Sea surface floating small target detection method and device based on feature optimization and false alarm controllable three-dimensional concave packing

Abstract

This invention discloses a method and apparatus for detecting small floating targets on the sea surface based on feature optimization and controllable false alarm three-dimensional concave hull. The method includes: extracting eight-dimensional feature vectors of sea clutter and the target sample from radar echo reception; selecting the optimal three-dimensional feature vector from the eight-dimensional feature vectors of both the sea clutter and the target sample, using the optimal three-dimensional feature vector of the sea clutter as training sample points and the optimal three-dimensional feature vector of the target sample as the target sample point; using a controllable false alarm alpha concave hull algorithm, prioritizing maximum single-pass concave hull volume loss, and successively deleting false alarm points from the training sample points according to the false alarm rate to update the training sample points; obtaining a convex hull region containing all training sample points; transforming the convex hull region into a concave hull decision region containing all training sample points; determining the position of the target sample point corresponding to the concave hull decision region to obtain the detection result. Accurate sea surface target detection is achieved while maintaining controllable false alarms.

Description

Technical Field

[0001] This invention belongs to the field of radar target classification, specifically relating to a method and device for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms. Background Technology

[0002] Detecting small floating targets against a sea clutter background has always been a key focus and challenge for experts and scholars both domestically and internationally. Because small targets have very small radar cross sections (RCS) and weak radar echoes, traditional energy-based detectors often suffer from low detection probabilities. Non-energy-based feature detection techniques offer an effective solution to this problem.

[0003] Early feature detectors focused on single-feature detection, primarily distinguishing between sea clutter and target echoes by studying their different characteristics across various transform domains. However, single-feature target detection algorithms have limitations when dealing with different sea conditions. To improve detection performance by utilizing more features, Shui et al. proposed a three-feature convex hull detector based on amplitude and Doppler spectrum, achieving joint detection of time-domain and frequency-domain features. Since sea clutter and target echoes are more separable in the time-frequency three-feature space, Shui et al. further proposed a convex hull detector based on these features, significantly improving its performance. However, comparisons of detection results revealed that these two three-feature convex hull detection algorithms performed better on different datasets. Furthermore, the distribution of sea clutter in the three-dimensional feature space depends on feature selection; in most cases, this distribution is concave. When using the convex hull to determine the detection area composed of sea clutter features, forcing a concave distribution to become convex inevitably expands the decision region, thus reducing detection probability.

[0004] Furthermore, in the era of big data, both the volume and dimensionality of data are constantly increasing. How to extract highly differentiated features from high-dimensional data is a crucial issue. Feature selection is one of the most effective dimensionality reduction techniques currently available. It reduces the dimensionality of data by removing relevant and redundant features while retaining irrelevant features, forming an optimal feature subset. Summary of the Invention

[0005] Purpose of the invention: To address the problem of sea clutter affecting the detection of small floating targets on the sea surface, this invention proposes a method and device for detecting small floating targets on the sea surface based on feature optimization and controllable false alarm three-dimensional concave hull. By using the mRMR algorithm to remove redundant and highly correlated feature vectors, the optimal three-dimensional feature vector is selected, and combined with the controllable false alarm three-dimensional concave hull algorithm to complete the detection, excellent detection performance is achieved.

[0006] Technical solution: To achieve the objectives of this invention, the technical solution adopted is as follows:

[0007] In a first aspect, the present invention proposes a method for detecting small floating targets on the sea surface based on feature optimization and controllable false alarm three-dimensional concave hull, comprising the following steps:

[0008] Collect radar echoes and extract the eight-dimensional feature vectors of sea clutter and the eight-dimensional feature vectors of the sample to be detected from the radar echoes.

[0009] The optimal three-dimensional feature vectors are selected from the eight-dimensional feature vectors of the sea clutter and the eight-dimensional feature vectors of the sample to be detected using a feature optimization algorithm. The optimal three-dimensional feature vectors of the sea clutter are used as training sample points, and the optimal three-dimensional feature vectors of the sample to be detected are used as the sample points to be detected.

[0010] Using the alpha-indentation algorithm with controllable false alarms, the algorithm prioritizes maximizing the loss of the indentation volume in a single attempt. False alarm points are then successively removed from the training sample points based on the false alarm rate, thus updating the training sample points.

[0011] The convex hull learning algorithm is used to obtain the convex hull region containing all training sample points, and the convex hull region is transformed into the concave hull decision region containing all training sample points.

[0012] The location of the sample point to be detected corresponding to the concave hull decision region is determined to obtain the detection result.

[0013] In conjunction with the first aspect, further, the eight-dimensional feature vectors extracted from sea clutter and the sample to be detected include: the Normalized Hurst Exponent (NHE), Relative Average Amplitude (RAA), Relative Doppler Peak Height (RDPH), Relative Vector Entropy (RVE), Ridge Integration (RI), Maximum Size of Connected Regions (MS), Number of Connected Regions (NR), and the Normalized Sample Covariance Matrix and Generalized Likelihood Ratio Test (NSCM-GLRT) based on the radar received echo. These eight features are then used to form the eight-dimensional feature vectors.

[0014] In conjunction with the first aspect, furthermore, a feature optimization algorithm is used to select the optimal three-dimensional feature vector from the eight-dimensional feature vector of the sea clutter and the eight-dimensional feature vector of the sample to be detected, respectively. The specific steps include:

[0015] The eight-dimensional feature vector of the sea clutter and the eight-dimensional feature vector of the sample to be detected are concatenated into a hybrid eight-dimensional feature vector;

[0016] The minimum redundancy maximum correlation feature optimization algorithm mRMR is used to select the best one-dimensional mixed feature vector from the mixed eight-dimensional feature vectors.

[0017] Using mRMR, the second and third best one-dimensional mixed feature vectors are selected sequentially from the mixed eight-dimensional feature vectors, and together with the best one-dimensional mixed feature vector, they form the best three-dimensional mixed feature vector;

[0018] The optimal three-dimensional hybrid feature vector is separated into the optimal three-dimensional feature vector of sea clutter and the optimal three-dimensional feature vector of the sample to be detected.

[0019] Building upon the first aspect, further, the minimum redundancy maximum correlation feature optimization algorithm (mRMR) is used to select the optimal one-dimensional mixed feature vector from the mixed eight-dimensional feature vectors. The specific steps include:

[0020] The correlation between each vector in the mixed feature vector and the stability label vector is calculated based on the definition of mutual information. The set of feature vectors with the strongest correlation is taken as the optimal one-dimensional mixed feature vector, as shown in the following formula:

[0021]

[0022]

[0023] Where g1 represents the optimal one-dimensional mixed feature vector, MI is the mutual information entropy value, and R... G Represents a mixed feature vector, a j Indicates belonging to R G The one-dimensional vector elements, b represents the stability label vector, a j It belongs to vector a j The elements of the vector b, p(a) j b) is a j The joint probability density function of a and b, p(a j p(b) and p(b) are respectively a j The probability density function of b.

