Marine navigation radar signal processing method based on morphological characteristics

Through the marine navigation radar signal processing method based on morphological characteristics, the weak areas in the radar signal are identified and filled, and the problem of uneven signal strength and weakness under special ship types is solved, and the clear restoration of the target image and the improvement of navigation safety is achieved.

CN119596262APending Publication Date: 2025-03-11CSSC MARINE TECH CO LTD
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Patent Information

Application Number
CN202411518208.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-29
Publication Date
2025-03-11

AI Technical Summary

Technical Problem

In some special ship types, the marine navigation radar has uneven distribution of reflected signals, resulting in target echo fluctuations. Commonly used clutter suppression methods can easily lead to the splitting of the same target along the distance, affecting the driver's judgment and navigation safety.

Method used

A marine navigation radar signal processing method based on morphological characteristics is adopted to detect peaks and blank points of scanning lines, identify and fill places with weak echoes, and perform the first and second fillings to restore the real radar target image.

Benefits of technology

Effectively prevent the splitting and discontinuity of the same target, provide clearer and more realistic radar detection targets, improve navigation safety, reduce computing complexity, and have real-time online processing capabilities.

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Abstract

The invention relates to a marine navigation radar signal processing method based on morphological characteristics. The method comprises the following steps: step 1, receiving a starting request of a radar image display function; 2, checking whether echo data of the antenna transceiver is received or not, and if so, entering the next step; step 3, checking whether the same target is split and discontinuous in the echo data, that is, a certain target point has a weak echo, and if yes, judging whether the two split echoes belong to the same target or not; 4, closed point detection and second filling are carried out, and if a small-area'vulnerability 'exists in a detected target, second filling is carried out on the detected target to form an image; and 5, outputting the image to a next processing algorithm. According to the processing method, online real-time processing can be carried out, false vulnerabilities and real holes can be distinguished, real navigation perception is provided for users, navigation safety is improved, and engineering implementation is easy.
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Description

Technical Field

[0001] The invention relates to the field of ship navigation radar image and signal processing, and in particular to a ship navigation radar signal processing method based on morphological features. Background Art

[0002] Marine radar is a radar installed on ships for navigation avoidance, ship positioning, and narrow waterway pilotage. It provides necessary observation means for sailors when visibility is poor.

[0003] Marine navigation radar may have uneven distribution of reflected signal strength in some special ship types. This phenomenon is related to many factors, including the hull structure, the installation position of the radar antenna, the sea conditions, and the complexity of the surrounding environment. Some large ships (such as container ships or ships with complex superstructures) may block radar signals in certain parts of the hull, resulting in blind spots in certain directions of the echo. This will cause the echo signal to have uneven signal strength distribution at specific angles.

[0004] The signal strength of this echo is unevenly distributed, which makes the target echo fluctuate and some amplitude values ​​are weak. When the commonly used clutter suppression method is used, it is easy to cause the same target to split along the distance. This sometimes causes confusion to the pilot, making it difficult to distinguish between multiple targets or a single target, thus affecting the pilot's judgment and bringing navigation risks. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the existing technology will cause the same target to be split or discontinuous when the reflected signal strength is unevenly distributed in some special ship types. The present invention adopts a marine navigation radar signal processing method based on morphological features, which backfills the weak signal distribution areas of the radar target echo image according to the actual situation, restores the real radar target image as much as possible, and presents a clearer and more realistic radar detection target.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution provided by the present invention is as follows:

[0007] A method for processing marine navigation radar signals based on morphological features comprises the following steps:

[0008] The first step is to accept the request to enable the radar image display function;

[0009] The second step is to check whether the echo data from the antenna transceiver is received. If it is received, proceed to the next step. If not, the processing ends directly.

