Implicit modeling method and device of three-dimensional geological body, electronic equipment and storage medium

Abstract

The present application belongs to the technical field of three-dimensional geological modeling, and provides a kind of implicit modeling method, device, electronic equipment and storage medium of three-dimensional geological body, wherein the method comprises: using line boundary constraint generalization model to carry out modeling processing, to obtain three-dimensional geological body model;Line boundary constraint generalization model is obtained by the following steps: when carrying out radial basis function implicit modeling processing according to point set, optimization is carried out by minimizing energy function, to obtain normal vector and implicit function;Line constraint is carried out to implicit function, and the implicit function is processed by solving matrix to line constraint, to obtain implicit function parameter, and the line boundary constraint generalization model is determined according to implicit function and implicit function parameter.The beneficial effects of the present application are: the modeling precision of spatial data of geological exploration is improved.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional implicit modeling technology, and in particular to an implicit modeling method, apparatus, electronic device and storage medium for three-dimensional geological bodies. Background Technology

[0002] Current 3D implicit modeling methods, whether the basic radial basis method or the Hermite radial basis method, are all point constraint methods. Point constraint methods typically require a large amount of geological point data. In actual geological exploration, obtaining complete and high-density geological point data often places very high demands on technology and cost. At the same time, the accuracy and precision of point constraint methods depend on the input geological point data, but this data may contain errors or inaccuracies, including positional deviations, uneven sampling density, and data noise, all of which can lead to deviations in the modeling results. Summary of the Invention

[0003] Aimed at at least in solving one of the technical problems existing in the prior art, the present invention provides an implicit modeling method, apparatus, electronic device and storage medium for three-dimensional geological bodies, thereby improving the accuracy of implicit modeling of three-dimensional geological bodies.

[0004] One aspect of the present invention provides an implicit modeling method for three-dimensional geological bodies, comprising:

[0005] The three-dimensional geological body of the target area is obtained, and a line boundary constraint generalization model is used for modeling to obtain a three-dimensional geological body model.

[0006] The generalized model of line boundary constraints is obtained through the following steps:

[0007] When obtaining the point set of a three-dimensional geological body and performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and the implicit function;

[0008] Line constraints are applied to the implicit functions. The implicit functions are processed by solving the matrix to obtain the implicit function parameters. Based on the implicit functions and their parameters, a generalized model for the line boundary constraints is determined.

[0009] According to the implicit modeling method for three-dimensional geological bodies, when obtaining a point set of the three-dimensional geological body and performing implicit modeling processing based on the point set using radial basis functions, optimization is performed by minimizing the energy function to obtain the normal vector and implicit function, including:

[0010] Obtain the discretized point set of the sampling contour line of the three-dimensional geological body, and use HRBF-type radial basis functions to determine the implicit functions;

[0011] By using the energy function and preset adjustment parameters, a first objective function to be minimized is determined as the optimization objective. for:

[0012] ;

[0013] The constraint for minimizing the first objective function is: Among them, the central sampling points ,and , The total number of sampling points in the point set. Implicit function for preset adjustment parameters The zero-level set is an implicit surface of a three-dimensional geological body. Let be the energy function, and:

[0014] ;

[0015] Based on the implicit function, the function value and gradient value of each sampling point in the point set are calculated. Hermite data is determined based on the function value and gradient value. The first objective function to be minimized is optimized using the Hermite data to obtain the second objective function to be minimized. for:

[0016] ;

[0017] The constraint for minimizing the second objective function is: , The gradient value represents the gradient of a single sampling point; The function value vector of the sampling points. This indicates that the function value at each sampling point will be... The column vector formed by collecting them; This is the smooth implicit function approximation solution obtained based on Hermite data, i.e., the optimal solution obtained after optimization. ;

[0018] Based on the minimization of the second objective function and its constraints, the third objective function is determined to be:

[0019] ;

[0020] The constraint for minimizing the third objective function is: ,in Let be the normal vector, where the normal vector is... By analyzing the gradient value The result is obtained by normalization and integration.