[0024] Building upon the first aspect, further, using mRMR, the second and third best one-dimensional mixed feature vectors are selected sequentially from the mixed eight-dimensional feature vectors, and these are combined with the best one-dimensional mixed feature vector to form the best three-dimensional mixed feature vector. Specific steps include:

[0025] Using the best one-dimensional mixed feature vector, the feature vector that satisfies the following formula is taken as the second best one-dimensional mixed feature vector.

[0026]

[0027]

[0028]

[0029] Where g2 represents the second-best one-dimensional hybrid feature vector, MI is the mutual information entropy value, and a' j Indicates belonging to (R) G One-dimensional vector elements of -g1), (R G -g1) represents the set of eigenvectors remaining after removing the best one-dimensional mixed eigenvector g1, a' j It belongs to vector a' j The element, p(a' j b) is a' j The joint probability density function of b, p(a') j ) is a' j The probability density function, where g1 is an element belonging to vector g1, p(a' j g1) is a' j The joint probability density function of g1 and g2, p(g1) is the probability density function of g1.

[0030] Using the best and second-best one-dimensional hybrid feature vectors, the feature vector satisfying the following formula is taken as the third-best one-dimensional hybrid feature vector.

[0031]

[0032]

[0033]

[0034] Where g3 represents the third-best one-dimensional hybrid feature vector, MI is the mutual information entropy value, G = {g1, g2}, (R G -G) represents the set of eigenvectors remaining after removing the best one-dimensional mixed eigenvector g1 and the second best one-dimensional mixed eigenvector g2, g i It belongs to vector g i The element, p(a' j ,g i ) is a' j and g i The joint probability density function, p(g) i ) is g i The probability density function.

[0035] Building upon the first aspect, further, an alpha-based indentation algorithm with controllable false alarms is used. Based on the principle of maximizing the loss of the indentation volume in a single iteration, false alarm points are successively removed from the training sample points according to the false alarm rate, thus updating the training sample points. Specific steps include:

[0036] Step 1.1: Calculate the number of sample points Q in the set ζ consisting of training sample points;

[0037] Step 1.2: Based on the false alarm rate P F Calculate the number of false alarms: N f =Q×P F ;

[0038] Step 1.3: Iteration count v = 1, operation set ζ v =ζ;

[0039] Step 1.4: Generate the operation set ζ according to the alpha concave hull algorithm. v The concave hull;

[0040] Step 1.5: From the operation set ζ v Remove one vertex from the concave hull and calculate the volume reduction of the concave hull;

[0041] Step 1.6: Find the hull vertex that maximizes the reduction in hull volume;

[0042] Step 1.7: From the operation set ζ v Delete the concave hull vertices found in step 1.6, and the iteration count v = v + 1 to obtain a new operation set ζ. v If the number of iterations v≤N f If the problem persists, return to step 1.4; otherwise, end the iteration. Finally, obtain the set ζ of deleted false alarm points. Nf .

[0043] Building upon the first aspect, the convex hull region is further transformed into a concave hull decision region encompassing all training sample points. Specific steps include:

[0044] Step 2.1: Based on the set ζ of deleted false alarm points Nf The original convex hull Ω, consisting of D triangular faces, is generated using a convex hull learning algorithm. original D is the number of triangular faces;

[0045] Step 2.2: Calculate the perimeter L of all triangular faces of the original convex hull. d ,d=0,1,...,D;

[0046] Step 2.3: Calculate the average perimeter of all triangular faces and use it as the threshold th;

[0047] Step 2.4: Intracut number i = 1, iteration number j = 1, operation region Ω i,j =Ω original Set the maximum number of cuts, dig_num.

[0048] Step 2.5: If j ≤ dig_num, proceed to steps 2.6-2.10; otherwise, end the iteration and jump to step 2.11.

[0049] Step 2.6: Calculate the operating region Ω i,j The perimeter L of all triangular faces j,d ,d=0,1,...,D;

[0050] Step 2.7: Calculate the perimeter L of all triangular faces. j,d The maximum value L in d = 0, 1, ..., D j,max ;

[0051] Step 2.8: If L is satisfied j,max If the condition is met, proceed to steps 2.9-2.10; otherwise, end the iteration and jump to step 2.11.

[0052] Step 2.9: For the operating region Ω i,j Perform the inner section algorithm operation, with the inner section number i = i + 1 and the iteration number j = j, to obtain the updated operation region Ω. i,j ;

[0053] Step 2.10: For the operating region Ω i,j Perform the filling algorithm operation, with the number of iterations j = j + 1 and the number of incisions i = i, to obtain the updated operation region Ω. i,j Skip to step 2.5;

[0054] Step 2.11: Obtain the final concave hull decision region: Ω final =Ω i,j .

[0055] In conjunction with the first aspect, the steps of the Riche algorithm operation further include:

[0056] Step 3.1: Input the operation area Ω i,j ;

[0057] Step 3.2: Find the maximum perimeter L. j,max The corresponding first triangular surface △ m1,i ;

[0058] Step 3.3: Locate the first triangular face △ m1,i The longest side in the triangle is obtained by finding the side of the triangle △. m1,i The second trigonal surface △ sharing the side m2,i;

[0059] Step 3.4: Put the data in set ζ Nf Remove the part about the operating area Ω i,j The vertex is identified, and the remaining points are taken as interior points. From the interior points, the point closest to the center point of the edge side is identified as the intangent point P0.

[0060] Step 3.5: Let the first triangular surface △ m1,i Second trigonal surface △ m2,i Let F be the set of points, and use the set of points F and the intangent point P0 to construct a new face △. 1,i ,△ 2,i ,△ 3,i ,△ 4,i And satisfy the following formula:

[0061]

[0062] Step 3.6: From the operating area Ω i,j Delete the first and second triangular faces △ m1,i ,△ m2,i Add 4 more △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i This completes the update; from a spatial perspective, it is equivalent to Ω. i,j The space was cut off by these 6 faces △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i ,△ m1,i ,△ m2,i The hexahedron PO dig ;

[0063] Step 3.7: Output the updated operating region Ω i,j .

