Edge detection filter based on structure tensor and softsign function

Abstract

The application discloses an edge detection filter based on a structure tensor and a softsign function, and performs edge detection filtering based on a three-dimensional structure tensor and a softsign function for processing and interpretation analysis of a gravity gradient tensor. The application can quickly determine the horizontal distribution range of a target, effectively reduces problems such as divergence, fuzziness and deformation, can clearly and accurately delineate the boundary of a deep abnormal body under the condition of less prior information, avoids false boundaries between positive and negative anomalies, can adapt to abnormal data of different targets or scales, reduces human intervention, simplifies the screening process, and ensures the reliability of the screening result in quality and quantity.

Description

Technical Field

[0001] The present invention relates to the field of geophysics, and in particular to an edge detection filter based on a structure tensor and a softsign function. Background Art

[0002] Boundary identification is a crucial component of geophysical data processing and interpretation, playing a key role in fields such as mineral delineation and structural research. Potential field tensor gradient data consists of nine components and is typically obtained through field measurements or numerical calculations. Compared to standard potential field data, potential field tensor gradient data provides higher-frequency signals, providing more detailed and accurate geological information for structural research.

[0003] The development of boundary detectors began with the use of the zero value of the first-order derivative of potential field data to identify edge locations. For example, the total horizontal derivative and the maximum amplitude of the analytical signal can directly delineate the boundaries of anomalies, but these methods have low resolution and are not as effective at identifying deep anomalies as shallow anomalies. Tilt angle, as the first equalization filter, effectively addresses the shortcomings of previous methods in equalizing different amplitudes. However, these equalization filters still have low recognition resolution and are prone to generating erroneous information when both positive and negative anomalies exist in the study area.

[0004] To address the above problems, researchers have proposed methods based on higher-order derivatives, such as a tilt angle filter based on the total horizontal derivative. This method can reduce the generation of false information while balancing different amplitude information. However, its edge detection filtering results are often more divergent, especially for deep-source anomalies, where the recognition results often exceed the actual boundary range. In addition, the introduction of higher-order derivatives inevitably amplifies the noise, affecting the stability of the recognition results. The structural tensor is a technology used to analyze image features. Applying this method to potential field data and detecting geological body boundaries through its eigenvalues ​​can effectively solve the problem of false anomalies caused by the simultaneous occurrence of positive and negative anomalies. The Gaussian envelope used in the structural tensor reduces sensitivity to noise, but fails to effectively balance the amplitude information at different depths.

[0005] This patent proposes a filter based on a three-dimensional structure tensor that can be applied to complex synthetic models and real gravity data. The patent also compares and analyzes the new method with traditional boundary detection methods to verify its reliability and effectiveness. The proposed edge detection filter significantly enhances boundary recognition capabilities in geophysical applications, overcoming the limitations of existing technologies and providing a more reliable subsurface analysis tool for geophysical research. Summary of the Invention

[0006] The purpose of the present invention is to provide an edge detection filter based on structure tensor and softsign function to address the above problems existing in current fracture identification.

[0007] The above-mentioned purpose of the present invention is achieved through the following technical solutions:

[0008] An edge detection filter based on structure tensor and softsign function includes vertical Bouguer gravity anomaly data calculation module, gravity gradient tensor calculation module, three-dimensional structure tensor matrix calculation module and filtering module in sequence;

[0009] Vertical Bouguer gravity anomaly data calculation module: used to input gravity observation data and terrain data of each gravity point to obtain vertical Bouguer gravity anomaly data;

[0010] Gravity gradient tensor calculation module: used to input vertical Bouguer gravity anomaly data and obtain gravity gradient tensor;

[0011] Three-dimensional structure tensor matrix calculation module: used to input the gravity gradient tensor and obtain the three-dimensional structure tensor matrix based on the gravity gradient tensor and Gaussian envelope;

[0012] Filtering module: used to input the three-dimensional structure tensor matrix, filter it based on the softsign function, and output the edge detection filtering result.