[0021] According to the implicit modeling method for the three-dimensional geological body, the line constraints include integral constraints and endpoint derivative constraints. The integral constraints are used to characterize any known line segment on the implicit surface. The integral is treated as zero, and the integral constraint is expressed as:

[0022] ;

[0023] The endpoint derivative constraint is used to characterize the gradient at the endpoint of a line segment that is perpendicular to the direction vector of the line segment. The endpoint derivative constraint is as follows: , This represents the direction vector of the line segment. It is calculated by the difference between the coordinates of the endpoint and the starting point of the line segment.

[0024] According to the implicit modeling method for three-dimensional geological bodies, the implicit functions are linearly constrained. The implicit functions are processed by solving matrices to obtain implicit function parameters. Based on the implicit functions and their parameters, a generalized model for line boundary constraints is determined, including:

[0025] The implicit function of the line constraint is:

[0026] ;

[0027] in, ; It is a radial basis function. This indicates the second variable in the kernel function. The gradient at; where, , , , , , and Let be the scalar coefficients to be solved. Let be the three-dimensional vector to be solved. Indicates the number of line segments and sampling points. The system of linear equations satisfied is expressed as:

[0028] ;

[0029] in, The system of linear equations corresponding to the constraints of minimizing the third objective function. The unknown vector to be solved Here are the constraints, where for:

[0030] ;

[0031] in, ;

[0032] matrix The The elements are , It is a scalar, and the matrix It is a symmetric matrix; The first in The element is ; Representation matrix transpose of matrix The The element is ,in , and A point in three-dimensional space;

[0033] matrix The The element is ;matrix The The element is ;matrix The (i, j)th element is ;matrix The The element is , Indicates that under line constraints, the first The normal vector is obtained by normalizing the direction vector of a line segment;

[0034] matrix The The element is a size of The Hessian matrix, and the matrix It is also a symmetric matrix; matrix The The element is ;matrix Points in and Both refer to the endpoints of a line segment. and The direction vector of the line segment;

[0035] Using the Romberg algorithm to solve the linear equation system The implicit function parameters are obtained through calculation:

[0036] ;

[0037] The generalized model of line boundary constraints is determined based on the implicit function and its parameters.

[0038] According to the implicit modeling method for three-dimensional geological bodies, the Romberg algorithm is used to model the linear equation system. Calculations are performed, including:

[0039] The first in element The calculation method is as follows:

[0040] ;

[0041] in, , Representing line segments respectively The two endpoints of the line segment The equation is , , , , All are coordinate components of the integral term, and , , , , , , , , It is a point The three coordinate components;

[0042] matrix The The element is The calculation method is as follows:

[0043] ;

[0044] in, , , , and , They are line segments and line segments The starting point and the ending point, , , Let be the coordinate components of the integral term, where and It is a scalar;

[0045] matrix The element for:

[0046] ;

[0047] in, , , , for The three components, variables The gradient at is:

[0048] ;

[0049] matrix The element for:

[0050] ;

[0051] Among them, point This represents a control point, a point. These represent the endpoints of a line segment;

[0052] matrix The element The calculation method is as follows:

[0053] ;

[0054] In its second variable The gradient at is:

[0055] ;

[0056] matrix The element for:

[0057] ;

[0058] matrix The The elements are:

[0059] ;

[0060] in, for:

[0061] ;

[0062] matrix The The element is , which is:

[0063] ;

[0064] matrix The The elements are:

[0065] .

[0066] According to the implicit modeling method for three-dimensional geological bodies, the method further includes:

[0067] An improved moving cube algorithm is used to visualize implicit function surfaces.

[0068] According to the implicit modeling method for three-dimensional geological bodies, the method further includes:

[0069] The effectiveness of the line constraints is evaluated using the MAE loss function and RMSE loss.

[0070] Another aspect of the embodiments of the present invention discloses an implicit modeling apparatus for three-dimensional geological bodies, comprising:

[0071] The first module is used to obtain the three-dimensional geological body of the target area. It uses a line boundary constraint generalization model for modeling to obtain a three-dimensional geological body model.

[0072] The generalized model of line boundary constraints is obtained through the following modules:

[0073] The second module is used to obtain the point set of the three-dimensional geological body. When performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and the implicit function.

[0074] The third module is used to apply line constraints to implicit functions. It processes the implicit functions with line constraints by solving matrices to obtain the implicit function parameters, and determines the generalized model of line boundary constraints based on the implicit functions and their parameters.