[0064] In conjunction with the first aspect, the steps of the filling algorithm operation further include:

[0065] Step 4.1: Input the operation area Ω i,j ;

[0066] Step 4.2: Use the operating area Ω i,j External training sample points Z h The set Z = {Z1, ..., Zn} is formed. H H is Z h Quantity;

[0067] Step 4.3: First iteration number t = 1, second iteration number h = 1;

[0068] Step 4.4: If t≤4 is satisfied, proceed to steps 4.5-4.13; otherwise, end the iteration and jump to step 4.14.

[0069] Step 4.5: Calculate the distance from the external training sample point set Z to the surface Δ. 1,i ,△ 2,i ,△ 3,i ,△ 4,i The distances are respectively distance 1, distance 2, distance 3, and distance 4: di1, di2, di3, di4;

[0070] Step 4.6: In the t-th iteration, the external training sample point set Z is transferred to the surface △ t,i The distance is di t If di is satisfied t If the sum is min{di1,di2,di3,di4}, proceed to step 4.7; otherwise, skip to step 4.5.

[0071] Step 4.7: Transfer the external training sample points Z h Store in set J s In the second iteration, h = h + 1. If h ≤ H, jump to step 4.5; otherwise, jump to step 4.8.

[0072] Step 4.8: Set J s Points in the middle, according to distance from the plane △ t,i After sorting from nearest to farthest, we get a new set J' s ={J'1,...,J' S}, S is a set J s The number of midpoints;

[0073] Step 4.9: Third iteration number s = 1;

[0074] Step 4.10: In the operating area Ω i,j Find the distance point J' among all the triangular faces of the surface. s The nearest face △ near ;

[0075] Step 4.11: Let the distance point J' be... s The nearest face △ near All vertices are a point set F';

[0076] Step 4.12: Use point set F' and point J' s Establish a new face △ 5,j ,△ 6,j ,△ 7,j And satisfy:

[0077]

[0078] Step 4.13: From the operating area Ω i,j Delete distance point J' s The nearest face △ near Add these 3 faces △ 5,j ,△ 6,j ,△ 7,j , complete Ω i,j The update; from a spatial perspective, it is equivalent to Ω. i,j The space is filled with these four △ faces 5,j ,△ 6,j ,△ 7,j ,△ near The tetrahedron PO formed fill The third iteration number s = s + 1, the first iteration number t = t + 1, if s ≤ S, jump to step 4.10, otherwise jump to step 4.4;

[0079] Step 4.14: Output the updated operating region Ω i,j .

[0080] In conjunction with the first aspect, the further steps to determine the location of the sample point to be detected corresponding to the concave hull decision region and obtain the detection result include:

[0081] First, determine whether the sample point to be detected lies within the original convex hull Ω. original If not, determine the sample to be tested as the target; otherwise, continue to determine whether the sample point to be tested is within the hexahedron PO. dig If not, the sample to be tested is determined to be sea clutter; otherwise, continue to determine whether the sample point to be tested is within the tetrahedral PO. fill If not, the sample to be tested is determined to be the target; otherwise, the sample to be tested is determined to be sea clutter.

[0082] In conjunction with the first aspect, further, it is determined that the sample point to be detected lies within the original convex hull Ω. original hexahedral PO dig Tetrahedral PO fill The specific operations include:

[0083] Judgment area Ω final From the original convex hull Ω original Several hexahedral POs were removed from the middle dig and filling several tetrahedral PO fill Composition, and the original convex hull Ω original hexahedral PO dig tetrahedral PO fill Both belong to convex polyhedra, and each face of a convex polyhedron is a triangle, so the primitive convex hull Ω original hexahedral PO dig tetrahedral PO fill They can be represented as:

[0084]

[0085]

[0086]

[0087] Where SP{} represents the convex hull formed by the triangles, Represents the original convex hull Ω original The vertex of each triangular face in the diagram, where D is the number of triangular faces. Represents a hexahedron PO dig The vertices of each triangular face, Represents tetrahedron PO fill Find the vertices of each triangular face; find all POs. dig and PO fill Since they are stored in two separate sets, it is only necessary to sequentially determine the samples to be detected, η. opt In Ω original PO dig PO fill The location. Calculate its detection statistic as follows:

[0088]

[0089]

[0090]

[0091] If ρ(η) opt If η ≤ 0, then η opt In Ω original Similarly, we can obtain ρ'(η) opt If η ≤ 0, then η opt In PO dig Inside, ρ (η) opt If η ≤ 0, then η opt In PO fill Inside.

[0092] Secondly, this invention proposes a device for detecting small floating targets on the sea surface based on feature optimization and controllable false alarm three-dimensional concave hull, comprising:

[0093] The data acquisition module is used to collect radar echoes and extract the eight-dimensional feature vector of sea clutter and the eight-dimensional feature vector of the sample to be detected from the radar echoes.

[0094] The data processing module performs the following operations:

[0095] The optimal three-dimensional feature vectors are selected from the eight-dimensional feature vectors of the sea clutter and the eight-dimensional feature vectors of the sample to be detected using a feature optimization algorithm. The optimal three-dimensional feature vectors of the sea clutter are used as training sample points, and the optimal three-dimensional feature vectors of the sample to be detected are used as the sample points to be detected.

[0096] The training module performs the following operations:

[0097] Using the alpha-indentation algorithm with controllable false alarms, the algorithm prioritizes maximizing the loss of the indentation volume in a single attempt. False alarm points are then successively removed from the training sample points based on the false alarm rate, thus updating the training sample points.

[0098] The convex hull learning algorithm is used to obtain the convex hull region containing all training sample points, and the convex hull region is transformed into the concave hull decision region containing all training sample points.

[0099] The detection module is used to determine the position of the sample point to be detected corresponding to the concave hull decision region and obtain the detection result.

[0100] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0101] This invention proposes a method and apparatus for detecting small floating targets on the sea surface based on feature optimization and a controllable 3D concave hull with controlled false alarms. The method uses the mRMR algorithm to remove redundant and highly correlated feature vectors, maximizing the dependence of the selected 3D feature vectors on the labels. This is combined with a controllable 3D concave hull algorithm to complete the detection. Experiments show that the mRMR algorithm has an excellent feature search strategy, selecting important features first. Combined with the proposed controllable 3D concave hull algorithm, excellent detection performance is achieved. Attached Figure Description

[0102] Figure 1 This is an overall flowchart of the method of the present invention;

[0103] Figure 2 This is a flowchart illustrating the operation of detecting small floating targets on the sea surface according to the present invention.

