River cross-section point cloud sampling approximation and evaluation method

Abstract

A sampling approximation and evaluation method for river cross-section point clouds is characterized by the following steps: First, cross-section reduction is performed, and evaluation factors are set. Quantitative evaluation is conducted through similarity factors, quantitative proximity factors, and cross-section compression rates. Control parameters can be set and adjusted as needed. Subsequently, cross-section features are sampled and extracted by iteratively calculating the difference values ​​of cross-section features. During the iterative sampling process, the approximation degree of the approximating cross-section is judged until the cross-section approximation factor meets the requirements. This ensures the quantification and uniformity of the refined cross-section after sampling approximation. The algorithm of this invention is reasonable. Under the condition of ensuring quantifiable river cross-section approximation indicators, there will be no cases of missing cross-section feature points or interpolated points. Furthermore, data redundancy is greatly reduced, the computational load is small, and the data acquisition is accurate and comprehensive.

Description

Technical Field

[0001] This invention relates to a method for sampling approximation and evaluation of point cross-sections, and more particularly to a method for sampling approximation and evaluation of point clouds of river cross-sections, belonging to the field of river survey data processing technology. Background Technology

[0002] Complete three-dimensional cross-sectional data of a river channel includes both the land surface and the underwater riverbed. Land surface data is typically acquired using lidar sensors, while the underwater riverbed data is usually obtained using sonar penetrating the water. Currently, the main methods for representing river channel spatial information using the acquired surface and riverbed data include three-dimensional models, digital elevation models, digital line maps, and cross-sections. Among these, the river cross-section is an important representation method, typically laid out perpendicular to the direction of water flow across both banks of the river. River cross-sections, as crucial data, are used in reservoir capacity and sediment deposition analysis, water and sediment mathematical models, engineering quantity calculations, and river numerical simulations. They provide essential foundational data for flood forecasting, river channel management, and scour and sedimentation analysis.

[0003] After acquiring cross-sectional point cloud data, it is generally necessary to perform cross-sectional feature sampling to reduce data redundancy while ensuring that the sampled cross-sections reflect the actual morphology. Cross-sectional feature sampling mainly involves cross-sectional undulations, i.e., elevation change feature points along the cross-section line, including maximum, minimum, maxima, minima, and slope change points. During cross-sectional feature sampling, extraction needs to be performed according to a specific level of precision; therefore, a quantifiable method for evaluating the precision of cross-sectional feature sampling approximation is required to maintain a consistent approximation scale across multiple cross-sections in the same series.

[0004] Existing methods for sampling and approximating cross-section feature points typically rely on manual judgment. However, this method, with its manual control of the extraction scale, makes it difficult to maintain consistency in the degree of approximation and quantify the approximation. When processing multiple cross-sections simultaneously, it can lead to inconsistent cross-section accuracy and low efficiency. Another approach typically involves batch extracting elevation points at a relatively conservative distance for cross-section line reconstruction. This method can improve efficiency through programming, but it may result in missed cross-section feature points. If the distance is set too small, it can lead to significant data redundancy, extremely high computational cost, and difficulty in quantifying and unifying the approximation degree. There has long been a lack of a technical means to quantify the approximation degree of river cross-sections, allow for the setting and adjustment of control parameters as needed to ensure no missed cross-section feature points are extracted, and minimize computational cost, thus addressing these technical problems. Summary of the Invention

[0005] The purpose of this invention is to address the numerous drawbacks of traditional methods for sampling and approximating river cross-section feature points, which rely on manual judgment. These methods cannot quantify the degree of approximation, cannot reflect the characteristics of the river cross-section according to different spatial resolutions, and are prone to missing feature points, resulting in significant data redundancy and computational complexity, severely impacting the accuracy of sampling and evaluation. This invention provides a method for sampling, approximating, and evaluating river cross-section point clouds that features a reasonable algorithm, quantifies the degree of approximation, allows for setting and adjusting control parameters as needed, avoids missing feature points, significantly reduces data redundancy, and provides accurate and comprehensive data acquisition.

