Urban land identification method based on remote sensing image

By combining high-definition UAV remote sensing imagery with the Sobel algorithm, accurate extraction and refined classification of urban land use outlines were achieved, solving the problems of insufficient outline extraction accuracy and unreasonable regional division in traditional methods, and improving the efficiency and scientific nature of urban land use planning.

CN120876889AActive Publication Date: 2025-10-31HUNAN UNIV +1

Patent Information

Application Number
CN202511370556.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-09-24
Publication Date
2025-10-31
Estimated Expiration
2045-09-24

AI Technical Summary

Technical Problem

Traditional urban land use identification methods suffer from insufficient contour extraction accuracy, limited ability to capture feature edges, lack of fine-grained processing, inability to reflect the spatial distribution characteristics of feature edges, and a single regional division strategy, making it difficult to meet the needs of land use coordination and functional agglomeration in urban planning.

Method used

By combining high-resolution remote sensing imagery from high-definition UAVs with the Sobel algorithm, and through gradient pixel identification, grayscale processing, contour feature quantization, and refinement point selection, the optimal combination of pixel mean and variance features is used to generate urban land use contours, thereby achieving accurate extraction and refined classification of urban land use contours.

Benefits of technology

It significantly improves the accuracy of contours and classification, and the generated combined areas are highly consistent with the needs of urban planning, reducing classification errors and improving planning efficiency and scientific rigor.

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Abstract

The invention discloses an urban land identification method based on a remote sensing image, relates to the technical field of urban land planning, solves the problem of insufficient refined features of an original identification mode, and locks core boundary pixels from a complex gradient pixel point set through pixel interval quantization, feature circle construction and refined point screening. The contour precision is obviously improved; compared with a traditional single-line contour, the refined contour can more completely represent the surface feature form, is especially suitable for irregular terrains, and reduces classification errors. According to the method, the pixel mean value and variance features are taken as measurement, the number of combination areas and the similarity of internal features are considered, the optimal combination is screened through weighted calculation, scattered division or excessive combination is avoided, the generated optimal combination areas highly meet the requirements of function aggregation and land cooperation in urban planning, and the planning efficiency and scientificity are remarkably improved.
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Description

Technical Field

[0001] This invention relates to the field of urban land use planning technology, specifically to a method for urban land use identification based on remote sensing imagery. Background Technology

[0002] With the acceleration of urbanization, urban land use planning has an increasingly urgent need for high-precision and high-efficiency feature identification and zoning. Traditional urban land use identification relies on manual on-site surveys or low-resolution remote sensing imagery, which has limitations such as low efficiency, large errors, and difficulty in capturing complex terrain details.

[0003] While existing technologies include automated identification methods based on remote sensing images, they generally suffer from the following problems: First, the contour extraction accuracy is insufficient, with limited ability to capture edge features of irregularly bounded areas such as lakes and forests, and is easily affected by spectral interference, leading to contour shifts. Second, there is a lack of refined processing, as features are represented only by single-line contours, failing to reflect the spatial distribution characteristics of feature edges and affecting the accuracy of subsequent classification. Third, the regional division strategy is simplistic, failing to consider the spatial correlation and functional similarity between features, making it difficult for the division results to meet the needs of land use coordination and functional agglomeration in urban planning.