[0104] Figure 3 This is a comparison chart of the implementation results of the present invention;

[0105] Figure 4 This is a schematic diagram of the target detection device of the present invention. Detailed Implementation

[0106] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0107] This invention proposes a method for detecting small floating targets on the sea surface based on feature optimization and controllable false alarm 3D concave hull, such as... Figure 1As shown, the specific steps include the following:

[0108] Step A. Acquire radar echoes and extract the eight-dimensional feature vectors of sea clutter and the eight-dimensional feature vectors of the sample to be detected from the radar echoes.

[0109] In this embodiment, eight features are extracted from the radar received echo: normalized Hurst exponent NHE, relative average amplitude RAA, relative Doppler peak height RDPH, relative vector entropy RVE, ridge accumulation RI, maximum connected region size MS, number of connected regions NR, and generalized likelihood ratio detector NSCM-GLRT based on normalized sample covariance matrix. These features are then used to form an eight-dimensional feature vector.

[0110] Step B. Use the feature optimization algorithm to select the best three-dimensional feature vectors from the eight-dimensional feature vectors of the sea clutter and the eight-dimensional feature vectors of the sample to be detected. Use the best three-dimensional feature vector of the sea clutter as the training sample point and the best three-dimensional feature vector of the sample to be detected as the sample point to be detected.

[0111] Step B01. Concatenate the eight-dimensional feature vector of the sea clutter and the eight-dimensional feature vector of the sample to be detected into a hybrid eight-dimensional feature vector.

[0112] Step B02. Use the minimum redundancy maximum correlation feature optimization algorithm mRMR to select the best one-dimensional mixed feature vector from the mixed eight-dimensional feature vectors.

[0113] The correlation between each vector in the mixed feature vector and the stability label vector is calculated based on the definition of mutual information. The set of feature vectors with the strongest correlation is taken as the optimal one-dimensional mixed feature vector, as shown in the following formula:

[0114]

[0115]

[0116] Where g1 represents the optimal one-dimensional mixed feature vector, MI is the mutual information entropy value, and R... G Represents a mixed feature vector, a j Indicates belonging to R G The one-dimensional vector elements, b represents the stability label vector, a j It belongs to vector a j The elements of the vector b, p(a) j b) is a j The joint probability density function of a and b, p(a j p(b) and p(b) are respectively a j The probability density function of b.

[0117] Step B03. Using mRMR, select the second and third best one-dimensional mixed feature vectors from the mixed eight-dimensional feature vectors in sequence, and combine them with the best one-dimensional mixed feature vector to form the best three-dimensional mixed feature vector.

[0118] Using the best one-dimensional hybrid feature vector, the feature vector that satisfies the following formula is taken as the second best one-dimensional hybrid feature vector.

[0119]

[0120]

[0121]

[0122] Where g2 represents the second-best one-dimensional mixed feature vector, MI is the mutual information entropy value, and a' j Indicates belonging to (R) G One-dimensional vector elements of -g1), (R G -g1) represents the set of eigenvectors remaining after removing the best one-dimensional mixed eigenvector g1, a' j It belongs to vector a' j The element, p(a' j b) is a' j The joint probability density function of b, p(a') j ) is a' j The probability density function, where g1 is an element belonging to vector g1, p(a' j g1) is a' j The joint probability density function of g1 and g2, p(g1) is the probability density function of g1.

[0123] Using the best and second-best one-dimensional hybrid feature vectors, the feature vector that satisfies the following formula is taken as the third-best one-dimensional hybrid feature vector.

[0124]

[0125]

[0126]

[0127] Where g3 represents the third-best one-dimensional hybrid feature vector, MI is the mutual information entropy value, G = {g1, g2}, (R G -G) represents the set of eigenvectors remaining after removing the best one-dimensional mixed eigenvector g1 and the second best one-dimensional mixed eigenvector g2, g i It belongs to vector g i The element, p(a' j ,g i ) is a'j and g i The joint probability density function, p(g) i ) is g i The probability density function.

[0128] Step B04. Separate the optimal three-dimensional hybrid feature vector into the optimal three-dimensional feature vector of the sea clutter and the optimal three-dimensional feature vector of the sample to be detected.

[0129] Step B05. Use the best three-dimensional feature vector of the sea clutter as the training sample point, and the best three-dimensional feature vector of the sample to be detected as the sample point to be detected.

[0130] Step C. Using the alpha-based indentation algorithm with controllable false alarms, and based on the principle of maximizing the loss of the indentation volume in a single attempt, false alarm points are successively removed from the training sample points according to the false alarm rate, thus completing the update of the training sample points.

[0131] Step C01: Calculate the number Q of sample points in the set ζ consisting of training sample points;

[0132] Step C02, based on the false alarm rate P F Calculate the number of false alarms: N f =Q×P F ;

[0133] Step C03, iteration count v = 1, operation set ζ v =ζ;

[0134] Step C04: Generate the operation set ζ according to the alpha concave hull algorithm. v The concave hull;

[0135] Step C05, from the operation set ζ v Remove one vertex from the concave hull and calculate the volume reduction of the concave hull;

[0136] Step C06: Find the hull vertex that maximizes the reduction in hull volume;

[0137] Step C07, from the operation set ζ v Delete the concave hull vertex found in step C06, and the iteration count v = v + 1 to obtain a new operation set ζ. v If the number of iterations v≤N f Return to step C04; otherwise, end the iteration. Finally, obtain the set ζ of deleted false alarm points. Nf .

[0138] Step D. Use the convex hull learning algorithm to obtain the convex hull region containing all training sample points.

[0139] Step E. Use the alpha concave hull algorithm with controllable false alarms to transform the convex hull region into a concave hull decision region containing all training sample points.

[0140] Step E01: Based on the set ζ of deleted false alarm points Nf The original convex hull Ω, consisting of D triangular faces, is generated using a convex hull learning algorithm. original D is the number of triangular faces;

[0141] Step E02: Calculate the perimeter L of all triangular faces of the original convex hull. d ,d=0,1,...,D;

[0142] Step E03: Calculate the average perimeter of all triangular faces and use it as the threshold th;

[0143] Step E04: Intracut number i = 1, iteration number j = 1, operation region Ω i,j =Ω original Set the maximum number of cuts to 150;

[0144] Step E05: If j ≤ dig_num, proceed to steps E06-E10; otherwise, end the iteration and jump to step E11.

[0145] Step E06: Calculate the operating region Ω i,j The perimeter L of all triangular faces j,d ,d=0,1,...,D;

[0146] Step E07: Calculate the perimeter L of all triangular faces. j,d The maximum value L in d = 0, 1, ..., D j,max ;

[0147] Step E08: If L is satisfied j,max If the iteration ends, proceed to steps E09-E10; otherwise, end the iteration and jump to step E11.