[0010] The third step is to check whether the echo data of the antenna transceiver is split or discontinuous for the same target, that is, if there is a weak echo at a certain target point, it is determined that the first filling is required;

[0011] S31. Start the radar gain processing algorithm to obtain the echo intensity of each point on the scan line;

[0012] S32. Detect the peak value of the scan line, detect the peak value of the scan line through the sliding window and record it;

[0013] S33. When the distance between two peaks is less than the same target judgment threshold D, it is considered that all points between the two peaks belong to the same target. If the amplitude of the blank points between the two peaks is greater than a set value, it is considered to be a fault point. If it is determined to be a fault point, the first filling is performed, that is, filling according to the scan line;

[0014] The fourth step is to detect closed points and perform a second filling. After filling according to the scan line, if there is a small hole in the middle of the target, the hole is detected and filled for the second time;

[0015] The above inspection and second filling process includes the following steps:

[0016] S41. Scan line accumulation: after the first filling, the scan lines are accumulated to form an image of size L×R, where L is the number of scan lines accumulated and R is the length of each scan line.

[0017] S42. Binarize the image, forming a new 0-1 image by binarizing the image of size L×R;

[0018] S43. traverse the entire image and search for the first point that is 0, in a traversal manner, from the direction of small direction to the direction of large direction, from near to far;

[0019] S44. The first point that is 0 is regarded as the current point. Starting from the current point, the top, bottom, left, and right directions of the current point are traversed and filled with 1. The points that are not 0 in the top, bottom, left, and right directions of the current point are added to the queue to be searched, and the current point is added to the queue of suspected vulnerability points;

[0020] S45. Take the first point from the queue to be searched as the current point, traverse the current point up, down, left, and right and fill it with 1, add the points that are not 0 in the four directions of the current point up, down, left, and right to the queue to be searched, and add the current point to the queue of suspected vulnerability points;

[0021] S46. Recursively perform the operation step by step until the queue to be searched is cleared, and obtain the final queue of suspected vulnerability points;

[0022] S47. Check the final suspected vulnerability point queue. If there is an image boundary point in the queue, discard the entire suspected vulnerability point queue, go to step S43, and continue searching for the next point that is 0;

[0023] S48. Determine whether the vulnerability point in the suspected vulnerability point queue is a fault vulnerability. The queue size of the suspected vulnerability point queue represents the size of the vulnerability area. If the vulnerability area is too large, it is considered that the vulnerability is not a fault vulnerability, but a normal echo hole. If it is a normal echo hole, the area of ​​the vulnerability is between 25㎡ and 50㎡. If it is not a fault vulnerability, discard the entire suspected vulnerability point queue and go to step S43 to continue searching for the next point that is 0;

[0024] S49. Then determine whether the length and width of the shape of the suspected vulnerability point conform to a normal ratio. If the vulnerability is a significantly long and narrow shape, it is also considered that the vulnerability is not a fault vulnerability, and the remaining vulnerabilities in the suspected vulnerability point queue are all identified as fault vulnerabilities;

[0025] S410. Traverse the entire checked vulnerability point queue, calculate the average value of the amplitude of all points where the vulnerability is wrapped, and fill the positions of all vulnerability points with the average value;

[0026] S411. Go to step S43 until no 0 point is found, and the second filling is completed to obtain the filled image;

[0027] The fifth step is to output the image to the next processing algorithm of the marine navigation radar signal processing and end the processing.

[0028] In S32, the peak value of the scan line is detected by sliding window detection. For consecutive identical values, the peak value is calculated according to the first and last values ​​of the same value, that is, when A′ r >A′ r+1 And A′ r >A′ r-1 When A′ r is a peak value of the scan line. If there are points on the scan line with continuous equal amplitudes, it is calculated based on the boundaries of all equal values, that is, if A′ r+1 =A′ r+2 =A′ r+3 =…A′ r+i , then when A′ r+i >A′ r+i+1 And A′ r >A′ r-1 When A′ r+i / 2 is a peak value of the scan line, and the position of the peak value is recorded to form a peak value set P = {r1, r2, r3, ...}, where,

[0029] r is the distance of a point on the scan line,

[0030] A′ r is the echo intensity of the point at distance r on the scan line after radar gain processing,

[0031] A′ r+i is the echo intensity of the point r+i on the scanning line after radar gain processing,

[0032] In S33, if the distance between two peaks is less than the judgment threshold D, and the amplitudes of all blank points between the peaks are greater than a preset value, they are considered to be fault points and need to be filled.