[0075] Another aspect of the present invention provides an electronic device, including a processor and a memory;

[0076] The memory is used to store programs;

[0077] The processor executes the program to implement the method as described above.

[0078] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the methods described above.

[0079] The beneficial effects of this invention are as follows: by adding line segment integral constraints on the basis of sampling point position constraints and normal constraints, the point constraints on continuous high-density sampling points are transformed into line segment line integral constraints between low-density sampling points. This allows for effective constraints on the intermediate points of coefficient sampling points without using high-density sampling points, thereby enhancing the modeling accuracy of spatial data in geological exploration. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of the implicit modeling process of a three-dimensional geological body according to an embodiment of the present invention;

[0081] Figure 2 This is a schematic diagram of the implicit modeling process of HRBF-type radial basis functions according to an embodiment of the present invention;

[0082] Figure 3 This is a schematic diagram of geological exploration point data modeling in a mining area according to an embodiment of the present invention;

[0083] Figure 4 This is a schematic diagram showing the comparison results of the HRBF method, integral constraints, and integral endpoint derivative constraints in an embodiment of the present invention.

[0084] Figure 5 This is a schematic diagram showing the modeling comparison results of the embodiments of the present invention, wherein (a) is the implicit modeling using HRBF type radial basis functions; and (b) is the modeling using line segment constraints of the embodiments of the present invention.

[0085] Figure 6 This is a schematic diagram of the implicit modeling device for three-dimensional geological bodies according to an embodiment of the present invention. Detailed Implementation

[0086] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings. Throughout the description, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions. In the following description, suffixes such as "module," "part," or "unit" used to denote elements are used only for the purpose of illustrative purposes and have no specific meaning in themselves. Therefore, "module," "part," or "unit" can be used interchangeably. Terms such as "first," "second," etc., are used only to distinguish technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the sequential relationship of the indicated technical features. In the following description, the consecutive reference numerals for method steps are for ease of review and understanding. Adjusting the implementation order of steps, in conjunction with the overall technical solution of the present invention and the logical relationship between the various steps, will not affect the technical effect achieved by the technical solution of the present invention. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0087] refer to Figure 1 A schematic diagram of the implicit modeling process for three-dimensional geological bodies, including but not limited to steps S100~S300:

[0088] S100: Obtain the three-dimensional geological body of the target area, and use the line boundary constraint generalization model for modeling to obtain the three-dimensional geological body model.

[0089] In some embodiments, the three-dimensional geological body is three-dimensional spatial data, which can be obtained by using geological profiles, geophysical exploration and remote sensing methods in the target area (mining area).

[0090] In some embodiments, the line boundary constraint generalization model is obtained through steps S200~S300, wherein:

[0091] S200: Obtain the point set of the 3D geological body. When performing implicit modeling of radial basis functions based on the point set, optimize by minimizing the energy function to obtain the normal vector and implicit function.

[0092] In some embodiments, reference Figure 2 The schematic diagram of the implicit modeling process for HRBF-type radial basis functions shown includes, but is not limited to, steps S210~S230:

[0093] S210: Obtain the point set of the discretized sampling contour of the three-dimensional geological body, and use HRBF-type radial basis functions to determine the implicit function.

[0094] In some embodiments, HRBF is used in the following forms:

[0095] ;

[0096] S220 determines the first objective function to be minimized as the optimization objective by using the energy function and preset adjustment parameters.

[0097] The first objective function to be minimized for:

[0098] ;

[0099] The constraint for minimizing the first objective function is: , indicating that the magnitude of the gradient at each sampling point is 1; where the sampling points are in the point set. ,and , The total number of sampling points in the point set. Implicit function for preset adjustment parameters The zero-level set is an implicit surface of a three-dimensional geological body. Let be the energy function, and:

[0100] ;

[0101] S230: Based on the implicit function, calculate the function value and gradient value of each sampling point in the point set, determine the Hermite data based on the function value and gradient value, and optimize the minimized first objective function using the Hermite data to obtain the minimized second objective function.