[0013] As described above, the vertical Bouguer gravity anomaly data calculation module calculates the free air gravity anomaly value, terrain correction value and Bouguer correction value corresponding to each gravity point based on the input gravity observation data and terrain data of each gravity point;

[0014] For each gravity point, the corresponding free air gravity anomaly value, terrain correction value and Bouguer correction value are added together to obtain the corresponding vertical Bouguer gravity anomaly value. The vertical Bouguer gravity anomaly data G z Includes the coordinates of all gravity points and the corresponding vertical Bouguer gravity anomalies.

[0015] As mentioned above, the gravity gradient tensor calculation module is based on the vertical Bouguer gravity anomaly data G z , the gravity gradient tensor is calculated by the following formula:

[0016]

[0017] G xz , G yz and G zz They are the x-, y- and z-components of the gravity gradient tensor respectively; the z-direction is the direction of gravity, and the x- and y-directions are two directions perpendicular to each other in the horizontal plane.

[0018] As mentioned above, the three-dimensional structure tensor matrix calculation module calculates the three-dimensional structure tensor matrix using the following formula:

[0019]

[0020] Among them, T is the three-dimensional structure tensor matrix, G σ (x,y) is the Gaussian envelope, * is the convolution symbol;

[0021]

[0022] Among them, σ x and σ y are the components of the standard deviation of the Gaussian envelope in the x and y directions, and the standard deviation of the Gaussian envelope

[0023] The three-dimensional structure tensor matrix T is as follows:

[0024]

[0025] Among them, T 11 、T 12 、T 13 、T 21 、T 22 、T 23 、T 31 、T 32 , and T 33 are all components in the three-dimensional structure tensor matrix T.

[0026] As described above, the filtering module includes a first filter, and the edge detection filtering result of the first filter is:

[0027]

[0028] Among them, the intermediate quantity THDTED satisfies:

[0029]

[0030] Among them, TDRTED represents the edge detection filtering result of the first filter, THDTED x 、THDTED y and THDTED z are the first-order derivatives of the intermediate quantity THDTED in the x, y and z directions, tan -1 Represents the inverse tangent function.

[0031] As described above, the filtering module further includes a second filter, and the edge detection filtering result corresponding to the second filter is:

[0032]

[0033] Wherein, SFTED is the edge detection filtering result of the second filter, and k is a positive value.

[0034] The edge detection filtering method based on the structure tensor and the softsign function realizes any one of the edge detection filters based on the structure tensor and the softsign function in claims 1-6.

[0035] A computer device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements any one of the above-mentioned edge detection filters based on a structure tensor and a softsign function.

[0036] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements any one of the above-mentioned edge detection filters based on a structure tensor and a softsign function.

[0037] A computer program product comprises a computer program, wherein when the computer program is executed by a processor, the computer program implements any one of the above-mentioned edge detection filters based on a structure tensor and a softsign function.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] Boundary identification can be used to delineate the horizontal distribution range of a target and is an essential step in potential field data interpretation. Traditional boundary identification methods are prone to problems such as divergence, blurring, and deformation. This paper studies an edge detection filter based on the structure tensor and softsign function, focusing on the processing and interpretation of gravity gradient tensors. Compared to existing technologies, this paper has the following significant advantages:

[0040] (1) Efficient boundary recognition: The present invention can quickly determine the horizontal distribution range of the target and effectively reduce problems such as divergence, blurring, and deformation.

[0041] (2) Accurate anomaly identification: Processing and analyzing the gravity gradient tensor can clearly and accurately delineate the boundaries of deep anomalies with less prior information, avoiding the generation of false boundaries between positive and negative anomalies.

[0042] (3) Strong adaptability: The present invention can adapt to abnormal data of different targets or scales, reduce human intervention, simplify the screening process, and ensure the reliability of the screening results in terms of quality and quantity. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is the process of implementing filtering by the edge detection filter of the present invention.

[0044] Figure 2: The figure compares the edge detection filtering results of the present invention with those of the prior art; wherein, (a) is the edge detection filtering result of the total horizontal gradient method; (b) is the edge detection filtering result of the analytical signal method; (c) is the edge detection filtering result of the tilt angle method; (d) is the edge detection filtering result of the Theta graph method; (e) is the edge detection filtering result of the first filter of the present invention; (f) is the edge detection filtering result of the second filter of the present invention; x and y are two directions perpendicular to each other in the horizontal plane. DETAILED DESCRIPTION

[0045] Example 1:

[0046] The edge detection filter based on the structure tensor and the softsign function includes a vertical Bouguer gravity anomaly data calculation module, a gravity gradient tensor calculation module, a three-dimensional structure tensor matrix calculation module and a filtering module.