[0033] In S33, the distance between the two peaks is used to determine whether the two echoes are the same target. When the distance between the two peaks is less than the same target judgment threshold D, that is,

[0034] r i+1 -r i <D

[0035] Think i to r i+1 All points in between may belong to the same target;

[0036] Traverse all r i to r i+1 If there is a point between If the point r j is a blank point. If the original amplitude of the blank point is smaller than the gain threshold but still strong, then the point can be considered as a fault point. If the number of fault points is within r i to r i+1 When the number of all points between is low, it is considered that r i to r i+1 All fault points between them should be filled with a larger amplitude;

[0037] If (α is the comparison threshold of the original amplitude, usually 0.3), let r i to r i+1 The number of all fault points between is N, r i to r i+1 The number of all points between is M, then When (τ is the maximum ratio, generally 0.4), it is considered that all fault points should be filled, that is,

[0038]

[0039] In the fourth step, after the first filling by scanning line in the third step, the second filling by image filling is performed.

[0040] In the fourth step, a preliminary image is first formed through the scan line accumulation method to prepare for subsequent filling judgment. The scan line is one-dimensional, and it takes the accumulation of multiple scan lines to form an image. The accumulated number L of scan lines is related to the current range. The larger the range, the smaller the target, and the smaller the accumulated number L of scan lines; the smaller the range, the larger the target, and the larger the accumulated number L of scan lines. After the scan lines are accumulated, an image of size LXR is formed.

[0041] In S46, a recursive method is used to search the queue step by step to form a final queue of suspected vulnerability points. After inspection and judgment, all vulnerability points are found, and the vulnerability point has a small blank part in the middle.

[0042] For a small blank area found, whether it is a real vulnerability is determined by whether it is connected to the boundary and the size of the area, that is, the aspect ratio.

[0043] In S49, the method for calculating the shape of the vulnerability point is: traverse the suspected vulnerability point queue and find the maximum value (x max ,y max ) and the minimum value (x min ,y min ),

[0044] The aspect ratio is If R a >R amax or R a <R amin , it is considered that the aspect ratio does not conform to the integral ratio, and the vulnerability point queue is discarded. Generally, R amax Take 10 to 20, R amin Take 0.1 to 0.05.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. When the marine navigation radar detects ships, if the reflected signal strength of some special ship types is unevenly distributed, the use of existing signal processing technology will cause the same target to be split or discontinuous. The present invention can fill the signal before the existing signal processing technology to prevent the occurrence of such problems and affect the observation effect.

[0047] 2. The method of the present invention has low computational complexity, reduces the burden on the computing system, and is easy to implement in engineering.

[0048] 3. The present invention can perform real-time processing during the normal operation of the radar and has online processing capabilities.

[0049] 4. The present invention can distinguish between a false hole in a target and a real hole included in the target, which is helpful to give users a more realistic navigation perception and improve navigation safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The present invention is a flow chart of a method for processing marine navigation radar signals based on morphological features. DETAILED DESCRIPTION

[0051] Below we further elaborate on the technical solution of the present invention in combination with the accompanying drawings and specific embodiments, in order to more clearly understand its operating principle and workflow, but this cannot be used to limit the protection scope of the present invention.

[0052] The present invention is a marine navigation radar signal processing method based on morphological features. Aiming at the uneven distribution of the strength of the same target signal, the morphological features in the radar echo signal are extracted and analyzed to identify and process specific special targets and provide decision support. The method can accurately identify important targets in complex marine environments and ensure the safe navigation of ships.

[0053] like Figure 1 As shown, the present invention is a marine navigation radar signal processing method based on morphological features, which aims to solve the problem that when the reflection signal strength is unevenly distributed on certain special ship types, the use of existing technologies will cause the same target to be split or discontinuous.

[0054] In terms of specific operation, the processing method of the present invention includes the following steps:

[0055] The first step is to accept the request to enable the radar image display function;

[0056] The second step is to check whether the echo data from the antenna transceiver is received. If so, proceed to the next step;

[0057] The third step is to check whether the echo data of the antenna transceiver is split or discontinuous for the same target, that is, if there is a weak echo at a certain target point, fill it with a stronger echo to ensure the integrity of the target.

