments, which will not be elaborated here.

[0132] Figure 9 An example of the physical structure diagram of an electronic device is shown as Figure 9 shown. The electronic device may include: a processor 901, a communication interface 902, a memory 903, and a communication bus 904. Among them, the processor 901, the communication interface 902, and the memory 903 complete mutual communication through the communication bus 904. The processor 901 can call the logical instructions in the memory 903 to execute a method for directly converting the projection coordinates of a small sample based on neural network classification determination. The method includes: obtaining the projection coordinates in the first reference system to be converted; for the projection coordinates in the first reference system to be converted, obtaining the projection coordinates in the second reference system by polynomial fitting; inputting the projection coordinates in the first reference system and the obtained projection coordinates in the second reference system into a trained neural network model to determine whether the distance conversion error is within a preset distance error range and output the distribution of the conversion error in the horizontal direction and the corresponding probability value, as well as the distribution of the conversion error in the vertical direction and the corresponding probability value; if the distance conversion error is not within the preset distance error range, then correcting the output probability value based on Bayes' law and Monte Carlo simulation, and correcting the obtained projection coordinates in the second reference system based on the corrected probability value.

[0133] In addition, when the above-mentioned logical instructions in the memory 903 are implemented in the form of a software functional unit and sold or used as an independent product, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The foregoing storage medium includes: various media such as a USB flash drive, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk, or an optical disc that can store program codes.

[0134] An embodiment of the present invention also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions that, when executed by a computer, enable the computer to execute the direct conversion method of small sample projection coordinates based on neural network classification determination provided in each of the above method embodiments.

[0135] An embodiment of the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the direct conversion method of small sample projection coordinates based on neural network classification determination provided in each of the above method embodiments.

[0136] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in each of the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of each embodiment of the present invention.

Claims

1. A direct conversion method for small sample projection coordinates based on neural network classification determination, characterized in that Including: Obtain the projection coordinates in the first reference system to be converted; For the projection coordinates in the first reference system to be converted, obtain their projection coordinates in the second reference system through polynomial fitting; Input the projection coordinates in the first reference system and the projection coordinates in the second reference system obtained by fitting into the trained neural network model to determine whether the distance conversion error is within the preset distance error range and output the distribution of the conversion error in the horizontal direction and the corresponding probability value, as well as the distribution of the conversion error in the vertical direction and the corresponding probability value; If the distance conversion error is not within the preset distance error range, correct the output probability value based on Bayes' law and Monte Carlo simulation, and correct the projection coordinates in the second reference system obtained by fitting based on the corrected probability value.

2. The direct conversion method of small-sample projection coordinates based on neural network classification determination according to claim 1, characterized in that The training process of the neural network model includes: Obtain a control point set and divide it into a training set and a test set. For any point in the training set, use the projection coordinates of the point in the first reference system and the projection coordinates of the point in the second reference system obtained by polynomial fitting as the input of the preset neural network, and use whether the distance conversion error is within the preset distance error range and the distribution of the conversion error in the horizontal direction and the vertical direction as the output of the preset neural network to optimize the parameters of the neural network.

3. The small-sample projection coordinate direct conversion method based on neural network classification determination according to claim 2, characterized in that Using whether the distance conversion error is within the preset distance error range and the distribution of the conversion error in the horizontal direction and the vertical direction as the output of the preset neural network specifically includes: Use the first parameter to represent whether the distance conversion error is within the preset distance error range, use the second parameter, the third parameter, and the fourth parameter to comprehensively represent whether the conversion error in the horizontal direction is within the preset horizontal error range, and use the fifth parameter, the sixth parameter, and the seventh parameter to comprehensively represent whether the conversion error in the vertical direction is within the preset vertical error range.

4. The small-sample projection coordinate direct conversion method based on neural network classification determination according to claim 2, characterized in that Using whether the distance conversion error is within the preset distance error range and the distribution of the conversion error in the horizontal direction and the vertical direction as the output of the preset neural network specifically includes: Use the first parameter to represent whether the distance conversion error is within the preset distance error range, use the second parameter to represent whether the conversion error in the horizontal direction is negative or positive, use the third parameter to represent whether the conversion error in the vertical direction is negative or positive, and use the fourth parameter, the fifth parameter, and the sixth parameter to comprehensively represent the distribution of the slope or the difference between the absolute values of the conversion errors in the horizontal direction and the vertical direction.

5. The direct conversion method of small sample projection coordinates based on neural network classification determination according to claim 3, characterized in that, If the distance conversion error is not within the preset distance error range, correct the output probability value based on Bayes' law and Monte Carlo simulation, and correct the projection coordinates in the second reference system obtained by fitting based on the corrected probability value, specifically including: If the distance conversion error is not within the preset distance error range, but the conversion errors in the horizontal direction and the vertical direction are both within their respective preset error ranges, then do not correct the projection coordinates in the second reference system; If the distance conversion error is not within the preset distance error range, and one of the conversion errors in the horizontal and vertical directions is within the corresponding preset error range while the other is not within the corresponding preset error range, then only the probability value corresponding to the conversion error that is not within the corresponding preset error range is corrected; If the distance conversion error is not within the preset distance error range, and the conversion errors in both the horizontal and vertical directions are not within their respective corresponding preset error ranges, then the probability values corresponding to the conversion errors in both directions are corrected; Correspondingly, correcting the projected coordinates in the second reference system obtained by fitting based on the corrected probability value includes: determining whether the corrected probability value is greater than a preset first probability threshold. If so, adjusting the corresponding conversion error by N times L. If not but greater than the second probability threshold, adjusting the corresponding conversion error by N times ; where L represents a preset distance error threshold; the first probability threshold is greater than the second probability threshold, and N is a positive number less than or equal to 1.

6. The method for directly converting small-sample projection coordinates based on neural network classification determination according to any one of claims 1 to 5, characterized in that The neural network uses a backpropagation neural network.

7. A small-sample projection coordinate direct conversion device based on neural network classification determination, characterized in that It includes: An acquisition module for acquiring the projected coordinates in the first reference system to be converted; A coordinate conversion module for, for the projected coordinates in the first reference system to be converted, obtaining the projected coordinates in the second reference system through polynomial fitting; An error judgment module for inputting the projected coordinates in the first reference system and the projected coordinates in the second reference system obtained by fitting into a trained neural network model to judge whether the distance conversion error is within the preset distance error range and output the distribution and corresponding probability value of the conversion error in the horizontal direction, as well as the distribution and corresponding probability value of the conversion error in the vertical direction; A coordinate correction module for, when the distance conversion error is not within the preset distance error range, correcting the output probability value based on Bayes' law and Monte Carlo simulation, and correcting the projected coordinates in the second reference system obtained by fitting based on the corrected probability value.

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method according to any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method according to any one of claims 1 to 6.

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