[0006] To achieve the above-mentioned objectives, the technical solution of this invention is: a method for sampling approximation and evaluation of point clouds in river cross-sections, comprising the following steps:

[0007] Step 1: Perform cross-sectional calculation; the cross-sectional line is usually represented by the coordinates of the two ends of the cross-section, i.e., L0[(X L0 ,Y L0 ), (X R0 ,Y R0 )], where X L0 Y L0 X R0 Y R0 Let x represent the north and east coordinates of the left and right bank endpoints, respectively. The mileage (S) and elevation (H) of each point on the cross-section line L0 are calculated by fusing the land and underwater point clouds, and the points are arranged in mileage order, thus forming the discrete three-dimensional point cloud set [Tn(x...]. n ,y n H n The sequence is transformed into a two-dimensional ordered point sequence [t1(S1,H1), t2(S2,H2), t3(S3,H3)...t]. n (S n H n [ ], that is, the horizontal axis is the mileage S and the vertical axis is the elevation H;

[0008] Step 2: Set evaluation factors; Evaluation factors include cross-sectional approximation factor and cross-sectional compression ratio. The cross-sectional approximation factor consists of shape similarity factor and quantity similarity factor. The basic idea of ​​the shape similarity factor is to calculate the ratio of the area enclosed by the sampled cross-sectional line and the original cross-sectional line to the cross-sectional length. The shape similarity factor λ = Δs / d is a length quantity. The basic idea of ​​the quantity similarity factor is to calculate the ratio of the difference between the area enclosed by the point cloud cross-section and the sampled cross-section and the horizontal axis to the cross-sectional length, which is φ = (NM) / d.

[0009] Step 3: Sampling and extraction of cross-sectional features; extracting the first and last points t1(S1,H1), t... n (S n Hn Connect them into a line segment, i.e., t1->t n The equation of the straight line is expressed as (s-S1)(H1-H n )=(S1-S n (h-H1);

[0010] Step 4: Using the initial characteristic section t1->t n Using the line segment as a reference, calculate t for each point in the point sequence. k (S k H k On line segment S k The ordinate value h at the location k ,

[0011] h k =A*S k +B, where: A=(H1-H n ) / (S1-S n ), B = (H n S1-S n H1) / (S1-S n );

[0012] Step 5: Perform a comprehensive calculation of the difference in cross-sectional features; determine the point cloud elevation H. k Elevation h of line segment at this point k The absolute value of the difference is Δd k =|H k -h k | According to the method, traverse the interval [S1, S2] of this line segment. n Find the difference between all points within the range and find the maximum value of Δd. max1 This is called the feature difference value. At this point, the approximation factor is also used as the threshold for judging feature values ​​within each cross-sectional interval, i.e., if Δd max1 If the approximation factor is greater than or equal to the approximation factor, then the corresponding cross-sectional point t max1 (S max1 H max1 This is the first sampling point, forming a new line segment t1->t. max1 ->t n If Δd max1 If the value is less than the approximation factor, no additional sampling feature points are needed within this line segment. Then, a judgment is made based on the set cross-sectional approximation factor. If the requirement is met, extraction stops; otherwise, feature point extraction continues.

[0013] Step 6: Change the new line segment t1->t max1 ->t n According to [S1,S max1 ] and [S max1 ,S nRepeat step four iteratively for each interval to find the cross-sectional feature points in each interval until the cross-sectional approximation factor meets the requirements, then stop the approximation factor verification.

[0014] Step 7: Continue iterating to find the feature values ​​of each line segment interval and determine the threshold Δd. max Is there still Δd? max If the value is greater than or equal to the approximation factor, and if so, continue to extract feature points through threshold iteration until Δd is found within all cross-sectional line segment intervals. max Feature point extraction stops when all values ​​are less than the approximation factor.

[0015] Step 8: Form a new point sequence from the feature points obtained in the above steps, which is the cross-sectional feature point sequence. Then, use the cross-sectional feature point sequence to quantitatively evaluate the similarity factor, the quantitative similarity factor, and the cross-sectional data compression rate.

