Edge detection filter based on structure tensor and softsign function

Abstract

The invention discloses an edge detection filter based on a structure tensor and a softsign function, and aims at processing and interpretation analysis of a gravity gradient tensor, and edge detection filtering is carried out based on a three-dimensional structure tensor and the softsign function. The method can quickly determine the horizontal distribution range of the target, and effectively reduces the problems of divergence, fuzziness, deformation and the like. The boundary of the deep anomalous body can be clearly and accurately delineated under the condition of less prior information, and false boundaries between positive and negative anomalous bodies are avoided; the method can adapt to abnormal data of different targets or scales, human intervention is reduced, the screening process is simplified, and meanwhile the reliability of screening results in quality and quantity is ensured.

Description

Technical Field

[0001] The 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 an important part of geophysical data processing and interpretation, and plays a key role in fields such as mineral delineation and structural research. Potential field tensor gradient data contains nine components, which are usually obtained through actual measurement or numerical calculation. Compared with ordinary 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 derivative of the potential field data to identify the edge location. For example, the total horizontal derivative and the maximum value of the analytical signal amplitude can directly depict the boundary of the anomaly, but these methods have low resolution and are not as effective in identifying deep anomalies as shallow anomalies. The tilt angle, as the first equalization filter, effectively solves the shortcomings of previous methods in equalizing different amplitudes. However, the recognition resolution of these equalization filters is still low and is prone to erroneous information when both positive and negative anomalies exist in the study area.

[0004] In order to solve the above problems, researchers have proposed methods based on high-order derivatives, such as the 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, the recognition results often exceed the actual boundary range. In addition, the introduction of high-order derivatives inevitably amplifies the noise and affects 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 the boundaries of geological bodies through its eigenvalues ​​can effectively solve the problem of false anomalies caused by the simultaneous appearance of positive and negative anomalies. The Gaussian envelope used in the structural tensor reduces the sensitivity to noise, but fails to effectively balance the amplitude information at different depths.

[0005] This patent proposes a filter based on three-dimensional structure tensors to be applied to complex synthetic models and actual gravity data, and compares and analyzes it with traditional boundary recognition methods to verify the reliability and effectiveness of the new method. The edge detection filter proposed in this invention significantly enhances the boundary recognition capability in geophysical applications, overcomes the limitations of existing technologies, and provides a more reliable underground 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 a structure tensor and a softsign function to address the above problems existing in current fracture identification.

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

[0008] An edge detection filter based on a structure tensor and a 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 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 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 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-direction 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 by 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, respectively, and the standard deviation of the Gaussian envelope

[0023] The three-dimensional structure tensor matrix T is recorded 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 They 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 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 above-mentioned edge detection filters based on a structure tensor and a softsign function is implemented.

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

[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 edge detection filters based on the structure tensor and the softsign function as described above.

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

[0039] Boundary recognition can be used to delineate the horizontal distribution range of the target, and is an indispensable work link in the interpretation of potential field data. Traditional boundary recognition methods are prone to divergence, blur, deformation and other problems. The present invention focuses on the processing and interpretation analysis of gravity gradient tensors, and studies edge detection filters based on structure tensors and softsign functions. Compared with the prior art, the present invention 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, blur 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 The edge detection filter of the present invention realizes the filtering process.

[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] Embodiment 1:

[0046] The edge detection filter based on structure tensor and softsign function comprises 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 in sequence.

[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, and 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 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 indicates the distribution of the vertical Bouguer gravity anomaly value of the gravity point; Gzfa is the free air gravity anomaly data, indicating the distribution of the free air gravity anomaly values ​​of the gravity point; TC is the terrain correction data, indicating the distribution of the terrain correction values ​​of the gravity point; BG is the Bouguer correction data, indicating 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-order derivatives in the x-direction, y-direction, and z-direction, respectively. The z-direction is the direction of gravity, and the x-direction and y-direction are two directions perpendicular to each other 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 that contain both positive and negative density; or there may be problems with insufficient image resolution; or the stability of 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 are 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 recorded 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 They 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 result, 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 filter of the first filter are reduced.

[0077] Furthermore, based on the first filter, the filtering module also includes a second filter, and 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 based on the first filter. The edge detection filter result of the second filter is as follows: Figure 2 (f) as 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] Embodiment 2:

[0083] The edge detection filtering method based on structure tensor and softsign function, using the edge detection filter based on structure tensor and softsign function described in Example 1, comprises 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 indicates the distribution of the vertical Bouguer gravity anomaly value of the gravity point; G zfa is the free air gravity anomaly data, indicating the distribution of the free air gravity anomaly values ​​of the gravity point; TC is the terrain correction data, indicating the distribution of the terrain correction values ​​of the gravity point; BG is the Bouguer correction data, indicating 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 by the following formula:

[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-order derivatives in the x-direction, y-direction and z-direction respectively. The z-direction is the direction of gravity, and the x-direction and y-direction are two directions perpendicular to each other 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 are 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 recorded 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 result:

[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-mentioned 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. When the computer program is executed by a processor, the edge detection filter based on the structure tensor and the softsign function in the above embodiment 1 is implemented.

[0115] It should be noted that the specific embodiments described in the present invention are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the attached claims.

Claims

1. An edge detection filter based on a structure tensor and a softsign function, characterized in that: It 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 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 based on the softsign function, and output the edge detection filtering result.

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 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. The edge detection filter based on structure tensor and softsign function according to claim 2, characterized in that: 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 They are the x-, y- and z-direction 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.

4. The edge detection filter based on structure tensor and softsign function according to claim 3, characterized in that: The three-dimensional structure tensor matrix calculation module calculates the three-dimensional structure tensor matrix by 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, respectively, and the standard deviation of the Gaussian envelope The three-dimensional structure tensor matrix T is recorded as follows: Among them, T 11 、T 12 、T 13 、T 21 、T 22 、T 23 、T 31 、T 32 , and T 33 They are all components in the three-dimensional structure tensor matrix T.

5. The edge detection filter based on structure tensor and softsign function according to claim 4, characterized in that: 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.

6. The edge detection filter based on structure tensor and softsign function according to claim 5, characterized in that: 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.

7. 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 1-6.

8. 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 1-6 is implemented.

9. 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 the processor, the edge detection filter based on the structure tensor and the softsign function in any one of claims 1 to 6 is implemented.

10. 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 in any one of claims 1 to 6 when being executed by a processor.

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