[0004] To address the aforementioned pain points, there is an urgent need for a technical solution that integrates high-precision image processing and intelligent analysis to achieve accurate extraction of urban land use outlines, refined classification of terrain features, and scientific and rational regional combinations, thereby providing reliable support for the optimal allocation of urban land resources. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for urban land use identification based on remote sensing imagery, which solves the problem of insufficient fine-grained features in the original identification method.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for urban land use identification based on remote sensing imagery, comprising the following steps: Step 1: Acquire remote sensing images of the area to be planned and confirm gradient pixels. From the confirmed gradient pixels, sequentially label the contour regions existing in the remote sensing image. The specific method is as follows: The RGB values ​​associated with different image points within the remote sensing image are confirmed, and the confirmed RGB values ​​are then converted to grayscale. The grayscale value associated with the corresponding image point is confirmed using the formula: HD = R × 0.114 + G × 0.587 + B × 0.299. Based on the different grayscale values ​​associated with different image points, the remote sensing image is converted to grayscale to confirm the grayscale image. The Sobel algorithm is used to identify the vertical gradient and the vertical gradient associated with different pixels in the grayscale image, and the identified vertical gradient is denoted as C. iThe confirmed vertical gradient is denoted as S. i Where i represents different pixels, using Confirm the overall gradient ZH associated with the corresponding pixel. i ; Will satisfy: ZH i >Pixels with Y1 are labeled as gradient pixels, and Y1 is a preset value; otherwise, no labeling is performed. The gradient pixels associated with the grayscale image are identified sequentially, and the middle area included by the consecutive gradient pixels is recorded as the contour region. The contour regions associated with the grayscale image are then marked sequentially. Step 2: Based on the contour features of the contour region, quantize the contour features numerically, then select refinement points from the quantized feature values, connect these refinement points to confirm the refined contour belonging to the corresponding contour region. The specific method is as follows: Several contour regions marked in the remote sensing image are identified, and the edge contour of the corresponding contour region is locked from the identified single contour region. The pixel values ​​associated with several gradient pixels in the edge contour are confirmed in turn, and the minimum and maximum values ​​are determined to lock the contour pixel range. The corresponding edge contour-locked pixel range is numerically quantized, with the minimum value quantized to 0 and the maximum value quantized to 2. The quantization ratio is then determined as (maximum value - minimum value) ÷ 2 = quantization ratio. Several pixel values ​​within the contour pixel range are then quantized using X. i ÷ Quantification ratio = L i Confirm the quantization value L corresponding to the pixel. i ; Combine the corresponding contour region with the two-dimensional coordinate system, and confirm the different two-dimensional coordinates associated with different pixels. Average the two-dimensional coordinates of several groups of pixels, confirm the average coordinates, and simultaneously mark them in this contour region as the center point of this contour region. Lock the pixel farthest from this center point from the edge contour of the contour region and record it as the feature edge point. With the center point as the center and the straight-line distance between the center point and the feature edge point as the radius, confirm a set of feature circles. Using the edge circle points of the feature circle as the association endpoints, confirm the association lines between the center point and the association endpoints. Record the portion of the association line within the edge contour as a contour line. Record the several pixels where each contour line intersects as a pixel set. Select refinement points from each different pixel set: confirm the different quantization values ​​L associated with different pixels in the pixel set. i Using: Cz i =|L i -1| Confirm the feature difference Cz associated with the corresponding pixel.i Then, from the different feature differences Cz associated with different pixels i In the middle, select Cz i The pixels associated with min are selected as the thinning points; Based on the selected thinning points of each pixel set, connect adjacent thinning points to confirm the thinning contour belonging to this contour region, and re-use the thinning contour as the edge contour of this contour region. Step 3: Based on the specific pixel features of the corresponding contour region, determine the category to which this contour region belongs, and label the category accordingly. The specific method is as follows: Based on the edge contour after contour region refinement, the pixel values ​​of several pixels located within the edge contour are confirmed, and based on the confirmed minimum and maximum values, the pixel value range belonging to this contour region is confirmed. Verify and check the pixel value range with several preset ranges: confirm the intersection range of the pixel value range with different preset ranges, and determine the proportion of the intersection range located in the corresponding preset range. The proportion is calculated as the total length of the intersection range ÷ the total length of the preset range. The preset range that meets the requirement of a proportion ≥ 85% is taken as the adaptation range of this pixel value range, and the category associated with this adaptation range is taken as the category of this contour region, and is simultaneously marked in the remote sensing image. Step 4: Randomly combine several associated contour regions within the remote sensing image to generate combined regions. Based on different random combination processes, select the optimal process and display the combined regions associated with the optimal process as the optimal combined regions. The specific method is as follows: The average value of several pixels associated with each contour region is processed to determine the average pixel value of each contour region, and this value is used as the contour feature of the corresponding contour region. Adjacent contour regions within the remote sensing image are randomly combined to identify combined regions. Each combined region must include at least two sets of contour regions. The total number of combined regions identified in this random combination process is denoted as G. k Then, variance processing is performed on the contour features associated with several contour regions within the corresponding combined area to confirm the variance eigenvalue F associated with the corresponding combined area. k k represents different combinations of processes; G is adopted. k ×A1+F k ×A2=BZ k Determine the calibration feature value BZ associated with the corresponding combination process. k A1 and A2 are both preset fixed coefficient factors, representing different calibration characteristic values ​​BZ associated with different combination processes. k In the middle, select BZ kThe process associated with min is recorded as the optimal process. The combined region associated with the optimal process is recorded as the optimal combined region and displayed.