[0102] In some embodiments, for each input point Its function value ,gradient ,in A set of Hermite data for the sampling points was obtained. Therefore, the first objective function can be transformed into the second objective function. for:

[0103] ;

[0104] ;

[0105] The constraint for minimizing the second objective function is: , The gradient value represents the gradient of a single sampling point; The function value vector of the sampling points. This indicates that the function value at each sampling point will be... The column vector formed by collecting them; This is the smooth implicit function approximation solution obtained based on Hermite data, i.e., the optimal solution obtained after optimization. ;

[0106] S240, Based on the minimized second objective function and the constraints of the minimized second objective function, determine the minimized third objective function.

[0107] In some embodiments, the third objective function to be minimized is determined based on the minimized second objective function and the constraints of the minimized second objective function:

[0108] ;

[0109] The constraint for minimizing the third objective function is: ,in Let be the normal vector, where the normal vector is... By analyzing the gradient value The result is obtained by normalization and integration.

[0110] S300 applies line constraints to the implicit function. By solving the matrix, the implicit function parameters are obtained through processing the implicit function of the line constraint. Based on the implicit function and the implicit function parameters, the generalized model of the line boundary constraint is determined.

[0111] In some embodiments, line constraints include integral constraints and endpoint derivative constraints, whereby integral constraints are used to characterize any known line segment on the implicit surface. The integral is treated as zero, and the integral constraint is expressed as:

[0112] ;

[0113] The endpoint derivative constraint is used to characterize the set of endpoints of a line segment where the gradient at each endpoint is perpendicular to the direction vector of the line segment. The endpoint derivative constraint is: , This represents the direction vector of the line segment. It is calculated by the difference between the coordinates of the endpoint and the starting point of the line segment.

[0114] In some embodiments, the derivation process of integral constraints in line constraints is as follows:

[0115] objective function It consists of two parts, one is the data item (via The other is the regularization term (via...). (This is represented as an expression), and the objective function is optimized using the variational method. First, the objective function is defined. for Functions:

[0116] ;

[0117] in It is a constant;

[0118] Expanding and rearranging the above equation, we get:

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] make The change is The change in the objective function can be derived using the variational method. :

[0124] ;

[0125] The above equation can be viewed as the objective function. The linear approximation of the implicit function represents the response of the objective function to small changes in the implicit function. Objective function right Taking the derivative, we get:

[0126] ;

[0127] ;

[0128] Therefore:

[0129] ;

[0130] ;

[0131] Further derivation from the above formula yields:

[0132] ;

[0133] ;

[0134] ;

[0135] ;

[0136] ;

[0137] The first line integral constraint condition of the method in this embodiment of the invention is obtained, namely:

[0138] ;

[0139] In some embodiments, the implicit function of the line constraint is processed by solving the matrix to obtain the implicit function parameters. Based on the implicit function and the implicit parameters, a generalized model for the line boundary constraint is determined, including:

[0140] The implicit function of the line constraint is:

[0141] ;

[0142] in, ; It is a radial basis function. This indicates the second variable in the kernel function. The gradient at; where, , , , , , and Let be the scalar coefficients to be solved. Let be the three-dimensional vector to be solved. Indicates the number of line segments and sampling points. The system of linear equations satisfied is expressed as:

[0143] ;

[0144] Where A is the matrix established by the constraints, The unknown vector is the target that needs to be solved. To represent a constraint, it can be written as: And A has the following form:

[0145] ;

[0146] matrix The The elements are This value is a scalar, and the matrix It is a symmetric matrix, and its specific form is as follows:

[0147] ;

[0148] The first in The element is ,matrix The specific form is as follows:

[0149] ;

[0150] in, The calculation method is as follows:

[0151] ;

[0152] in , Representing line segments respectively The two endpoints of the line segment The equation is: , In the above formula, , , All are coordinate components of the integral term, and , , Their specific forms are: , , . , , It is a point The three coordinate components, due to The values ​​of are all known and are scalars. The integration method used in this embodiment of the invention is numerical integration, employing the Romberg algorithm. The Romberg quadrature formula, also known as the successive half-step acceleration method, is a method for accelerating integration calculations based on the relationships between the trapezoidal rule, Simpson's rule, and Cotes' rule. The Romberg algorithm converges faster and has smaller errors, improving accuracy without increasing computational load. Comparison results are shown in Table 1.