[0047] The gravity observation data and terrain data of each gravity point are input into the vertical Bouguer gravity anomaly data calculation module to obtain the vertical Bouguer gravity anomaly data;

[0048] The vertical Bouguer gravity anomaly data is input into the gravity gradient tensor calculation module and derived to obtain the gravity gradient tensor;

[0049] The gravity gradient tensor is input into the three-dimensional structure tensor matrix calculation module. The three-dimensional structure tensor matrix calculation module obtains the three-dimensional structure tensor matrix based on the gravity gradient tensor and the Gaussian envelope;

[0050] The filtering module inputs the three-dimensional structure tensor matrix, performs filtering based on the softsign function, and outputs the edge detection filtering result.

[0051] 1. Vertical Bouguer gravity anomaly data calculation module

[0052] The vertical Bouguer gravity anomaly data calculation module calculates the free air gravity anomaly value, terrain correction value and Bouguer correction value corresponding to each gravity point based on the input gravity observation data and terrain data of each gravity point;

[0053] For each gravity point, the corresponding free air gravity anomaly value, terrain correction value and Bouguer correction value are added together to obtain the corresponding vertical Bouguer gravity anomaly value. The vertical Bouguer gravity anomaly data includes the coordinates of all gravity points and the corresponding vertical Bouguer gravity anomaly values:

[0054] G z =G zfa +TC+BG

[0055] Among them, G z is the vertical Bouguer gravity anomaly data, which represents the distribution of vertical Bouguer gravity anomaly values ​​of the gravity point; Gzfa is the free-air gravity anomaly data, which indicates the distribution of the free-air gravity anomaly values ​​of the gravity point; TC is the terrain correction data, which indicates the distribution of the terrain correction values ​​of the gravity point; BG is the Bouguer correction data, which indicates the distribution of the Bouguer correction values ​​of the gravity point.

[0056] 2. Gravity gradient tensor calculation module

[0057] Based on the vertical Bouguer gravity anomaly data G z , the gravity gradient tensor is calculated by the following formula:

[0058]

[0059] G xz , G yz and G zz are the components of the gravity gradient tensor in the x direction, y direction, and z direction, which are equal to the vertical Bouguer gravity anomaly data G z The first derivatives in the x-, y-, and z-directions, respectively. The z-direction is the direction of gravity, and the x- and y-directions are two perpendicular directions in the horizontal plane.

[0060] The gravity gradient tensor is rich in information and contains high-frequency signals. Although it can be used for edge detection filtering, it still has limitations. For example, it may not be able to effectively identify amplitude anomalies at different depths; or it may introduce false boundaries when identifying anomalies containing both positive and negative density; or there may be problems with insufficient image resolution; or the stability of the edge detection filtering results may be affected by noise.

[0061] 3. Three-dimensional structure tensor matrix calculation module

[0062] Based on the gravity gradient tensor and Gaussian envelope G σ (x,y), the three-dimensional structure tensor matrix is ​​calculated by the following formula:

[0063]

[0064] Among them, T is the three-dimensional structure tensor matrix, G σ (x,y) is the Gaussian envelope, * is the convolution symbol;

[0065]

[0066] Among them, σ x and σ y The components of the standard deviation of the Gaussian envelope in the x and y directions, respectively, and the standard deviation of the Gaussian envelope

[0067] The three-dimensional structure tensor matrix T is as follows:

[0068]

[0069] Among them, T 11 、T 12 、T 13 、T 21 、T 22 、T 23 、T 31 、T 32 , and T 33 are all components in the three-dimensional structure tensor matrix T.

[0070] 4. Filter module

[0071] The filtering module includes a first filter, which performs filtering based on the components in the three-dimensional structure tensor matrix T to obtain the corresponding edge detection filtering results as follows:

[0072]

[0073] Among them, the intermediate quantity THDTED satisfies:

[0074]

[0075] Among them, TDRTED represents the edge detection filtering result of the first filter, THDTED x 、THDTED y and THDTED z are the first-order derivatives of the intermediate quantity THDTED in the x, y and z directions, tan -1 Represents the inverse tangent function.