[0007] This invention provides a method for urban land use identification based on remote sensing imagery. Compared with existing technologies, it has the following advantages: This invention combines high-resolution UAV imagery with the Sobel algorithm to accurately capture edge differences in different areas such as lakes and forests. Grayscale processing and gradient thresholding effectively filter out interference information, ensuring that the outline region division fits the true boundary of the ground features, laying a reliable foundation for subsequent analysis. By quantizing pixel intervals, constructing feature circles, and filtering refined points, core boundary pixels are locked from complex gradient pixel sets, significantly improving contour accuracy. Compared with traditional single-line contours, refined contours can more completely represent the morphology of ground features, especially suitable for irregular terrain, reducing classification errors. Using pixel mean and variance features as measures, and taking into account the number of combined areas and the similarity of internal features, the optimal combination is selected through weighted calculation to avoid scattered division or excessive merging. The generated optimal combination area is highly consistent with the needs of functional agglomeration and land use coordination in urban planning, which significantly improves planning efficiency and scientificity. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a schematic diagram illustrating the determination of the outline connection lines of the present invention. Detailed Implementation

[0009] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Example

[0010] Please see Figure 1 This application provides a method for urban land use identification based on remote sensing imagery, including the following steps: Step 1: Acquire remote sensing images of the area to be planned and confirm the gradient pixels of the acquired images. From the confirmed gradient pixels, the contour regions existing in the remote sensing images are sequentially labeled. Specifically, in the remote sensing images, different regional blocks within the images differ significantly from other areas at their edges. For example, lake areas have obvious contour features, and forest areas also have relatively obvious contour features. By confirming their corresponding gradient pixels, the contour regions can be specifically labeled, facilitating subsequent type identification of different blocks. The remote sensing images were acquired using a high-resolution drone, and the acquired images have high resolution. The specific processing method for labeling is as follows: The RGB values ​​associated with different image points within the remote sensing image are confirmed, and the confirmed RGB values ​​are then converted to grayscale. The grayscale value associated with the corresponding image point is confirmed using the formula: HD = R × 0.114 + G × 0.587 + B × 0.299. Based on the different grayscale values ​​associated with different image points, the remote sensing image is converted to grayscale to confirm the grayscale image. The Sobel algorithm is used to identify the vertical gradient and the vertical gradient associated with different pixels in the grayscale image, and the identified vertical gradient is denoted as C. i The confirmed vertical gradient is denoted as S. i Where i represents different pixels (its Sobel algorithm is based on the arrangement of corresponding pixels, taking the pixel to be determined as the center point, combining it with eight surrounding pixels, and assigning different weights to determine the relevant gradient data associated with the corresponding pixel; this content is quite common in existing technologies, so it will not be elaborated on here). Confirm the overall gradient ZH associated with the corresponding pixel. i ; Will satisfy: ZH i > The pixel point with Y1 is labeled as a gradient pixel point, and its Y1 is a preset value. The specific value is determined by the operator based on experience. Otherwise, no labeling is performed. The gradient pixels associated with the grayscale image are identified in sequence, and the middle area included by the several consecutive gradient pixels is recorded as the contour area (that is, the middle area formed by the several gradient pixels). The contour areas associated with the grayscale image are marked in sequence. Specifically, a loop will be generated between different gradient pixels, and the middle area generated by the loop is the corresponding contour area. Step 2: Based on several different contour regions identified within the remote sensing image, and based on the contour features of these regions, the contour features are numerically quantized. Then, refinement points are selected from the quantized feature values. These refinement points are connected to confirm the refined contour belonging to the corresponding contour region. Specifically, different edge contours have different contour features; their corresponding contour features are not just a single line, but a region. Such regions contain several gradient pixels. To achieve a better contour refinement effect, the optimal pixel is locked from the corresponding gradient pixels, and the contour is refined again. The specific confirmation process is as follows: Several contour regions marked in the remote sensing image are identified, and the edge contour of the corresponding contour region