[0153] Table 1. Convergence Comparison of Different Sequences at Different Discriminant Levels

[0154]

[0155] Representation matrix transpose of matrix The The element is ( The specific form of the matrix is ​​as follows:

[0156] ;

[0157] in, The calculation method is as follows:

[0158] ;

[0159] in , and , They are line segments and line segments The starting point and the ending point, , , , , and , , These are all coordinate components of the integral term, and their calculation is the same as above. , .because , , , Since all are known, the above equation can be obtained through numerical integration, and the matrix... Each element is also a scalar.

[0160] matrix The The element is Its specific form is as follows:

[0161] ;

[0162] in, , , , for The three components. Since the radial basis function used in this embodiment of the invention is... In its second variable The gradient at is:

[0163] ;

[0164] matrix The The element is Its specific form is as follows:

[0165] ;

[0166] midpoint This represents a control point, a point. These represent the endpoints of a line segment. The matrix represents the direction vector of a line segment. The The specific form of each element is as follows:

[0167] ;

[0168] matrix The The element is Its specific form is as follows:

[0169] ;

[0170] In its second variable The gradient at is:

[0171] ;

[0172] Therefore:

[0173] ;

[0174] matrix The The element is Its specific form is as follows:

[0175] ;

[0176] matrix The The element is a size of The Hessian matrix, and the matrix It is also a symmetric matrix, and its specific form is as follows:

[0177] ;

[0178] in, It has the following forms:

[0179] ;

[0180] matrix The The element is Its specific form is as follows:

[0181] ;

[0182] matrix Points in , Both refer to the endpoints of a line segment. , Both refer to the direction vector of a line segment, and the matrix. The specific form is as follows:

[0183] ;

[0184] At this point, the relevant knowledge regarding solving matrices from matrices includes:

[0185] ;

[0186] The calculated x matrix is ​​the implicit function parameter to be determined, where B is... This vector represents the constraint condition, where mean:

[0187] 1) The first part = 0, the implicit function is zero at the sampling point (the point is on the implicit surface);

[0188] 2) The second part = n, the gradient is equal to the normal vector constraint, that is, the gradient of HRBF must match the given normal vector;

[0189] 3) The third and fourth parts = 0, indicating some additional constraints, such as line segment constraints and line segment direction constraints in the embodiments of the present invention.

[0190] In some embodiments, an improved moving cube algorithm is used to visualize the implicit function surface.

[0191] In some embodiments, the MAE loss function and RMSE loss are used to evaluate the effectiveness of line constraints. The method proposed in this embodiment requires that the implicit function value at the midpoint of the line segment be equal to zero; therefore, calculating the loss function can further evaluate the accuracy of the implicit function. For the above two sets of data, this embodiment selects Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) as accuracy evaluation indicators. MAE refers to the target value... Compared with the predicted value The RMSE is the average of the absolute values ​​of the differences between the predicted values. With target value The square root of the mean of the sum of the squares of the differences between them, where This represents the total number of midpoints of the line segment. The formulas for calculating the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are as follows:

[0192] ;

[0193] ;

[0194] In some embodiments, reference Figure 3 This example illustrates modeling based on geological exploration point data from a mining area. In this case, the geological exploration point data includes three-dimensional point coordinates and the corresponding normal vector, while the line data includes the three-dimensional coordinates of the starting point and the ending point of the line segment. Figure 3 In the model, the points are control points, and the black points within the red boxes represent the start and end points of line segments. The black points are connected by line segments.

[0195] The results show that the model constructed by the proposed method passes through each control point in a relatively smooth manner, and the places with line constraints are all located on the three-dimensional implicit surface. In contrast, the HRBF method, due to the lack of line integral constraints, does not have line segments that completely fit the model surface.

[0196] To quantify this difference, the absolute value of the implicit function at the midpoint of each line segment was chosen as the evaluation metric to determine the effectiveness of the newly added line integral constraints and gradient constraints at the line endpoints. The experimental results are shown in Tables 2 and 3 below:

[0197] Table 2 Analysis of fracture surface data in the study area

[0198]

[0199] Table 3 Loss Function Calculation Table

[0200]

[0201] refer to Figure 3 ,Although Figure 3The models obtained by the two methods are visually similar overall, but current engineering and scientific research fields have extremely high requirements for accuracy and local shape control. The line segment constraint effect within the red box is a direct reflection of the core difference between point constraint and line constraint methods—HRBF (point constraint) can only ensure that discrete points such as the endpoints of the line segment fit the surface, but it cannot make the line segment continuous and fall on the surface as a whole; while the line constraint method in this embodiment of the invention introduces the line segment as a continuous constraint into the system through line integrals, realizing that the entire line segment, from the endpoint to the middle, precisely fits the surface. This precise local control improves the accuracy of 3D geological body modeling.