[0148] Step E09: For the operating area Ω i,j Perform the inner section algorithm operation, with the inner section number i = i + 1 and the iteration number j = j, to obtain the updated operation region Ω. i,j ;

[0149] Step E10: For the operating area Ω i,j Perform the filling algorithm operation, with the number of iterations j = j + 1 and the number of incisions i = i, to obtain the updated operation region Ω. i,j Jump to step E05;

[0150] Step E11: Obtain the final concave hull decision region: Ω final =Ωi,j .

[0151] In step E09, the specific steps of the Ricut algorithm operation are as follows:

[0152] Step 1: Input the operation area Ω i,j ;

[0153] Step 2: Find the maximum perimeter L. j,max The corresponding first triangular surface △ m1,i ;

[0154] Step 3: Locate the first triangular face △ m1,i The longest side in the triangle is obtained by finding the side of the triangle △. m1,i The second trigonal surface △ sharing the side m2,i ;

[0155] Step 4: Place the elements in set ζ Nf Remove the part about the operating area Ω i,j The vertex is identified, and the remaining points are taken as interior points. From the interior points, the point closest to the center point of the edge side is identified as the intangent point P0.

[0156] Step 5: Define the first triangular surface △ m1,i Second trigonal surface △ m2,i Let F be the set of points, and use the set of points F and the intangent point P0 to construct a new face △. 1,i ,△ 2,i ,△ 3,i ,△ 4,i And satisfy the following formula:

[0157]

[0158] Step 6: From the operating area Ω i,j Delete the first and second triangular faces △ m1,i ,△ m2,i Add 4 more △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i This completes the update; from a spatial perspective, it is equivalent to Ω. i,j The space was cut off by these 6 faces △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i ,△ m1,i ,△ m2,i The hexahedron PO dig ;

[0159] Step 7: Output the updated operand range Ω i,j .

[0160] In step E10, the specific steps of the filling algorithm operation are as follows:

[0161] Step 1: Input the operation area Ω i,j ;

[0162] Step 2: Use the operating area Ω i,j External training sample points Z h The set Z = {Z1, ..., Zn} is formed. H H is Z h Quantity;

[0163] Step 3: First iteration number t = 1, second iteration number h = 1;

[0164] Step 4: If t≤4 is satisfied, proceed to steps 5 through 13; otherwise, end the iteration and jump to step 14.

[0165] Step 5: Calculate the distance from the external training sample point set Z to the surface △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i The distances are respectively distance 1, distance 2, distance 3, and distance 4: di1, di2, di3, di4;

[0166] Step 6: If di is satisfied t If the sum is min{di1,di2,di3,di4}, proceed to step 7; otherwise, skip to step 5.

[0167] Step 7: Transfer the external training sample points Z h Store in set J s In the second iteration, h = h + 1. If h ≤ H, jump to step 5; otherwise, jump to step 8.

[0168] Step 8: Set J s Points in the middle, according to distance from the plane △ t,i After sorting from nearest to farthest, we get a new set J' s ={J'1,...,J' S}, S is a set J s The number of midpoints;

[0169] Step 9: Third iteration number s = 1;

[0170] Step 10: In the operating area Ω i,j Find the distance point J' among all the triangular faces of the surface. s The nearest face △ near ;

[0171] Step 11: Let the distance point J' be... s The nearest face △near All vertices are a point set F';

[0172] Step 12: Use point set F' and point J' s Establish a new face △ 5,j ,△ 6,j ,△ 7,j And satisfy:

[0173]

[0174] Step 13: From the operating area Ω i,j Delete distance point J' s The nearest face △ near Add these 3 faces △ 5,j ,△ 6,j ,△ 7,j , complete Ω i,j The update; from a spatial perspective, it is equivalent to Ω. i,j The space is filled with these four △ faces 5,j ,△ 6,j ,△ 7,j ,△ near The tetrahedron PO formed fill The third iteration number is s = s + 1, the first iteration number is t = t + 1. If s ≤ S, jump to the tenth step; otherwise, jump to the fourth step.

[0175] Step 14: Output the updated operand range Ω i,j .

[0176] Step F. Determine the position of the sample point to be detected corresponding to the concave hull decision region to obtain the detection result. The steps include:

[0177] First, determine whether the sample point to be detected lies within the original convex hull Ω. original If not, determine the sample to be tested as the target; otherwise, continue to determine whether the sample point to be tested is within the hexahedron PO. dig If not, the sample to be tested is determined to be sea clutter; otherwise, continue to determine whether the sample point to be tested is within the tetrahedral PO. fill If not, the sample to be tested is determined to be the target; otherwise, the sample to be tested is determined to be sea clutter.

[0178] Determine if the sample point to be detected lies in the original convex hull Ω original hexahedral PO dig Tetrahedral PO fill The specific operations include:

[0179] Judgment area Ω final From the original convex hull Ω original Several hexahedral POs were removed from the middle dig and filling several tetrahedral POfill Composition, and the original convex hull Ω original hexahedral PO dig tetrahedral PO fill Both belong to convex polyhedra, and each face of a convex polyhedron is a triangle, so the primitive convex hull Ω original hexahedral PO dig tetrahedral PO fill They can be represented as:

[0180]

[0181]

[0182]

[0183] Where SP{} represents the convex hull formed by the triangles, Represents the original convex hull Ω original The vertex of each triangular face in the diagram, where D is the number of triangular faces. Represents a hexahedron PO dig The vertices of each triangular face, Represents tetrahedron PO fill Find the vertices of each triangular face; find all POs. dig and PO fill Since they are stored in two separate sets, it is only necessary to sequentially determine the samples to be detected, η. opt In Ω original PO dig PO fill The location. Calculate its detection statistic as follows:

[0184]

[0185]

[0186]

[0187] If ρ(η) opt If η ≤ 0, then η opt In Ω original Similarly, we can obtain ρ'(η) opt If η ≤ 0, then η opt In PO dig Inside, ρ (η) opt If η ≤ 0, then η opt In PO fill Inside.

[0188] The following is a specific experiment to verify the effectiveness of the method of the present invention:

[0189] In this embodiment of the invention, IPIX sea clutter data collected in 1993 and 1998 by Professor Haykin's team at McMaster University in Canada are used. IPIX radar can emit horizontally and vertically polarized electromagnetic waves, and can complete horizontal and vertical reception using two linear receivers. Therefore, when the radar collects data, it can usually obtain radar echo data with four polarizations: HH, HV, VH, and VV.