[0058] The echo data of the antenna transceiver is transmitted in the form of a scan line. The echo intensity (i.e., amplitude) of a point on the scan line with an azimuth of θ is set as A. r , r is the distance of the point, and the total length of the scan line is R. The inspection and filling process includes the following steps:

[0059] S31. Radar gain processing algorithm. The current radar gain threshold is A, then the echo intensity at a point on the scan line is

[0060] A′ r =max(A r -A, 0)

[0061] S32. Scan line peak detection. Sliding window detects the peak value of the scan line. When A′ r >A′ r+1 And A′ r >A′ r-1 When A′ r is a peak value of the scan line. If there are points on the scan line with continuous equal amplitudes, it is calculated based on the boundaries of all equal values, that is, if A′ r+1 =A′ r+2 =A′ r+3 =…A′ r+i , then when A′ r+i >A′ r+i+1 And A′ r >A′ r-1 When A′ r+i / 2 It is a peak value of the scan line and the position of the peak value is recorded to form a peak value set P = {r1, r2, r3, ...}.

[0062] S33. When the distance between the two peaks is less than the same target judgment threshold D, that is,

[0063] r i+1 -r i <D

[0064] Think i to r i+1 All points in between may belong to the same object.

[0065] Traverse all r i to r i+1 If there is a point between If the point r j is a blank point. If the original amplitude of the blank point is smaller than the gain threshold but still strong, then the point can be considered as a fault point. If the number of fault points is within r i to r i+1 When the number of all points between is low, it is considered that r i to r i+1 All fault points in between should be filled with a larger amplitude.

[0066] If (α is the comparison threshold of the original amplitude, generally 0.3 is selected, which means it is still strong), let r i to r i+1 The number of all fault points between is N, r i to r i+1 The number of all points between is M, then When (T is the maximum ratio, generally 0.4 is selected, which means the ratio is low), it is considered that all fault points should be filled, that is,

[0067] This is the larger value that needs to be filled.

[0068] The fourth step is to detect and fill closed points. After filling according to the scan lines, there may be small "holes" in the middle of the target. It is necessary to check the holes and fill them again to form an image.

[0069] The inspection and filling process consists of the following steps:

[0070] S41. Scan line accumulation. The scan line is one-dimensional, and it takes the accumulation of multiple scan lines to form an image. According to the actual situation, the number of scan line accumulation L is related to the current range. The larger the range, the smaller the target, and the smaller the number of scan line accumulation L; the smaller the range, the larger the target, and the larger the number of scan line accumulation L. After the scan line is accumulated, an image of size L×N can be formed, where L is the number of scan line accumulations, and R is the length of each scan line. The size of the image is the product of L and R.

[0071] S42. Binarize the L×N image to form a new 0-1 image, setting all points with A′r>0 to 1 and all points with A′r=0 to 0.

[0072] S43. traverse the entire image and search for the first 0 point, and the traversal method is from the direction of small direction to the direction of large direction, from near to far.

[0073] S44. The first point that is 0 is regarded as the current point. Starting from the current point that is 0, the current point is traversed up, down, left, and right and filled with 1 by recursion (the tool used for recursion is depth-first search DFS). The points that are not 0 in the four directions of the current point are added to the queue to be searched, and the current point is added to the queue of suspected vulnerability points.

[0074] S45. Take the first point from the search team as the current point, traverse the current point up, down, left, and right and fill them with 1, add the points in the four directions of the current point that are not 0 to the queue to be searched, and add the current point to the queue of suspected vulnerability points.

[0075] S46. Recurse step by step until the search queue is empty.

[0076] S47. Check the suspected vulnerability point queue. If there are image boundary points in the queue, discard the entire suspected vulnerability point queue and go to step S43 to continue searching for the next point that is 0.

[0077] S48. The size of the suspected vulnerability point queue represents the size of the vulnerability area. If the vulnerability area is too large, it is considered that the vulnerability is not a fault vulnerability, but a normal echo hole. Generally, the area of ​​the vulnerability is 25m 2 Up to 50m 2 If it is not a fault vulnerability, the entire suspected vulnerability point queue is discarded, and the process goes to step S43 to continue searching for the next point that is 0.