[0016] Furthermore, the method for calculating the similarity factor in step two is as follows:

[0017] The area enclosed by the point cloud cross-section and the coordinate axes can be directly obtained using the trapezoidal area formula, i.e., A. 抽样 =(H1+H n )*(S n -S1) / 2, the area enclosed by the point cloud cross-section and the coordinate axes is calculated using the trapezoidal segmentation method, which divides the area into several smaller trapezoids for calculation. The calculation method is shown in the figure below. Where A k =(H k +H k+1 )×(S k+1 -S k If ) / 2, then the similarity factor λ=∑(|A 抽样 -A 点云 |) / d.

[0018] Furthermore, the calculation method for the proximity factor in step two is as follows:

[0019] It mainly calculates the area enclosed by the point cloud cross-section and the sampling cross-section with the horizontal axis, respectively. Each area is calculated as a whole, and the calculation methods are consistent. Taking the original point cloud cross-section as an example, the calculation method is as follows:

[0020] Finally, the calculation yields φ = (NM) / (S) n+1 -S1), where M is the cross-sectional area of ​​the original point cloud, N is the cross-sectional area of ​​the sampled section, and S n+1 -S1 is the total length of the cross-section from start to end.

[0021] Furthermore, the cross-sectional compression ratio in step two is another indicator with practical significance. The cross-sectional compression ratio is expressed as follows: Let the number of sampling approximation cross-sectional points be j and the number of point cloud cross-sectional points be k, then the cross-sectional compression ratio δ=(cj) / c is the morphological complexity of the cross-section calculated under the same point cloud density and approximation factor.

[0022] The beneficial effects of this invention are:

[0023] 1. This invention preprocesses data using cross-sectional reduction and sets variable evaluation factors for the degree of cross-sectional sampling approximation. It performs quantitative evaluation through similarity factors, quantitative similarity factors, and cross-sectional compression rates, and can set and adjust control parameters as needed.

[0024] 2. This invention employs cross-sectional feature sampling extraction and iteratively calculates the difference values ​​of cross-sectional features. During the iterative sampling process, the approximation degree of the approximating cross-section is judged until the cross-sectional approximation factor meets the requirements, thus ensuring the quantification and uniformity of the fine measurement of the cross-section after sampling approximation.

[0025] 3. The algorithm of this invention is reasonable. While ensuring quantifiable river cross-section approximation indicators, it quantitatively constrains the results in the vertical elevation direction, avoiding the omission of cross-section feature points and interpolation points. Furthermore, the data redundancy is greatly reduced, the computational load is small, and the data acquisition is accurate and comprehensive. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of existing technology.

[0027] Figure 2 This is a coordinate graph of the data preprocessing in this invention.

[0028] Figure 3 This is a coordinate graph of the shape resemblance factor of the present invention.

[0029] Figure 4 This is a coordinate graph of elevation and mileage of the present invention.

[0030] Figure 5 This is a coordinate graph of the quantity proximity factor of the present invention.

[0031] Figure 6 This is a point cloud cross-sectional polygonal diagram of Example 1 of the present invention.

[0032] Figure 7 This is a sampling section coordinate diagram of Example 1 of the present invention.

[0033] Figure 8 This is a sampling cross-sectional state diagram of Example 1 of the present invention.

[0034] Figure 9 This is a sampled cross-sectional view of Example 1 of the present invention.

[0035] Figure 10 This is the final cross-sectional view of Example 1 of the present invention.

[0036] Figure 11 This is a flowchart of the method of the present invention. Detailed Implementation

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] See Figures 1 to 11 The present invention provides a sampling approximation and evaluation method for point clouds of river cross sections, characterized by comprising the following steps:

[0039] Step 1: Perform cross-sectional calculation; the cross-sectional line is usually represented by the coordinates of the two ends of the cross-section, i.e., L0[(X L0 ,Y L0 ), (X R0 ,Y R0 )], where X L0 Y L0 X R0 Y R0 Let x represent the north and east coordinates of the left and right bank endpoints, respectively. The mileage (S) and elevation (H) of each point on the cross-section line L0 are calculated by fusing the land and underwater point clouds, and the points are arranged in mileage order, thus forming the discrete three-dimensional point cloud set [Tn(x...]. n ,y n H n The sequence is transformed into a two-dimensional ordered point sequence [t1(S1,H1), t2(S2,H2), t3(S3,H3)...t]. n (S n H n [ ], that is, the horizontal axis is the mileage S and the vertical axis is the elevation H;