is locked from the identified single contour region. The pixel values ​​associated with several gradient pixels in the edge contour are confirmed in turn, and the minimum and maximum values ​​are determined to lock the contour pixel range. The corresponding edge contour-locked pixel range is numerically quantized, with the minimum value quantized to 0 and the maximum value quantized to 2. The quantization ratio is then determined as (maximum value - minimum value) ÷ 2 = quantization ratio. Several pixel values ​​within the contour pixel range are then quantized using X. i ÷ Quantification ratio = L i Confirm the quantization value L corresponding to the pixel. i For example, suppose the associated contour pixel range is [20, 40], where 20 is quantized to 0 and 40 is quantized to 2. Then the associated quantization value is 20, and there are three pixels in the range, with associated pixel values ​​of 25, 30 and 35 respectively. 25 is quantized to 1.25, 30 is quantized to 1.5 and 35 is quantized to 1.75. The corresponding contour region is combined with a two-dimensional coordinate system, and the different two-dimensional coordinates associated with different pixels are identified. The two-dimensional coordinates of several sets of pixels are averaged to determine the average coordinates, which are then simultaneously marked within this contour region as the center point. The pixel furthest from this center point is then identified on the edge contour of the contour region and denoted as the feature edge point. A set of feature circles is identified with the center point as the center and the straight-line distance between the center point and the feature edge point as the radius. Figure 2 Based on the corresponding contour area, the corresponding center point is locked, and then the corresponding feature circle is constructed by combining the farthest edge point. Then the connection line is confirmed. After the connection line is confirmed, the contour line belonging to the corresponding edge contour can be locked, and the points associated with the contour line are selected for feature selection. The corresponding refinement point is locked from it. Based on the refinement point determined in sequence, the refinement contour belonging to this area can be locked. Using the edge circle points of the feature circle as the association endpoints, confirm the association lines between the center point and the association endpoints. Record the portion of the association line within the edge contour as the contour line. Record the several pixels where each contour line intersects as a pixel set, and select refinement points from each different pixel set. Identify the different quantization values ​​L associated with different pixels in the pixel set. i Using: Cz i =|L i -1| Confirm the feature difference Cz associated with the corresponding pixel. i Then, from the different feature differences Cz associated with different pixels i In the middle, select Cz i The pixels associated with min are selected as the thinning points; Based on the selected thinning points of each pixel set, adjacent thinning points are connected to confirm the thinning contour belonging to this contour region, and the thinning contour is re-used as the edge contour of this contour region. Specifically, the gradient pixel associated with the thinning contour is the most central pixel in the corresponding gradient region. This processing method can effectively complete the thinning of the edge contour of each different contour region, thereby achieving a better region division processing effect. Step 3: For the relevant contour areas in the remote sensing image that have been refined, based on the specific pixel features of the corresponding contour areas, confirm the classification of the contour areas and label the classification. Specifically, the classification includes relevant areas with different terrain features such as lakes, tree bark, and flat land. The specific method for calibration is as follows: Based on the edge contour after contour region refinement, the pixel values ​​of several pixels located within the edge contour are confirmed, and based on the confirmed minimum and maximum values, the pixel value range belonging to this contour region is confirmed. Verify and check the pixel value range with several preset ranges: confirm the intersection range of the pixel value range with different preset ranges, and determine the proportion of the intersection range located in the corresponding preset range. The proportion is calculated as the total length of the intersection range ÷ the total length of the preset range. Preset ranges that meet the requirement of a proportion ≥ 85% are used as the adaptation ranges for this pixel value range, and the category associated with this adaptation range is used as the category of this contour region. These are then simultaneously labeled in the remote sensing image. If the requirement is not met, no labeling is performed. Specifically, each contour region has an associated pixel value range, and the corresponding pixel value range intersects with the corresponding preset range. The preset ranges are all determined by the operator based on the terrain features and are all preset values. Each different contour region has its own category, so the specific category of the corresponding contour region can be determined by checking and verifying the corresponding range, which facilitates subsequent feature integration.