[0076] The edge detection filtering result of the first filter is as follows Figure 2 As shown in (e), compared with the prior art, the divergence, blurring and deformation of the edge detection filtering of the first filter are reduced.

[0077] Furthermore, based on the first filter, the filtering module also includes a second filter. The second filter calculates the corresponding edge detection filtering result based on the three-dimensional structure tensor matrix and the softsign function:

[0078]

[0079] Wherein, SFTED is the edge detection filtering result of the second filter, and k is a preset positive value.

[0080] The second filter further reduces the divergence, blur and deformation of the edge detection filter on the basis of the first filter. The edge detection filter result of the second filter is as follows: Figure 2 (f) shown.

[0081] The present invention processes and analyzes the gravity gradient tensor, and can clearly and accurately delineate the boundaries of deep anomalies with less prior information, avoiding the generation of false boundaries between positive and negative anomalies; and the edge detection filtering process is simple, while ensuring the reliability of the screening results in terms of quality and quantity.

[0082] Example 2:

[0083] The edge detection filtering method based on the structure tensor and the softsign function uses the edge detection filter based on the structure tensor and the softsign function described in Example 1, including the following steps:

[0084] Step 1: Calculate the vertical Bouguer gravity anomaly data G z ;

[0085] Step 1.1, based on the gravity observation data and terrain data of each gravity point, calculate the free air gravity anomaly value, terrain correction value and Bouguer correction value corresponding to each gravity point;

[0086] Step 1.2: For each gravity point, add the corresponding free air gravity anomaly value, terrain correction value and Bouguer correction value to obtain the corresponding vertical Bouguer gravity anomaly value. The vertical Bouguer gravity anomaly data G z Includes the coordinates of all gravity points and the corresponding vertical Bouguer gravity anomalies:

[0087] G z =G zfa +TC+BG

[0088] Among them, G z is the vertical Bouguer gravity anomaly data, which represents the distribution of vertical Bouguer gravity anomaly values ​​of the gravity point; G zfa is the free-air gravity anomaly data, which indicates the distribution of the free-air gravity anomaly values ​​of the gravity point; TC is the terrain correction data, which indicates the distribution of the terrain correction values ​​of the gravity point; BG is the Bouguer correction data, which indicates the distribution of the Bouguer correction values ​​of the gravity point.

[0089] Step 2: Based on the vertical Bouguer gravity anomaly data G z , the components of the gravity gradient tensor are calculated as follows:

[0090]

[0091] G xz , G yz and G zz are the components of the gravity gradient tensor in the x direction, y direction, and z direction, which are equal to the vertical Bouguer gravity anomaly data G zThe first derivatives in the x-, y-, and z-directions, respectively. The z-direction is the direction of gravity, and the x- and y-directions are two perpendicular directions in the horizontal plane.

[0092] Step 3: Based on the gravity gradient tensor and Gaussian envelope G σ (x,y), the three-dimensional structure tensor matrix is ​​calculated by the following formula:

[0093]

[0094] Among them, T is the three-dimensional structure tensor matrix, G σ (x,y) is the Gaussian envelope, * is the convolution symbol;

[0095]

[0096] Among them, σ x and σ y The components of the standard deviation of the Gaussian envelope in the x and y directions, respectively, and the standard deviation of the Gaussian envelope

[0097] The three-dimensional structure tensor matrix T is as follows:

[0098]

[0099] Among them, T 11 、T 12 、T 13 、T 21 、T 22 、T 23 、T 31 、T 32 , and T 33 are all components in the three-dimensional structure tensor matrix.

[0100] Step 4: Filter based on the components in the three-dimensional structure tensor matrix and the softsign function.

[0101] Step 4.1: The first filter performs filtering based on the components of the three-dimensional structure tensor matrix and outputs the corresponding edge detection filtering results:

[0102]

[0103] Among them, the intermediate quantity THDTED satisfies:

[0104]

[0105] Among them, TDRTED represents the edge detection filtering result of the first filter, THDTED x ,THDTED y and THDTED zare the first-order derivatives of the intermediate quantity THDTED in the x, y and z directions, tan -1 Represents the inverse tangent function.