[0190] In the experiment, a feature-optimized controllable three-dimensional concave hull detector (mRMR-Tri-ConcaveHull detector), a RAA-RDPH-RVE three-feature convex hull detector (Tri-feature Convex Hull detector), and a RI-NR-MS three-feature convex hull detector (TF-Tri-feature Convex Hull detector) were used as comparative experiments. The operation flow of the method of the present invention is as follows: Figure 2 As shown, the detection results of different algorithms under HH, HV, VH, and VV polarizations are as follows: Figure 3 As shown in the figure, the proposed mRMR-Tri-ConcaveHull detector achieved the best detection performance on 20 datasets compared with the other two detectors. Therefore, the detection performance of this invention is superior to other detection methods.

[0191] This invention proposes a device for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms, such as... Figure 4 As shown, the system mainly includes a data acquisition module 1, a data processing module 2, a training module 3, and a detection module 4. The data acquisition module collects radar echoes and extracts the eight-dimensional feature vectors of sea clutter and the eight-dimensional feature vectors of the sample to be detected from the radar echoes. The data processing module uses a feature optimization algorithm to select the optimal three-dimensional feature vectors from the eight-dimensional feature vectors of the sea clutter and the sample to be detected, respectively. The optimal three-dimensional feature vectors of the sea clutter are used as training sample points, and the optimal three-dimensional feature vectors of the sample to be detected are used as the sample points to be detected. The training module includes an alpha concave hull algorithm with controllable false alarms. Based on the principle of maximizing the loss of the concave hull volume in a single iteration, false alarm points are successively deleted from the training sample points according to the false alarm rate to update the training sample points; the convex hull region containing all training sample points is obtained; the convex hull is transformed into a concave hull to obtain the concave hull decision region containing all training sample points. The detection module determines the position of the sample point to be detected corresponding to the concave hull decision region and obtains the detection result.

[0192] This invention uses the mRMR algorithm to remove redundant and highly correlated feature vectors, maximizing the dependency between the selected 3D feature subset and the label. Then, it combines this with a 3D concave hull algorithm with controllable false alarms to complete the detection. Experiments show that the mRMR algorithm has an excellent feature search strategy, selecting important features first. The algorithm principle is relatively simple; the core issue is the calculation of mutual information. It has low data requirements and high computational efficiency. Finally, combined with the 3D concave hull algorithm with controllable false alarms, excellent detection performance is achieved.

[0193] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for detecting small floating targets on the sea surface based on feature optimization and controllable false alarm 3D concave hull, characterized in that, Includes the following steps: Collect radar echoes and extract the eight-dimensional feature vectors of sea clutter and the eight-dimensional feature vectors of the sample to be detected from the radar echoes. The optimal three-dimensional feature vectors are selected from the eight-dimensional feature vectors of the sea clutter and the eight-dimensional feature vectors of the sample to be detected using a feature optimization algorithm. The optimal three-dimensional feature vectors of the sea clutter are used as training sample points, and the optimal three-dimensional feature vectors of the sample to be detected are used as the sample points to be detected. Using the alpha-indentation algorithm with controllable false alarms, the algorithm prioritizes maximizing the loss of the indentation volume in a single attempt. False alarm points are then successively removed from the training sample points based on the false alarm rate, thus updating the training sample points. The convex hull learning algorithm is used to obtain the convex hull region containing all training sample points, and the convex hull region is transformed into the concave hull decision region containing all training sample points. The location of the sample point to be detected corresponding to the concave hull decision region is determined to obtain the detection result.

2. The method for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms according to claim 1, characterized in that, The eight-dimensional feature vectors extracted from sea clutter and the sample to be detected include: The eight features are: Normalized Hurst exponent (NHE), Relative average amplitude (RAA), Relative Doppler peak height (RDPH), Relative vector entropy (RVE), Ridge accumulation (RI), Maximum connected region size (MS), Number of connected regions (NR), and Generalized likelihood ratio detector (NSCM-GLRT) based on normalized sample covariance matrix.

3. The method for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms according to claim 1, characterized in that, The optimal three-dimensional feature vectors are selected from the eight-dimensional feature vectors of sea clutter and the eight-dimensional feature vectors of the sample to be detected using a feature optimization algorithm. The specific steps include: The eight-dimensional feature vector of the sea clutter and the eight-dimensional feature vector of the sample to be detected are concatenated into a hybrid eight-dimensional feature vector; The minimum redundancy maximum correlation feature optimization algorithm mRMR is used to select the best one-dimensional mixed feature vector from the mixed eight-dimensional feature vectors. Using mRMR, the second and third best one-dimensional mixed feature vectors are selected sequentially from the mixed eight-dimensional feature vectors, and together with the best one-dimensional mixed feature vector, they form the best three-dimensional mixed feature vector; The optimal three-dimensional hybrid feature vector is separated into the optimal three-dimensional feature vector of sea clutter and the optimal three-dimensional feature vector of the sample to be detected.

4. The method for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms according to any one of claims 1-3, characterized in that, Using the alpha-based indentation algorithm with controllable false alarms, and based on the principle of maximizing the loss of the indentation volume in a single attempt, false alarm points are successively removed from the training sample points according to the false alarm rate to complete the update of the training sample points. The specific steps include: Step 1.1: Calculate the number of sample points Q in the set ζ consisting of training sample points; Step 1.2: Based on the false alarm rate P F Calculate the number of false alarms: N f =Q×P F ; Step 1.3: Iteration count v = 1, operation set ζ v =ζ; Step 1.4: Generate the operation set ζ according to the alpha concave hull algorithm. v The concave hull; Step 1.5: From the operation set ζ v Remove one vertex from the concave hull and calculate the volume reduction of the concave hull; Step 1.6: Find the hull vertex that maximizes the reduction in hull volume; Step 1.7: From the operation set ζ v Delete the concave hull vertices found in step 1.6, and the iteration count v = v + 1 to obtain a new operation set ζ. v If the number of iterations v≤N f If the problem persists, return to step 1.4; otherwise, end the iteration. Finally, obtain the set ζ of deleted false alarm points. Nf .

5. The method for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms according to claim 4, characterized in that, The convex hull region is transformed into a concave hull decision region that includes all training sample points. The specific steps include: Step 2.1: Based on the set ζ of deleted false alarm points Nf The original convex hull Ω, consisting of D triangular faces, is generated using a convex hull learning algorithm. original D is the number of triangular faces; Step 2.2: Calculate the perimeter L of all triangular faces of the original convex hull. d ,d=0,1,...,D; Step 2.3: Calculate the average perimeter of all triangular faces and use it as the threshold th; Step 2.4: Intracut number i = 1, iteration number j = 1, operation region Ω i,j =Ω original Set the maximum number of cuts, dig_num. Step 2.5: If j ≤ dig_num, proceed to steps 2.6-2.10; otherwise, end the iteration and jump to step 2.