[0040] Step 2: Set evaluation factors; Evaluation factors include cross-sectional approximation factor and cross-sectional compression ratio. The cross-sectional approximation factor consists of shape similarity factor and quantity similarity factor. The basic idea of ​​the shape similarity factor is to calculate the ratio of the area enclosed by the sampled cross-sectional line and the original cross-sectional line to the cross-sectional length. The shape similarity factor λ = Δs / d is a length quantity. The basic idea of ​​the quantity similarity factor is to calculate the ratio of the difference between the area enclosed by the point cloud cross-section and the sampled cross-section and the horizontal axis to the cross-sectional length, denoted as φ = (NM) / d.

[0041] Step 3: Sampling and extraction of cross-sectional features; extracting the first and last points t1(S1,H1), t... n (S n H n Connect them into a line segment, i.e., t1->t n The equation of the straight line is expressed as (s-S1)(H1-Hn )=(S1-S n (h-H1);

[0042] Step 4: Using the initial characteristic section t1->t n Using the line segment as a reference, calculate t for each point in the point sequence. k (S k H k On line segment S k The ordinate value h at the location k ,

[0043] h k =A*S k +B, where: A=(H1-H n ) / (S1-S n ), B = (H n S1-S n H1) / (S1-S n );

[0044] Step 5: Perform a comprehensive calculation of the difference in cross-sectional features; determine the point cloud elevation H. k Elevation h of line segment at this point k The absolute value of the difference is Δd k =|H k -h k | According to the method, traverse the interval [S1, S2] of this line segment. n Find the difference between all points within the range and find the maximum value of Δd. max1 This is called the feature difference value. At this point, the approximation factor is also used as the threshold for judging feature values ​​within each cross-sectional interval, i.e., if Δd max1 If the approximation factor is greater than or equal to the approximation factor, then the corresponding cross-sectional point t max1 (S max1 H max1 This is the first sampling point, forming a new line segment t1->t. max1 ->t n If Δd max1 If the value is less than the approximation factor, no additional sampling feature points are needed within this line segment. Then, a judgment is made based on the set cross-sectional approximation factor. If the requirement is met, extraction stops; otherwise, feature point extraction continues.

[0045] Step 6: Change the new line segment t1->t max1 ->t n According to [S1,S max1 ] and [S max1 ,S n Repeat step four iteratively for each interval to find the cross-sectional feature points in each interval until the cross-sectional approximation factor meets the requirements, then stop the approximation factor verification.

[0046] Step 7: Continue iterating to find the feature values ​​of each line segment interval and determine the threshold Δd. max Is there still Δd? max If the value is greater than or equal to the approximation factor, and if so, continue to extract feature points through threshold iteration until Δd is found within all cross-sectional line segment intervals. max Feature point extraction stops when all values ​​are less than the approximation factor.

[0047] Step 8: Form a new point sequence from the feature points obtained in the above steps, which is the cross-sectional feature point sequence. Then, use the cross-sectional feature point sequence to quantitatively evaluate the similarity factor, the quantitative similarity factor, and the cross-sectional data compression rate.

[0048] The method for calculating the similarity factor in step two is as follows:

[0049] The area enclosed by the point cloud cross-section and the coordinate axes can be directly obtained using the trapezoidal area formula, i.e., A. 抽样 =(H1+H n )*(S n -S1) / 2, the area enclosed by the point cloud cross-section and the coordinate axes is calculated using the trapezoidal segmentation method, which divides the area into several smaller trapezoids for calculation. The calculation method is shown in the figure below. in

[0050] A k =(H k +H k+1 )×(S k+1 -S k If ) / 2, then the similarity factor λ=∑(|A 抽样 -A 点云 |) / d.