[0078] S49. During inspection, the length and width of the suspected vulnerability point should be in normal proportion. If the vulnerability is a significantly long and narrow shape, it is considered that the vulnerability is not a fault vulnerability.

[0079] The calculation method of the vulnerability point shape is: traverse the suspected vulnerability point queue and find the maximum value (x max ,y max ) and the minimum value (x min ,y min ),

[0080] The aspect ratio is If R a >R amax or R a <R amin , it is considered that the aspect ratio does not conform to the integral ratio, and the vulnerability point queue is discarded. Generally, R amax Take 10 to 20, R amin Take 0.1 to 0.05;

[0081] If it is not a fault vulnerability, discard the entire suspected vulnerability point queue, go to step S43, and continue searching for the next point that is 0.

[0082] S410. Traverse the entire vulnerability point queue, calculate the average value of the amplitudes of all points covered by the vulnerability, and fill the positions of all vulnerability points with the changed value.

[0083] S411. Go to step S43 until no 0 point is found, completing the second filling and obtaining the filled image.

[0084] Step 5: Output the filled image to the next processing algorithm.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A marine navigation radar signal processing method based on morphological features, characterized in that: The method comprises the following steps: The first step is to accept the request to enable the radar image display function; The second step is to check whether the echo data from the antenna transceiver is received. If it is received, proceed to the next step. If not, the processing ends directly. The third step is to check whether the echo data of the antenna transceiver is split or discontinuous for the same target, that is, if there is a weak echo at a certain target point, it is determined that the first filling is required; S31. Start the radar gain processing algorithm to obtain the echo intensity of each point on the scan line; S32. Detect the peak value of the scan line, detect the peak value of the scan line through the sliding window and record it; S33. When the distance between two peaks is less than the same target judgment threshold D, it is considered that all points between the two peaks belong to the same target. If the amplitude of the blank points between the two peaks is greater than a set value, it is considered to be a fault point. If it is determined to be a fault point, the first filling is performed, that is, filling according to the scan line; The fourth step is to detect closed points and perform a second filling. After filling according to the scan line, if there is a small hole in the middle of the target, the hole is detected and filled for the second time; The above inspection and second filling process includes the following steps: S41. Scan line accumulation: after the first filling, the scan lines are accumulated to form an image of size L×R, where L is the number of scan lines accumulated and R is the length of each scan line. S42. Binarize the image, forming a new 0-1 image by binarizing the image of size L×R; S43. traverse the entire image and search for the first point that is 0, in a traversal manner, from the direction of small direction to the direction of large direction, from near to far; S44. The first point that is 0 is regarded as the current point. Starting from the current point, the top, bottom, left, and right directions of the current point are traversed and filled with 1. The points that are not 0 in the top, bottom, left, and right directions of the current point are added to the queue to be searched, and the current point is added to the queue of suspected vulnerability points; S45. Take the first point from the queue to be searched as the current point, traverse the current point up, down, left, and right and fill it with 1, add the points that are not 0 in the four directions of the current point up, down, left, and right to the queue to be searched, and add the current point to the queue of suspected vulnerability points; S46. Recursively perform the operation step by step until the queue to be searched is cleared, and obtain the final queue of suspected vulnerability points; S47. Check the final suspected vulnerability point queue. If there is an image boundary point in the queue, discard the entire suspected vulnerability point queue, go to step S43, and continue searching for the next point that is 0; S48. Determine whether the vulnerability point in the suspected vulnerability point queue is a fault vulnerability. The queue size of the suspected vulnerability point queue represents the size of the vulnerability area. If the vulnerability area is too large, it is considered that the vulnerability does not belong to a fault vulnerability, but a normal echo hole. If it does not belong to a fault vulnerability, the entire suspected vulnerability point queue is discarded, and go to step S43 to continue searching for the next point that is 0; S49. Then determine whether the length and width of the shape of the suspected vulnerability point conform to a normal ratio. If the vulnerability is a significantly long and narrow shape, it is also considered that the vulnerability is not a fault vulnerability, and the remaining vulnerabilities in the suspected vulnerability point queue are all identified as fault vulnerabilities; S410. Traverse the entire checked vulnerability point queue, calculate the average value of the amplitude of all points where the vulnerability is wrapped, and fill the positions of all vulnerability points with the average value; S411. Go to step S43 until no 0 point is found, and the second filling is completed to obtain the filled image; The fifth step is to output the image to the next processing algorithm of the marine navigation radar signal processing and end the processing.