[0011] Step 4: Randomly combine several associated contour regions within the remote sensing image to generate combined regions. Based on different random combination processes, select the optimal process and display the combined regions associated with the optimal process as the optimal combined regions. The specific processing method for random combination is as follows: The average value of several pixels associated with each contour region is processed to determine the average pixel value of each contour region, and this value is used as the contour feature of the corresponding contour region. Adjacent contour regions within the remote sensing image are randomly combined to identify combined regions. Each combined region must include at least two sets of contour regions. The total number of combined regions identified in this random combination process is denoted as G. k Then, variance processing is performed on the contour features associated with several contour regions within the corresponding combined area to confirm the variance eigenvalue F associated with the corresponding combined area. k k represents different combinations of processes; G is adopted. k ×A1+F k ×A2=BZ k Determine the calibration feature value BZ associated with the corresponding combination process. k A1 and A2 are both preset fixed coefficient factors, the specific values ​​of which are determined by the operator based on experience, and are derived from different calibration characteristic values ​​BZ associated with different combination processes. k In the middle, select BZ k The process associated with the minimum combination process is denoted as the optimal process. The combination area associated with the optimal process is denoted as the optimal combination area and displayed. Each combination process is associated with different variance eigenvalues ​​and the total number of corresponding combination areas. When the total number of combination areas determined in the corresponding combination process is the minimum, and the associated variance eigenvalue is also the minimum, then the combination areas determined in this case are relatively similar. The characteristics of different contour areas within the corresponding combination area are relatively similar, and they are basically related areas belonging to the same category. After combination processing, the optimal combination effect can be achieved, which facilitates subsequent overall planning of urban areas in the designated area by relevant personnel.

[0012] Some of the data in the above formulas are numerical calculations with dimensions removed, and the contents not described in detail in this specification are all prior art known to those skilled in the art.

[0013] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A method for urban land use identification based on remote sensing imagery, characterized in that, Includes the following steps: Step 1: Acquire remote sensing images of the area to be planned and confirm gradient pixels. From the confirmed gradient pixels, mark the contour regions that exist in the remote sensing images in sequence. Step 2: Based on the contour features of the contour region, quantize the contour features numerically, select refinement points from the quantized feature values, connect the refinement points, and confirm the refinement contour belonging to the corresponding contour region. Step 3: Based on the specific pixel features of the corresponding contour region, confirm the category to which this contour region belongs, and label the category. Step 4: Randomly combine several contour regions associated with the remote sensing image to generate combined regions. Based on different random combination processes, select the optimal process and display the combined regions associated with the optimal process as the optimal combined regions.

2. The urban land use identification method based on remote sensing imagery according to claim 1, characterized in that, In step one, the specific method for sequentially marking the contour regions is as follows: The RGB values ​​associated with different image points within the remote sensing image are confirmed, and the confirmed RGB values ​​are then converted to grayscale. The grayscale value associated with the corresponding image point is confirmed using the formula: HD = R × 0.114 + G × 0.587 + B × 0.

299. Based on the different grayscale values ​​associated with different image points, the remote sensing image is converted to grayscale to confirm the grayscale image. The Sobel algorithm is used to identify the vertical gradient and the vertical gradient associated with different pixels in the grayscale image, and the identified vertical gradient is denoted as C. i The confirmed vertical gradient is denoted as S. i Where i represents different pixels, using Confirm the overall gradient ZH associated with the corresponding pixel. i ; Will satisfy: ZH i > The pixel point with Y1 is labeled as a gradient pixel point, and its Y1 is a preset value; Several gradient pixels associated with each other in the grayscale image are identified sequentially, and the middle area included by several consecutive gradient pixels is recorded as the contour region. Several contour regions associated with each other in the grayscale image are then labeled sequentially.

3. The urban land use identification method based on remote sensing imagery according to claim 2, characterized in that, For those who do not meet ZH i Pixels greater than Y1 are not calibrated.