[0051] The method for calculating the proximity factor in step two is as follows:

[0052] It mainly calculates the area enclosed by the point cloud cross-section and the sampling cross-section with the horizontal axis, respectively. Each area is calculated as a whole, and the calculation methods are consistent. Taking the original point cloud cross-section as an example, the calculation method is as follows:

[0053]

[0054] Finally, the calculation yields φ = (NM) / (S) n+1 -S1), where M is the cross-sectional area of ​​the original point cloud, N is the cross-sectional area of ​​the sampled section, and S n+1 -S1 is the total length of the cross-section from start to end.

[0055] The section compression ratio in step two is another indicator with practical significance. The section compression ratio is expressed as follows: Let the number of sampling approximation section points be j and the number of point cloud section points be k, then the section compression ratio δ=(cj) / c is the morphological complexity of the section calculated under the same point cloud density and approximation factor.

[0056] See Figures 1 to 5 This invention preprocesses data using cross-sectional reduction and sets a variable evaluation factor for the degree of cross-sectional sampling approximation, which can be adjusted as needed. Simultaneously, it samples and approximates dense point cloud cross-sections, greatly reducing data redundancy. During the iterative sampling process, the approximation degree of the approximated cross-sections is judged, ensuring the quantitative consistency and precision of the approximated cross-sections. The specific steps and principles are as follows:

[0057] The cross-sectional line of a river channel is usually represented by the coordinates of the two ends of the cross-section, i.e., L0[(X L0 ,Y L0 ), (X R0 ,Y R0 )], where X L0 Y L0 X R0 Y R0 Let x represent the north and east coordinates of the left and right bank endpoints, respectively. The mileage (S) and elevation (H) of each point on the cross-section line L0 are calculated by fusing the land and underwater point clouds, and the points are arranged in mileage order, thus forming the discrete three-dimensional point cloud set [Tn(x...]. n ,y n H n The sequence is transformed into a two-dimensional ordered point sequence [t1(S1,H1), t2(S2,H2), t3(S3,H3)...t]. n (S n H n [ ], that is, the horizontal axis is the mileage S and the vertical axis is the elevation H.

[0058] Since feature extraction does not perfectly recreate the original point cloud sequence cross-section, but rather approximates it through sampling, the sampling approximation process requires quantitative control, and the results need quantitative evaluation. Therefore, this invention addresses this by setting a cross-section approximation factor that balances quantitative control of the sampling process and quantitative evaluation of the results. The evaluation factors include the cross-section approximation factor and the cross-section compression rate. The approximation factor consists of a shape similarity factor and a quantitative similarity factor. The shape similarity factor focuses on evaluating the degree of detail restoration of the cross-section, while the quantitative similarity factor primarily quantifies the overall change in the approximated cross-section based on its cross-sectional area. In practice, the shape similarity factor functions as both a sampling process control factor and an approximation cross-section evaluation factor, while the quantitative similarity factor is typically used only as an evaluation factor.

[0059] The basic idea of ​​the similarity factor is to calculate the ratio of the area enclosed by the sampled section line and the original section line to the section length. See [link to relevant documentation]. Figure 3 As shown, the similarity factor λ = Δs / d is a length quantity. Figure 3 The enclosed area Δs is obtained by accumulating the areas of each independent region. The area of ​​each independent region is the absolute value of the difference between the area enclosed by the point cloud cross-section and the horizontal coordinate axis and the area enclosed by the sampling cross-section and the horizontal coordinate axis. For example... Figure 4 As shown, since the area enclosed by the sampling cross-section and the coordinate axis in each independent region is trapezoidal, the area of ​​the area enclosed by the point cloud cross-section and the coordinate axis can be directly obtained from the trapezoidal area calculation formula, i.e., A. 抽样 =(H1+H n )*(S n -S1) / 2. The area enclosed by the point cloud cross-section and the coordinate axes is calculated using the trapezoidal segmentation method, which divides the area into several smaller trapezoids for calculation. The calculation method is shown below.

[0060] A 点云 = Where A k =(H k +H k+1 )×(S k+1 -S k If ) / 2, then the similarity factor is λ=∑(|A 抽样 -A 点云 |) / d.