2. The method for processing marine navigation radar signals based on morphological features according to claim 1, characterized in that: In S32, the peak value of the scan line is detected by sliding window detection. For consecutive identical values, the peak value is calculated according to the first and last values ​​of the same value, that is, when A′ r >A′ r+1 And A′ r >A′ r-1 When A′ r is a peak value of the scan line. If there are points on the scan line with continuous equal amplitudes, it is calculated based on the boundaries of all equal values, that is, if A′ r+1 =A′ r+2 =A′ r+3 =…A′ r+i , then when A′ r+i >A′ r+i+1 And A′ r >A′ r-1 When A′ r+i / 2 is a peak value of the scan line, and the position of the peak value is recorded to form a peak value set P = {r1, r2, r3, ...}, where, r is the distance of a point on the scan line, A′ r is the echo intensity of the point at distance r on the scan line after radar gain processing, A′ r+i It is the echo intensity of the point at distance r+i on the scan line after radar gain processing.

3. The method for processing marine navigation radar signals based on morphological features according to claim 1, characterized in that: In S33, if the distance between the two peaks is less than the judgment threshold D, and the amplitudes of all blank points between the peaks are greater than a preset value, they are considered to be fault points and need to be filled.

4. The method for processing marine navigation radar signals based on morphological features according to claim 3 is characterized in that: In S33, the distance between the two peaks is used to determine whether the two echoes are the same target. When the distance between the two peaks is less than the same target judgment threshold D, that is, r i+1 -r i <D Think i to r i+1 All points in between may belong to the same target; Traverse all r i to r i+1 If there is a point between If the point r j is a blank point. If the original amplitude of the blank point is smaller than the gain threshold but still strong, the point is considered to be a fault point. If the number of fault points is within r i to r i+1 When the number of all points between is low, it is considered that r i to r i+1 All fault points between them should be filled with a larger amplitude; If α is the comparison threshold of the original amplitude, and 0.3 is generally selected as a strong threshold, which is considered to be a fault point; let r i to r i+1 The number of all fault points between is N, r i to r i+1 The number of all points between is M, then When τ is the maximum ratio, 0.4 is generally selected as a low ratio, and it is believed that all fault points should be filled, that is, the amplitude to be filled is:

5. The method for processing marine navigation radar signals based on morphological features according to claim 1, characterized in that: In the fourth step, after the first filling by scanning line in the third step, the second filling by image filling is performed.

6. The method for processing marine navigation radar signals based on morphological features according to claim 1, characterized in that: In the fourth step, a preliminary image is first formed through the scan line accumulation method in preparation for subsequent filling judgment. The scan line is one-dimensional, and it takes the accumulation of multiple scan lines to form an image. The accumulated number L of scan lines is related to the current range. The larger the range, the smaller the target, and the smaller the accumulated number L of scan lines; the smaller the range, the larger the target, and the larger the accumulated number L of scan lines. After the scan lines are accumulated, an image of size L×R is formed.

7. The method for processing marine navigation radar signals based on morphological features according to claim 1, characterized in that: In S46, a recursive method is used to search the queue step by step to form a final queue of suspected vulnerability points. After inspection and judgment, all vulnerability points are found, and the vulnerability point has a small blank part in the middle.

8. The method for processing marine navigation radar signals based on morphological features according to claim 7, characterized in that: For a small blank area found, whether it is a real vulnerability is determined by whether it is connected to the boundary and the size of the area, that is, the aspect ratio.

9. The method for processing marine navigation radar signals based on morphological features according to claim 1, characterized in that: In S49, the method for calculating the shape of the vulnerability point is: traverse the suspected vulnerability point queue and find the maximum value (x max ,y max ) and the minimum value (x min ,y min ), The aspect ratio is If R a >R amax or R a <R amin , it is considered that the aspect ratio does not conform to the integral ratio, and the vulnerability point queue is discarded. Generally, R amax Take 10 to 20, R amin Take 0.1 to 0.05.