11. Step 2.6: Calculate the operating region Ω i,j The perimeter L of all triangular faces j,d ,d=0,1,...,D; Step 2.7: Calculate the perimeter L of all triangular faces. j,d The maximum value L in d = 0, 1, ..., D j,max ; Step 2.8: If L is satisfied j,max If the condition is met, proceed to steps 2.9-2.10; otherwise, end the iteration and jump to step 2.

11. Step 2.9: For the operating region Ω i,j Perform the inner section algorithm operation, with the inner section number i = i + 1 and the iteration number j = j, to obtain the updated operation region Ω. i,j ; Step 2.10: For the operating region Ω i,j Perform the filling algorithm operation, with the number of iterations j = j + 1 and the number of incisions i = i, to obtain the updated operation region Ω. i,j Skip to step 2.5; Step 2.11: Obtain the final concave hull decision region: Ω final =Ω i,j .

6. The method for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms according to claim 5, characterized in that, The steps of the Riche algorithm operation include: Step 3.1: Input the operation area Ω i,j ; Step 3.2: Find the maximum perimeter L. j,max The corresponding first triangular surface △ m1,i ; Step 3.3: Locate the first triangular face △ m1,i The longest side in the triangle is obtained by finding the side of the triangle △. m1,i The second trigonal surface △ sharing the side m2,i ; Step 3.4: Put the data in set ζ Nf Remove the part about the operating area Ω i,j The vertex is identified, and the remaining points are taken as interior points. From the interior points, the point closest to the center point of the edge side is identified as the intangent point P0. Step 3.5: Let the first triangular surface △ m1,i Second trigonal surface △ m2,i Let F be the set of points, and use the set of points F and the intangent point P0 to construct a new face △. 1,i ,△ 2,i ,△ 3,i ,△ 4,i And satisfy the following formula: Step 3.6: From the operating area Ω i,j Delete the first and second triangular faces △ m1,i ,△ m2,i Add 4 more △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i This completes the update; from a spatial perspective, it is equivalent to Ω. i,j The space was cut off by these 6 faces △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i ,△ m1,i ,△ m2,i The hexahedron PO dig ; Step 3.7: Output the updated operating region Ω i,j .

7. The method for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms according to claim 6, characterized in that, The steps of the filling algorithm operation include: Step 4.1: Input the operation area Ω i,j ; Step 4.2: Use the operating area Ω i,j External training sample points Z h The set Z = {Z1, ..., Zn} is formed. H H is Z h Quantity; Step 4.3: First iteration number t = 1, second iteration number h = 1; Step 4.4: If t≤4 is satisfied, proceed to steps 4.5-4.13; otherwise, end the iteration and jump to step 4.

14. Step 4.5: Calculate the distance from the external training sample point set Z to the surface Δ. 1,i ,△ 2,i ,△ 3,i ,△ 4,i The distances are respectively distance 1, distance 2, distance 3, and distance 4: di1, di2, di3, di4; Step 4.6: In the t-th iteration, the external training sample point set Z is transferred to the surface △ t,i The distance is di t If di is satisfied t If the sum is min{di1,di2,di3,di4}, proceed to step 4.7; otherwise, skip to step 4.

5. Step 4.7: Transfer the external training sample points Z h Store in set J s In the second iteration, h = h + 1. If h ≤ H, jump to step 4.5; otherwise, jump to step 4.

8. Step 4.8: Set J s Points in the middle, according to distance from the plane △ t,i After sorting from nearest to farthest, we get a new set J' s ={J'1,...,J' S }, S is a set J s The number of midpoints; Step 4.9: Third iteration number s = 1; Step 4.10: In the operating area Ω i,j Find the distance point J' among all the triangular faces of the surface. s The nearest face △ near ; Step 4.11: Let the distance point J' be... s The nearest face △ near All vertices are a point set F'; Step 4.12: Use point set F' and point J' s Establish a new face △ 5,j ,△ 6,j ,△ 7,j And satisfy: Step 4.13: From the operating area Ω i,j Delete distance point J' s The nearest face △ near Add these 3 faces △ 5,j ,△ 6,j ,△ 7,j , complete Ω i,j The update; from a spatial perspective, it is equivalent to Ω. i,j The space is filled with these four △ faces 5,j ,△ 6,j ,△ 7,j ,△ near The tetrahedron PO formed fill The third iteration number s = s + 1, the first iteration number t = t + 1, if s ≤ S, jump to step 4.10, otherwise jump to step 4.4; Step 4.14: Output the updated operating region Ω i,j .

8. The method for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms according to claim 7, characterized in that, The steps to determine the location of the sample point to be detected corresponding to the indentation decision region and obtain the detection result include: First, determine whether the sample point to be detected lies within the original convex hull Ω. original If not, determine the sample to be tested as the target; otherwise, continue to determine whether the sample point to be tested is within the hexahedron PO. dig If not, the sample to be tested is determined to be sea clutter; otherwise, continue to determine whether the sample point to be tested is within the tetrahedral PO. fill If not, the sample to be tested is determined to be the target; otherwise, the sample to be tested is determined to be sea clutter.

9. A device for detecting small floating targets on the sea surface based on feature optimization and controllable three-dimensional concave hull with false alarms, characterized in that, include: The data acquisition module is used to collect radar echoes and extract the eight-dimensional feature vector of sea clutter and the eight-dimensional feature vector of the sample to be detected from the radar echoes. The data processing module performs the following operations: The optimal three-dimensional feature vectors are selected from the eight-dimensional feature vectors of the sea clutter and the eight-dimensional feature vectors of the sample to be detected using a feature optimization algorithm. The optimal three-dimensional feature vectors of the sea clutter are used as training sample points, and the optimal three-dimensional feature vectors of the sample to be detected are used as the sample points to be detected. The training module performs the following operations: Using the alpha-indentation algorithm with controllable false alarms, the algorithm prioritizes maximizing the loss of the indentation volume in a single attempt. False alarm points are then successively removed from the training sample points based on the false alarm rate, thus updating the training sample points. The convex hull learning algorithm is used to obtain the convex hull region containing all training sample points, and the convex hull region is transformed into the concave hull decision region containing all training sample points. The detection module is used to determine the position of the sample point to be detected corresponding to the concave hull decision region and obtain the detection result.