[0061] The basic idea of ​​the similarity factor is to calculate the ratio of the difference between the area enclosed by the point cloud cross-section and the sampled cross-section and the horizontal axis to the cross-sectional length, as shown in the figure below, which is φ=(NM) / d. Its area calculation method is similar to that of the shape similarity factor. The difference lies in that the similarity factor directly calculates the area of ​​the point cloud cross-section and the sampled cross-section as a whole and then calculates the difference. The result can be positive or negative, reflecting the amount and trend of change in the cross-sectional area.

[0062] Cross-sectional compression ratio is another practically significant indicator, calculated based on the results for evaluation. Let j be the number of sampled approximation cross-sectional points and k be the number of point cloud cross-sectional points, then the cross-sectional compression ratio δ = (cj) / c, representing the morphological complexity of the cross-section calculated under the same point cloud density and approximation factor. The cross-sectional approximation factor is selected according to requirements. The shape similarity factor is essentially the similarity between the sampled point cross-section and the original point cloud cross-section, i.e., the precision of reconstruction; the quantitative similarity factor is essentially the overall change between the sampled point cross-section and the original point cloud cross-section. One controls the microscopic change, and the other controls the macroscopic overall change. Over time, both approximation factors can be used together as indicators for evaluating cross-sectional approximation. For example, when the shape similarity factor reaches a certain limit, the quantitative similarity factor can be calculated and evaluated, and vice versa.

[0063] To extract cross-sectional features, firstly, the first and last points t1(S1,H1), t... n (S n H n Connect them into a line segment, i.e., t1->t n The equation of the straight line is expressed as (s-S1)(H1-H n )=(S1-S n (h-H1). Then, using the initial characteristic section t1->t n Using the line segment as a reference, calculate t for each point in the point sequence. k (S k H k On line segment S k The ordinate value h at the location k The calculation is performed using the following formula:

[0064] h k =A*S k +B, where: A=(H1-H n ) / (S1-S n ), B = (H n S1-S n H1) / (S1-S n ).

[0065] Next, calculate the point cloud elevation H. k Elevation h of line segment at this point k The absolute value of the difference is Δd k =|H k -h k | According to the method, traverse the interval [S1, S2] of this line segment. n Find the difference between all points within the range and find the maximum value of Δd. max1 This is called the feature difference value. At this point, the approximation factor is also used as the threshold for judging feature values ​​within each cross-sectional interval, i.e., if Δd max1 If the approximation factor is greater than or equal to the approximation factor, then the corresponding cross-sectional point t max1 (S max1 H max1 This is the first sampling point, forming a new line segment t1->t. max1 ->t n If Δd max1 If the value is less than the approximation factor, no additional sampling feature points are needed within this line segment. Then, a judgment is made based on the set cross-sectional approximation factor. If the requirement is met, extraction stops; otherwise, feature point extraction continues.

[0066] Change the new line segment t1->t max1 ->t n According to [S1,S max1 ] and [S max1 ,Sn Repeat step four iteratively for each interval to find the cross-sectional feature points within that interval until the cross-sectional approximation factor meets the requirements. Then stop the approximation and verify the result. Continue iteratively to find the feature values ​​of each line segment interval and determine the threshold Δd. max Is there still Δd? max If the value is greater than or equal to the approximation factor, and if so, continue to extract feature points through threshold iteration until Δd is found within all cross-sectional line segment intervals. max Feature point extraction stops when all points are less than the approximation factor. The feature points obtained in the above steps are combined into a new point sequence, which is the cross-sectional feature point sequence.

[0067] By completing the above steps, it is possible to approximate the original point cloud cross section with a small number of feature points and to quantitatively evaluate it from aspects such as similarity factor, quantitative proximity factor and cross section data compression rate, so as to determine whether it meets the application requirements and evaluate the approximation degree of the sampled cross section and the terrain complexity.

[0068] The specific implementation is as follows: Taking the measurement data of a certain river channel as an example, the land measurement is carried out by UAV-borne lidar, and the underwater riverbed part is measured by single-beam sonar along the cross-section line. The total length of the cross-section is 323m and the number of point clouds is 721. Now, the sampling cross-section is extracted according to the similarity factor of less than 0.1m.

[0069] First, the cross-section transforms the 3D coordinate data of the land and underwater point clouds into mileage and elevation, resulting in a dense point cloud cross-section polyline diagram. (See [link to diagram]). Figure 6 .