[0202] refer to Figure 4 A comparative diagram illustrating the HRBF method, integral constraints, and endpoint derivative constraints. The diagram also shows the modeling results of the constraints. In HRBF, the implicit function aims to minimize the energy functional.

[0203] ;

[0204] This energy term essentially requires the second derivative of the function to be as small as possible, i.e., it encourages the surface to be as smooth as possible in space. Therefore, the model often sacrifices local accuracy to ensure overall smoothness. However, the method proposed in this embodiment of the invention can make the surface satisfy the implicit function integration condition over the entire line segment, thereby controlling not only the surface's behavior at discrete points but also constraining the surface's spatial morphology at line segments. Further references Figure 3 , Figure 3 For visualization of the results, Figure 4 The local constraint effect of the implicit function was calculated by quantifying the implicit function values ​​at the midpoints of the seven line segments using different methods. The closer the implicit function value is to zero, the closer the midpoint of the line segment is to the implicit surface.

[0205] refer to Figure 5 ,in Figure 5 The figures show a comparison of the two methods for fine control of the local shape of the surface. In (a), the HRBF method can only control discrete points to be located on the implicit surface. The surface in this part is relatively smooth and rounded, without obvious edges and sharp changes. In (b), the line segment is introduced into the implicit function calculation process in the form of line integral. The line segment can be seen on the surface with obvious sharp turns and prominent pointed structures. It can be determined that the modeling accuracy of the embodiment of the line segment constraint used in the present invention is better than that of HRBF.

[0206] Based on the above results, it is clear that the HRBF (point constraint) method alone is insufficient to effectively constrain the implicit surface between points. Introducing line integral constraints significantly improves the fitting accuracy, making the function values ​​closer to the zero level set. Further introducing gradient direction constraints not only controls the function values ​​but also ensures tangential consistency, ultimately yielding the best results.

[0207] Figure 6 This is a schematic diagram of an implicit modeling device for three-dimensional geological bodies according to an embodiment of the present invention. The device includes a first module 610, a second module 620, and a third module 630.

[0208] The first module is used to acquire the three-dimensional geological body of the target area and to perform modeling processing using a line boundary constraint generalization model to obtain the three-dimensional geological body model. The line boundary constraint generalization model is obtained through the following modules: The second module is used to acquire the point set of the three-dimensional geological body. When performing implicit modeling processing of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and implicit function; The third module is used to apply line constraints to the implicit function. The implicit function with line constraints is processed by solving the matrix to obtain the implicit function parameters. The line boundary constraint generalization model is determined based on the implicit function and the implicit function parameters.

[0209] Exemplarily, with the cooperation of the first, second, and third modules in the device, the embodiment device can implement any of the aforementioned implicit modeling methods for three-dimensional geological bodies, namely, acquiring the three-dimensional geological body of the target area, performing modeling processing using a line boundary constraint generalization model, and obtaining a three-dimensional geological body model; the line boundary constraint generalization model is obtained through the following steps: acquiring the point set of the three-dimensional geological body, optimizing by minimizing the energy function when performing implicit modeling processing based on the point set, obtaining the normal vector and implicit function; applying line constraints to the implicit function, processing the implicit function with line constraints by solving the matrix, obtaining the implicit function parameters, and determining the line boundary constraint generalization model based on the implicit function and the implicit function parameters. The beneficial effects of the present invention are: by adding line segment integral constraints on the basis of sampling point position constraints and normal constraints, the point constraints on continuous high-density sampling points are transformed into line segment line integral constraints between low-density sampling points. This allows for effective constraints on the intermediate points of coefficient sampling points without using high-density sampling points, enhancing the modeling accuracy of spatial data in geological exploration.