10. The sea surface floating small target detection device based on feature optimization and controllable three-dimensional concave hull with false alarm as described in claim 9, characterized in that, The training module uses the alpha-based indentation algorithm with controllable false alarms. Based on the principle of maximizing the loss of the indentation volume in a single iteration, it successively removes false alarm points from the training sample points according to the false alarm rate, thus updating the training sample points. Specific steps include: Step 1.1: Calculate the number of sample points Q in the set ζ consisting of training sample points; Step 1.2: Based on the false alarm rate P F Calculate the number of false alarms: N f =Q×P F ; Step 1.3: Iteration count v = 1, operation set ζ v =ζ; Step 1.4: Generate the operation set ζ according to the alpha concave hull algorithm. v The concave hull; Step 1.5: From the operation set ζ v Remove one vertex from the concave hull and calculate the volume reduction of the concave hull; Step 1.6: Find the hull vertex that maximizes the reduction in hull volume; Step 1.7: From the operation set ζ v Delete the concave hull vertices found in step 1.6, and the iteration count v = v + 1 to obtain a new operation set ζ. v If the number of iterations v≤N f If the problem persists, return to step 1.4; otherwise, end the iteration. Finally, obtain the set ζ of deleted false alarm points. Nf ; The convex hull region is transformed into a concave hull decision region that includes all training sample points. The specific steps include: Step 2.1: Based on the set ζ of deleted false alarm points Nf The original convex hull Ω, consisting of D triangular faces, is generated using a convex hull learning algorithm. original D is the number of triangular faces; Step 2.2: Calculate the perimeter L of all triangular faces of the original convex hull. d ,d=0,1,...,D; Step 2.3: Calculate the average perimeter of all triangular faces and use it as the threshold th; Step 2.4: Intracut number i = 1, iteration number j = 1, operation region Ω i,j =Ω original Set the maximum number of cuts, dig_num. Step 2.5: If j ≤ dig_num, proceed to steps 2.6-2.10; otherwise, end the iteration and jump to step 2.

11. Step 2.6: Calculate the operating region Ω i,j The perimeter L of all triangular faces j,d ,d=0,1,...,D; Step 2.7: Calculate the perimeter L of all triangular faces. j,d The maximum value L in d = 0, 1, ..., D j,max ; Step 2.8: If L is satisfied j,max If the condition is met, proceed to steps 2.9-2.10; otherwise, end the iteration and jump to step 2.

11. Step 2.9: For the operating region Ω i,j Perform the inner section algorithm operation, with the inner section number i = i + 1 and the iteration number j = j, to obtain the updated operation region Ω. i,j ; Step 2.10: For the operating region Ω i,j Perform the filling algorithm operation, with the number of iterations j = j + 1 and the number of incisions i = i, to obtain the updated operation region Ω. i,j Skip to step 2.5; Step 2.11: Obtain the final concave hull decision region: Ω final =Ω i,j ; The steps of the Riche algorithm operation include: Step 3.1: Input the operation area Ω i,j ; Step 3.2: Find the maximum perimeter L. j,max The corresponding first triangular surface △ m1,i ; Step 3.3: Locate the first triangular face △ m1,i The longest side in the triangle is obtained by finding the side of the triangle △. m1,i The second trigonal surface △ sharing the side m2,i ; Step 3.4: Put the data in set ζ Nf Remove the part about the operating area Ω i,j The vertex is identified, and the remaining points are taken as interior points. From the interior points, the point closest to the center point of the edge side is identified as the intangent point P0. Step 3.5: Let the first triangular surface △ m1,i Second trigonal surface △ m2,i Let F be the set of points, and use the set of points F and the intangent point P0 to construct a new face △. 1,i ,△ 2,i ,△ 3,i ,△ 4,i And satisfy the following formula: Step 3.6: From the operating area Ω i,j Delete the first and second triangular faces △ m1,i ,△ m2,i Add 4 more △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i This completes the update; from a spatial perspective, it is equivalent to Ω. i,j The space was cut off by these 6 faces △ 1,i ,△ 2,i ,△ 3,i ,△ 4,i ,△ m1,i ,△ m2,i The hexahedron PO dig ; Step 3.7: Output the updated operating region Ω i,j ; The steps of the filling algorithm operation include: Step 4.1: Input the operation area Ω i,j ; Step 4.2: Use the operating area Ω i,j External training sample points Z h The set Z = {Z1, ..., Zn} is formed. H H is Z h Quantity; Step 4.3: First iteration number t = 1, second iteration number h = 1; Step 4.4: If t≤4 is satisfied, proceed to steps 4.5-4.13; otherwise, end the iteration and jump to step 4.

14. Step 4.5: Calculate the distance from the external training sample point set Z to the surface Δ. 1,i ,△ 2,i ,△ 3,i ,△ 4,i The distances are respectively distance 1, distance 2, distance 3, and distance 4: di1, di2, di3, di4; Step 4.6: In the t-th iteration, the external training sample point set Z is transferred to the surface △ t,i The distance is di t If di is satisfied t If the sum is min{di1,di2,di3,di4}, proceed to step 4.7; otherwise, skip to step 4.

5. Step 4.7: Transfer the external training sample points Z h Store in set J s In the second iteration, h = h + 1. If h ≤ H, jump to step 4.5; otherwise, jump to step 4.

8. Step 4.8: Set J s Points in the middle, according to distance from the plane △ t,i After sorting from nearest to farthest, we get a new set J' s ={J'1,...,J' S }, S is a set J s The number of midpoints; Step 4.9: Third iteration number s = 1; Step 4.10: In the operating area Ω i,j Find the distance point J' among all the triangular faces of the surface. s The nearest face △ near ; Step 4.11: Let the distance point J' be... s The nearest face △ near All vertices are a point set F'; Step 4.12: Use point set F' and point J' s Establish a new face △ 5,j ,△ 6,j ,△ 7,j And satisfy: Step 4.13: From the operating area Ω i,j Delete distance point J' s The nearest face △ near Add these 3 faces △ 5,j ,△ 6,j ,△ 7,j , complete Ω i,j The update; from a spatial perspective, it is equivalent to Ω. i,j The space is filled with these four △ faces 5,j ,△ 6,j ,△ 7,j ,△ near The tetrahedron PO formed fill The third iteration number s = s + 1, the first iteration number t = t + 1, if s ≤ S, jump to step 4.10, otherwise jump to step 4.4; Step 4.14: Output the updated operating region Ω i,j ; The steps to determine the location of the sample point to be detected corresponding to the indentation decision region and obtain the detection result include: First, determine whether the sample point to be detected lies within the original convex hull Ω. original If not, determine the sample to be tested as the target; otherwise, continue to determine whether the sample point to be tested is within the hexahedron PO. dig If not, the sample to be tested is determined to be sea clutter; otherwise, continue to determine whether the sample point to be tested is within the tetrahedral PO. fill If not, the sample to be tested is determined to be the target; otherwise, the sample to be tested is determined to be sea clutter.

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