[0070] Secondly, feature extraction is performed based on this. First, the first and second section points are connected into a line segment to form the initial sampling section. Figure 7 (As shown by the red line in the middle), see Figure 7 At this point, the similarity factor is 11.85m, which does not meet the requirements.

[0071] Then, feature sampling is performed according to the method in step five, and the resulting sampling cross-section is shown in the figure below. The initial sampling cross-section has a very low similarity to the point cloud cross-section, with a similarity factor of 5.38m. The difference between the two line segments is Δd. max1 These do not meet the requirements.

[0072] Next, continue with iterative feature sampling using the method in step five, calculating the maximum distance Δd between the two line segments. max The lengths are 8.96m and 12.62m respectively, therefore, characteristic points need to be sampled within both line segments, and the resulting sampling cross-sections are shown in the attached figure. Figure 8 As shown, the calculated similarity factor is 5.38m, which still does not meet the requirements.

[0073] Then, iterative feature sampling is performed using the method in step five. After a total of nine iterations, the Δd between the point cloud cross-section points and the sampled cross-section line segments within all cross-sectional intervals is calculated. max With a diameter less than 0.1m, a similarity factor of 0.09m, and a proximity factor of -0.03m, 46 sampling cross-sectional points were obtained that met the requirements. The cross-sectional data compression rate was 94%, and the final cross-sectional results are shown in the attached figure. Figure 10 As shown in the figure. This method avoids the problem of missing cross-sectional feature points and significantly reduces data redundancy, greatly improving the accuracy of sampling approximation and evaluation.

[0074] The following table shows the statistics of various parameters during the processing iteration:

[0075] Number of iterations Sampling area Point cloud area Cross-sectional length Cross area Form similarity factor Quantity near factor Number of nodes 1 517.40 359.92 32.36 191.73 11.85 9.73 2 2 291.22 359.92 32.36 86.98 5.38 -4.25 3 3 373.43 359.92 32.36 38.47 2.38 0.83 5 4 338.86 359.92 32.36 40.55 2.51 -1.30 9 5 366.63 359.92 32.36 21.39 1.32 0.41 15 6 358.52 359.92 32.36 8.68 0.54 -0.09 22 7 358.80 359.92 32.36 3.68 0.23 -0.07 28 8 359.67 359.92 32.36 2.59 0.16 -0.02 35 9 359.45 359.92 32.36 1.50 0.09 -0.03 46

[0076] The above description is a further detailed explanation of the present invention in conjunction with specific embodiments. It should not be considered that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, any simple modifications and substitutions made without departing from the concept of the present invention should be considered to fall within the protection scope of the present invention.