[0210] This invention also provides an electronic device, which includes a processor and a memory;

[0211] The memory stores the program;

[0212] The processor executes a program to perform the aforementioned implicit modeling method for three-dimensional geological bodies; the electronic device has the function of carrying and running the software system for implicit modeling of three-dimensional geological bodies provided in the embodiments of the present invention, such as a personal computer, minicomputer, mainframe, workstation, network or distributed computing environment, standalone or integrated computer platform, or communicating with charged particle tools or other imaging devices, etc.

[0213] This invention also provides a computer-readable storage medium storing a program that is executed by a processor to implement the implicit modeling method for three-dimensional geological bodies as described above.

[0214] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented in the embodiments of this invention. Alternative embodiments are contemplated, in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0215] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned implicit modeling method for three-dimensional geological bodies.

[0216] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, considering the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed in the embodiments of the invention, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0217] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0218] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can include, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0219] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0220] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0221] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0222] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0223] The above is a detailed description of the preferred embodiments of the present invention, but the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A method of implicit modeling of a three-dimensional geological body, characterized in that, include: The three-dimensional geological body of the target area is obtained, and a line boundary constraint generalization model is used for modeling to obtain a three-dimensional geological body model. The generalized model of line boundary constraints is obtained through the following steps: When obtaining the point set of a three-dimensional geological body and performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and the implicit function; Line constraints are applied to the implicit functions. The implicit functions of the line constraints are processed by solving the matrix to obtain the implicit function parameters. Based on the implicit functions and implicit function parameters, the generalized model of the line boundary constraints is determined. When acquiring the point set of the three-dimensional geological body and performing implicit modeling of the radial basis function based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and implicit function, including: Obtain the discretized point set of the sampling contour line of the three-dimensional geological body, and use HRBF-type radial basis functions to determine the implicit functions; By means of the energy function and the preset adjustment parameters, a minimized first objective function is determined as the optimization target, wherein the minimized first objective function is: The constraint for minimizing the first objective function is: Among them, the central sampling points ,and , The total number of sampling points in the point set. Implicit function for preset adjustment parameters The zero-level set is an implicit surface of a three-dimensional geological body. It is an energy function, and Based on the implicit function, the function value and gradient value of each sampling point in the point set are calculated. Hermite data is determined based on the function value and gradient value. The first objective function to be minimized is optimized using the Hermite data to obtain the second objective function to be minimized. for: The constraint for minimizing the second objective function is: , The gradient value represents the gradient of a single sampling point; The function value vector of the sampling points. This indicates that the function value at each sampling point will be... The column vector formed by collecting them; This is the smooth implicit function approximation solution obtained based on Hermite data, i.e., the optimal solution obtained after optimization. ; Based on the minimization of the second objective function and its constraints, the third objective function is determined to be: The constraint for minimizing the third objective function is: ,in Let be the normal vector, where the normal vector is... By analyzing the gradient value The result is obtained by normalization and integration; The line constraints include integral constraints and endpoint derivative constraints. The integral constraints are used to characterize any known line segment on the implicit surface. The integral is treated as zero, and the integral constraint is expressed as: The endpoint derivative constraint is used to characterize the gradient at the endpoint of a line segment that is perpendicular to the direction vector of the line segment. The endpoint derivative constraint is as follows: , This represents the direction vector of the line segment. It is calculated by the difference between the coordinates of the endpoint and the starting point of the line segment.

2. The implicit modeling method for three-dimensional geological bodies according to claim 1, characterized in that, The process of applying line constraints to the implicit function involves processing the implicit function through matrix solving to obtain its parameters. Based on the implicit function and its parameters, a generalized model for the line boundary constraints is determined, including: The implicit function of the line constraint is: in, ; It is a radial basis function. This indicates the second variable in the kernel function. The gradient at; where, , , , , , and Let be the scalar coefficients to be solved. Let be the three-dimensional vector to be solved. Indicates the number of line segments and sampling points. The system of linear equations satisfied is expressed as: in, The system of linear equations corresponding to the constraints of minimizing the third objective function. The unknown vector to be solved Here are the constraints, where for: in, ; matrix The The elements are , It is a scalar, and the matrix It is a symmetric matrix; The first in The element is ; Representation matrix transpose of matrix The The element is ,in , and A point in three-dimensional space; matrix The The element is ;matrix The The element is , Under line constraints, the first The normal vector obtained by normalizing the direction vector of a line segment; matrix The The element is ;matrix The The element is ; matrix The The element is a size of The Hessian matrix, and the matrix It is also a symmetric matrix; matrix The The element is ;matrix Points in and Both refer to the endpoints of a line segment. and The direction vector of the line segment; Using the Romberg algorithm to solve the linear equation system The implicit function parameters are obtained through calculation: The generalized model of line boundary constraints is determined based on the implicit function and its parameters.