[0106] Step 4.2: The second filter calculates the corresponding edge detection filter result based on the three-dimensional structure tensor matrix and the softsign function:

[0107]

[0108] Wherein, SFTED is the edge detection filtering result of the second filter, and k is a preset positive value.

[0109] Example 3

[0110] A computer device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, the edge detection filter based on the structure tensor and the softsign function in the above embodiment 1 is implemented.

[0111] Example 4

[0112] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the edge detection filter based on the structure tensor and the softsign function in the above-mentioned embodiment 1.

[0113] Example 5

[0114] A computer program product includes a computer program, which implements the edge detection filter based on the structure tensor and the softsign function in the above embodiment 1 when the computer program is executed by a processor.

[0115] It should be noted that the specific embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. An edge detection filter based on structure tensor and softsign function, characterized in that, It includes vertical Bouguer gravity anomaly data calculation module, gravity gradient tensor calculation module, three-dimensional structure tensor matrix calculation module and filtering module in sequence; Vertical Bouguer gravity anomaly data calculation module: used to input gravity observation data and terrain data of each gravity point to obtain vertical Bouguer gravity anomaly data; Gravity gradient tensor calculation module: used to input vertical Bouguer gravity anomaly data and obtain gravity gradient tensor; Three-dimensional structure tensor matrix calculation module: used to input the gravity gradient tensor and obtain the three-dimensional structure tensor matrix based on the gravity gradient tensor and Gaussian envelope; Filtering module: used to input the three-dimensional structure tensor matrix, filter it based on the softsign function, and output the edge detection filtering result; The gravity gradient tensor calculation module is based on the vertical Bouguer gravity anomaly data G z , the gravity gradient tensor is calculated by the following formula: G xz , G yz and G zz are the x-, y-, and z-components of the gravity gradient tensor, respectively; the z-direction is the direction of gravity, and the x- and y-directions are two directions perpendicular to each other in the horizontal plane; The three-dimensional structure tensor matrix calculation module calculates the three-dimensional structure tensor matrix using the following formula: Among them, T is the three-dimensional structure tensor matrix, G σ (x,y) is the Gaussian envelope, * is the convolution symbol; Among them, σ x and σ y are the components of the standard deviation of the Gaussian envelope in the x and y directions, and the standard deviation of the Gaussian envelope The three-dimensional structure tensor matrix T is as follows: Among them, T 11 、T 12 、T 13 、T 21 、T 22 、T 23 、T 31 、T 32 , and T 33 are all components in the three-dimensional structure tensor matrix T; The filtering module includes a first filter, and the edge detection filtering result of the first filter is: Among them, the intermediate quantity THDTED satisfies: Among them, TDRTED represents the edge detection filtering result of the first filter, THDTED x 、THDTED y and THDTED z are the first-order derivatives of the intermediate quantity THDTED in the x, y and z directions, tan -1 represents the inverse tangent function; The filtering module further includes a second filter, and the edge detection filtering result corresponding to the second filter is: Wherein, SFTED is the edge detection filtering result of the second filter, and k is a positive value.

2. The edge detection filter based on structure tensor and softsign function according to claim 1, characterized in that The vertical Bouguer gravity anomaly data calculation module calculates the free air gravity anomaly value, terrain correction value and Bouguer correction value corresponding to each gravity point based on the input gravity observation data and terrain data of each gravity point; For each gravity point, the corresponding free air gravity anomaly value, terrain correction value and Bouguer correction value are added together to obtain the corresponding vertical Bouguer gravity anomaly value. The vertical Bouguer gravity anomaly data G z Includes the coordinates of all gravity points and the corresponding vertical Bouguer gravity anomalies.

3. An edge detection filtering method based on structure tensor and softsign function, characterized in that: Implement any one of the edge detection filters based on the structure tensor and the softsign function in claims 1-2.

4. A computer device, characterized in that: The invention comprises a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, any one of the edge detection filters based on the structure tensor and the softsign function in claims 1-2 is implemented.

5. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the edge detection filter based on the structure tensor and the softsign function according to any one of claims 1 to 2 is implemented.

6. A computer program product, characterized in that The invention comprises a computer program, which implements the edge detection filter based on the structure tensor and the softsign function according to any one of claims 1 to 2 when the computer program is executed by a processor.

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