Claims

1. A sampling approximation and evaluation method for point clouds in river cross-sections, comprising the following steps: Step 1: Perform cross-sectional calculation; the cross-sectional line is usually represented by the coordinates of the two ends of the cross-section, i.e., L0[(X L0 ,Y L0 ), (X R0 ,Y R0 )], where X L0 Y L0 X R0 Y R0 Let x represent the north and east coordinates of the left and right bank endpoints, respectively. The point cloud of the fused land and underwater cross-sections will have its mileage (S) and elevation (H) calculated point by point along the cross-section line L0. The points will then be arranged in mileage order, forming the discrete three-dimensional point cloud set [Tn(x...]. n ,y n H n The sequence is transformed into a two-dimensional ordered point sequence [t1(S1,H1), t2(S2,H2), t3(S3,H3)...t]. n (S n H n [ ], that is, the horizontal axis is the mileage S and the vertical axis is the elevation H; Step 2: Set evaluation factors; Evaluation factors include cross-sectional approximation factor and cross-sectional compression ratio. The cross-sectional approximation factor consists of shape similarity factor and quantity similarity factor. The basic idea of ​​the shape similarity factor is to calculate the ratio of the area enclosed by the sampled cross-sectional line and the original cross-sectional line to the cross-sectional length. The shape similarity factor λ = Δs / d is a length quantity. The basic idea of ​​the quantity similarity factor is to calculate the ratio of the difference between the area enclosed by the point cloud cross-section and the sampled cross-section and the horizontal axis to the cross-sectional length, denoted as φ = (NM) / d. Step 3: Sampling and extraction of cross-sectional features; extracting the first and last points t1(S1,H1), t... n (S n H n Connect them into a line segment, i.e., t1->t n The equation of the straight line is expressed as (s-S1)(H1-H n )=(S1-S n (h-H1); Step 4: Using the initial characteristic section t1->t n Using the line segment as a reference, calculate t for each point in the point sequence. k (S k H k On line segment S k The ordinate value h at the location k , h k =A*S k +B, where: A=(H1-H n ) / (S1-S n ), B = (H n S1-S n H1) / (S1-S n ); Step 5: Perform a comprehensive calculation of the difference in cross-sectional features; determine the point cloud elevation H. k Elevation h of line segment at this point k The absolute value of the difference is Δd k =|H k -h k | According to the method, traverse the interval [S1, S2] of this line segment. n Find the difference between all points within the range and find the maximum value of Δd. max1 This is called the feature difference value. At this point, the approximation factor is also used as the threshold for judging feature values ​​within each cross-sectional interval, i.e., if Δd max1 If the approximation factor is greater than or equal to the approximation factor, then the corresponding cross-sectional point t max1 (S max1 H max1 This is the first sampling point, forming a new line segment t1->t. max1 ->t n If Δd max1 If the value is less than the approximation factor, no additional sampling feature points are needed within this line segment; then, a judgment is made based on the set cross-section approximation factor. If the requirements are met, extraction stops; otherwise, feature point extraction continues. Step 6: Change the new line segment t1->t max1 ->t n According to [S1,S max1 ] and [S max1 ,S n Repeat step four iteratively for each interval to find the cross-sectional feature points in each interval until the cross-sectional approximation factor meets the requirements, then stop the approximation factor verification. Step 7: Continue iterating to find the feature values ​​of each line segment interval and determine the threshold Δd. max Is there still Δd? max If the value is greater than or equal to the approximation factor, and if so, continue to extract feature points through threshold iteration until Δd is found within all cross-sectional line segment intervals. max Feature point extraction stops when all values ​​are less than the approximation factor. Step 8: Form a new point sequence from the feature points obtained in the above steps, which is the cross-sectional feature point sequence. Then, use the cross-sectional feature point sequence to quantitatively evaluate the similarity factor, the quantitative similarity factor, and the cross-sectional data compression rate.

2. The sampling approximation and evaluation method for point clouds of river cross sections according to claim 1, characterized in that: The method for calculating the similarity factor in step two is as follows: The area enclosed by the point cloud cross-section and the coordinate axes can be directly obtained using the trapezoidal area formula, i.e., A. 抽样 =(H1+H n )*(S n -S1) / 2, the area enclosed by the point cloud cross-section and the coordinate axes is calculated using the trapezoidal segmentation method, which divides the area into several smaller trapezoids for calculation. The calculation method is shown in the figure below. in A k =(H k +H k+1 )×(S k+1 -S k If ) / 2, then the similarity factor λ=Σ(|A 抽样 -A 点云 |) / d.

3. The sampling approximation and evaluation method for point clouds of river cross sections according to claim 1, characterized in that: The method for calculating the proximity factor in step two is as follows: The areas enclosed by the point cloud cross-section and the sampling cross-section and the horizontal axis are calculated separately, using a unified calculation method. The calculation method is consistent. Taking the original point cloud cross-section as an example, the calculation method is as follows: Finally, the calculation yields φ = (NM) / (S) n+1 -S1), where M is the cross-sectional area of ​​the original point cloud, N is the cross-sectional area of ​​the sampled section, and S n+1 -S1 is the total length of the cross-section from start to end.

4. The sampling approximation and evaluation method for point clouds of river cross sections according to claim 1, characterized in that: The section compression ratio in step two is another indicator with practical significance. The section compression ratio is expressed as follows: Let the number of sampling approximation section points be j and the number of point cloud section points be c, then the section compression ratio δ=(cj) / c is the morphological complexity of the section calculated under the same point cloud density and approximation factor.

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