3. The implicit modeling method for three-dimensional geological bodies according to claim 2, characterized in that, The Romberg algorithm is used to process the linear equation system. The calculations include: The first in element The calculation method is as follows: in, , Representing line segments respectively The two endpoints of the line segment The equation is , , , , All are coordinate components of the integral term, and , , , , , , , , It is a point The three coordinate components; matrix The The element is The calculation method is as follows: in, , , , and , They are line segments and line segments The starting point and the ending point, , , Let be the coordinate components of the integral term, where and It is a scalar; matrix The element for: in, , , , for The three components, variables The gradient at is: matrix The element for: Among them, point This represents a control point, a point. These represent the endpoints of a line segment; matrix The element The calculation method is as follows: In its second variable The gradient at is: in, Representing three-dimensional points in space and three-dimensional points The distance scalar between them; matrix The element for: matrix The The elements are: in, for: matrix The The element is , which is: matrix The The elements are: 。 4. The implicit modeling method for three-dimensional geological bodies according to claim 1, characterized in that, The method further includes: An improved moving cube algorithm is used to visualize implicit function surfaces.

5. The implicit modeling method for three-dimensional geological bodies according to claim 1, characterized in that, The method further includes: The effectiveness of the line constraints is evaluated using the MAE loss function and RMSE loss.

6. An implicit modeling device for three-dimensional geological bodies, characterized in that, include: The first module is used to obtain the three-dimensional geological body of the target area. It uses a line boundary constraint generalization model for modeling to obtain a three-dimensional geological body model. The generalized model of line boundary constraints is obtained through the following modules: The second module is used to obtain the point set of the three-dimensional geological body. When performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and the implicit function. The third module is used to apply line constraints to implicit functions. It processes the implicit functions of the line constraints by solving the matrix to obtain the implicit function parameters, and determines the line boundary constraint generalization model based on the implicit functions and implicit function parameters. When acquiring the point set of the three-dimensional geological body and performing implicit modeling of the radial basis function based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and implicit function, including: Obtain the discretized point set of the sampling contour line of the three-dimensional geological body, and use HRBF-type radial basis functions to determine the implicit functions; By using the energy function and preset adjustment parameters, a first objective function to be minimized is determined as the optimization objective. for: The constraint for minimizing the first objective function is: Among them, the central sampling points ,and , The total number of sampling points in the point set. Implicit function for preset adjustment parameters The zero-level set is an implicit surface of a three-dimensional geological body. It is an energy function, and Based on the implicit function, the function value and gradient value of each sampling point in the point set are calculated. Hermite data is determined based on the function value and gradient value. The first objective function to be minimized is optimized using the Hermite data to obtain the second objective function to be minimized. for: The constraint for minimizing the second objective function is: , The gradient value represents the gradient of a single sampling point; The function value vector of the sampling points. This indicates that the function value at each sampling point will be... The column vector formed by collecting them; This is the smooth implicit function approximation solution obtained based on Hermite data, i.e., the optimal solution obtained after optimization. ; Based on the minimization of the second objective function and its constraints, the third objective function is determined to be: The constraint for minimizing the third objective function is: ,in Let be the normal vector, where the normal vector is... By analyzing the gradient value The result is obtained by normalization and integration; The line constraints include integral constraints and endpoint derivative constraints. The integral constraints are used to characterize any known line segment on the implicit surface. The integral is treated as zero, and the integral constraint is expressed as: The endpoint derivative constraint is used to characterize the gradient at the endpoint of a line segment that is perpendicular to the direction vector of the line segment. The endpoint derivative constraint is as follows: , This represents the direction vector of the line segment. It is calculated by the difference between the coordinates of the endpoint and the starting point of the line segment.

7. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the implicit modeling method for three-dimensional geological bodies as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The storage medium stores a program that is executed by a processor to implement the implicit modeling method for three-dimensional geological bodies as described in any one of claims 1-5.

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