4. The urban land use identification method based on remote sensing imagery according to claim 1, characterized in that, In step two, the specific method for refining the edge contour of the contour region is as follows: Several contour regions marked in the remote sensing image are identified, and the edge contour of the corresponding contour region is locked from the identified single contour region. The pixel values ​​associated with several gradient pixels in the edge contour are confirmed in turn, and the minimum and maximum values ​​are determined to lock the contour pixel range. The corresponding edge contour-locked pixel range is numerically quantized, with the minimum value quantized to 0 and the maximum value quantized to 2. The quantization ratio is then determined as (maximum value - minimum value) ÷ 2 = quantization ratio. Several pixel values ​​within the contour pixel range are then quantized using X. i ÷ Quantification ratio = L i Confirm the quantization value L corresponding to the pixel. i ; Combine the corresponding contour region with the two-dimensional coordinate system, and confirm the different two-dimensional coordinates associated with different pixels. Average the two-dimensional coordinates of several groups of pixels, confirm the average coordinates, and simultaneously mark them in this contour region as the center point of this contour region. Lock the pixel farthest from this center point from the edge contour of the contour region and record it as the feature edge point. With the center point as the center and the straight-line distance between the center point and the feature edge point as the radius, confirm a set of feature circles. Using the edge circle points of the feature circle as the associated endpoint, the associated connection between the center point and the associated endpoint is confirmed. The part of the connection within the associated connection that is located on the edge contour is recorded as the contour connection. Several pixels intersecting each contour connection are recorded as a set of pixels. And refinement points are selected from each different set of pixels. Based on the selected thinning points of each pixel set, adjacent thinning points are connected to confirm the thinning contour belonging to this contour region, and the thinning contour is re-established as the edge contour of this contour region.

5. The urban land use identification method based on remote sensing imagery according to claim 4, characterized in that, The selection method for choosing refinement points from a set of pixels is as follows: Identify the different quantization values ​​L associated with different pixels in the pixel set. i Using: Cz i =|L i -1| Confirm the feature difference Cz associated with the corresponding pixel. i Then, from the different feature differences Cz associated with different pixels i In the middle, select Cz i The pixels associated with min are selected as the thinning points.

6. The urban land use identification method based on remote sensing imagery according to claim 1, characterized in that, In step three, the specific method for labeling the category is as follows: Based on the edge contour after contour region refinement, the pixel values ​​of several pixels located within the edge contour are confirmed, and based on the confirmed minimum and maximum values, the pixel value range belonging to this contour region is confirmed. Verify and check the pixel value range with several preset ranges: confirm the intersection range of the pixel value range with different preset ranges, and determine the proportion of the intersection range located in the corresponding preset range. The proportion is calculated as the total length of the intersection range ÷ the total length of the preset range. The preset range that meets the requirement of a proportion ≥ 85% is taken as the adaptation range of this pixel value range, and the category associated with this adaptation range is taken as the category of this contour region, and is simultaneously marked in the remote sensing image.

7. The urban land use identification method based on remote sensing imagery according to claim 1, characterized in that, No calibration will be performed for the preset range that does not meet the requirement of a percentage value ≥ 85%.

8. The urban land use identification method based on remote sensing imagery according to claim 1, characterized in that, In step four, the specific method for randomly combining several contour regions is as follows: The average value of several pixels associated with each contour region is processed to determine the average pixel value of each contour region, and this value is used as the contour feature of the corresponding contour region. Adjacent contour regions within the remote sensing image are randomly combined to identify combined regions. Each combined region must include at least two sets of contour regions. The total number of combined regions identified in this random combination process is denoted as G. k Then, variance processing is performed on the contour features associated with several contour regions within the corresponding combined area to confirm the variance eigenvalue F associated with the corresponding combined area. k k represents different combinations of processes; G is adopted. k ×A1+F k ×A2=BZ k Determine the calibration feature value BZ associated with the corresponding combination process. k A1 and A2 are both preset fixed coefficient factors, representing different calibration characteristic values ​​BZ associated with different combination processes. k In the middle, select BZ k The process associated with min is recorded as the optimal process. The combined region associated with the optimal process is recorded as the optimal combined region and displayed.

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