A binary classification precision evaluation method and system based on boundary space offset, and a storage medium

Abstract

The application belongs to the technical field of resource and environment analysis, and particularly relates to a binary classification precision evaluation method based on boundary space offset, which comprises the following steps: S1, obtaining binary classification results of a target region to obtain extracted classification boundary vector data; S2, obtaining reference classification boundary vector data of the same target region; S3, performing equidistant sampling on the extracted boundary to obtain a sampling point set; S4, calculating the shortest distance of each sampling point to the reference boundary; S5, calculating a boundary mean offset index BMSI; and S6, determining the extraction error type according to the size of the BMSI value and the spatial distribution thereof. The application quantifies the classification boundary precision from the spatial position dimension through the boundary mean offset index BMSI, and solves the problem that the traditional classification precision evaluation method ignores the spatial position information and cannot distinguish the algorithm boundary positioning performance.

Description

Technical Field

[0001] This invention belongs to the field of resource and environmental analysis technology, specifically relating to a binary classification accuracy evaluation method, system, and storage medium based on boundary space offset. Background Technology

[0002] In existing technologies, the accuracy evaluation of remote sensing land cover classification mainly relies on pixel statistical indicators, such as overall accuracy (OA) and F1 score. These indicators measure whether pixels have been correctly classified by comparing the classification results with reference samples. However, these methods essentially only focus on matching category attributes, ignoring the shape and boundary information of land covers as geographic objects. For example, in water body extraction tasks, even if the pixel classification accuracy is high, issues such as blurred or offset boundaries may still be overlooked, making it impossible to quantitatively evaluate the positioning error in practical applications.

[0003] The limitation of traditional metrics lies in their inability to reflect the geometric consistency of classification boundaries. Taking water body extraction as an example, pixels inside the water body may be accurately identified, but the mixed pixels and spectral heterogeneity at the water-land interface significantly affect boundary accuracy. Due to the lack of quantitative metrics for spatial location, the differences in boundary localization among different algorithms are difficult to distinguish, resulting in a lack of clear direction for model optimization. Furthermore, existing methods rely heavily on reference boundaries; if the reference data is biased, the reliability of the evaluation results will also be affected.

[0004] This invention quantifies the accuracy of classification boundaries from a spatial location dimension using the Boundary Mean Offset Index (BMSI). The challenge lies in accurately calculating the boundary offset and ensuring the universality of the index. For example, equidistant sampling needs to balance image resolution and boundary complexity, shortest distance calculation requires handling the geometric relationship between the perpendicular foot and endpoint of a line segment, and the design of the BMSI formula needs to balance statistical significance and intuitiveness in practical applications. Furthermore, maintaining the stability of the index across different land cover types (such as water bodies, vegetation, and built-up land), and handling complex scenes such as shadows and mixed pixels, all require extensive experimental verification to validate the technical feasibility. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a binary classification accuracy evaluation method based on boundary space offset. This method addresses the problem of traditional classification accuracy evaluation methods neglecting spatial location information and failing to distinguish the performance of algorithm boundary positioning by quantifying boundary space offset.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] One of the objectives of this invention is to provide a binary classification accuracy evaluation method based on boundary spatial offset. By using the Boundary Average Offset Index (BMSI) to quantify the classification boundary accuracy from the spatial location dimension, this invention solves the problem that traditional classification accuracy evaluation methods ignore spatial location information and cannot distinguish the algorithm boundary positioning performance.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A binary classification accuracy evaluation method based on boundary space offset includes the following steps:

[0010] A binary classification accuracy evaluation method based on boundary space offset, characterized by the following steps:

[0011] S1. Obtain the binary classification result of the target region and extract the classification boundary vector data;

[0012] S2. Obtain reference classification boundary vector data for the same target region;

[0013] S3. Perform equidistant sampling on the extraction boundary to obtain a set of sampling points;

[0014] S4. Calculate the shortest distance from each sampling point to the reference boundary;

[0015] S5. Calculate the Boundary Mean Offset Index (BMSI);

[0016] S6. Determine the extraction error type based on the magnitude and spatial distribution of the BMSI value.

[0017] Further optimization of the design results in the binary classification, which divides the land surface into two categories: target features and non-target features.

[0018] Further optimization of the design: the reference classification boundary vector data is obtained through manual visual interpretation of high-resolution remote sensing images. The high-resolution remote sensing images include Google Earth platform images, WorldView images, QuickBird images, or Jilin-1 images, and the image imaging time differs from the classification result image by no more than 30 days, with a cloud cover rate of less than 5%.

[0019] Further design optimization: the equal-interval sampling is set according to the spatial resolution of the remote sensing image, the sampling interval is 1 to 2 times the spatial resolution of the image, the sampling points are arranged at fixed intervals along the total length of the boundary line, and the starting point and the ending point are both included in the sampling point set.

[0020] To further optimize the design, when calculating the shortest distance from each sampling point to the reference boundary, all line segments on the reference boundary are traversed:

[0021] If the foot of the perpendicular falls within the range of the line segment, then the distance is the length of the perpendicular.

[0022] If the foot of the perpendicular falls outside the endpoints of the line segment, then the distance is the shortest distance from the sampling point to both endpoints of the line segment. The minimum value among all line segment distances is taken as the shortest distance for that sampling point.

[0023] Further optimization of the design, the formula for calculating the Boundary Average Offset Index (BMSI) is as follows:

[0024]

[0025] Where N is the number of sampling points, pi is the i-th sampling point, Sr is the reference boundary, D(pi, Sr) is the shortest Euclidean distance from point pi to boundary Sr, and BMSI unit is meters.

[0026] Further design optimization: Based on the magnitude and spatial distribution of BMSI values, the extraction error type is determined: when the BMSI value is high, it is determined that the algorithm is severely affected by terrain shadows or mixed pixels, and the classification strategy is adjusted to optimize the boundary positioning accuracy.

[0027] With further design optimization, the method is not limited to water body extraction, but can be applied to the binary classification accuracy evaluation of various land features in remote sensing images. Only the reference boundary and the extraction boundary need to be input to achieve a quantitative evaluation of the boundary positioning accuracy.

[0028] The second objective of this invention is to provide a binary classification accuracy evaluation system based on boundary space offset, for running the above-mentioned binary classification accuracy evaluation method based on boundary space offset on a computer.

[0029] To achieve the above objectives, the technical solution of the present invention is as follows:

[0030] A binary classification accuracy evaluation system based on boundary space offset includes a data acquisition module, a sampling module, a distance calculation module, and a BMSI calculation module.

[0031] The data acquisition module is configured to: acquire the binary classification result of the target region and obtain the extracted classification boundary vector data, and acquire the reference classification boundary vector data of the same target region;

[0032] The sampling module is configured to perform equidistant sampling on the extraction boundary;

[0033] The distance calculation module is configured to calculate the shortest distance from each sampling point to the reference boundary.

[0034] The BMSI calculation module is configured to calculate the Boundary Average Offset Index (BMSI) based on the distance between sampling points and output the evaluation results.

[0035] A third objective of this invention is to provide a computer-readable storage medium for implementing the aforementioned binary classification accuracy evaluation method based on boundary space offset.

[0036] To achieve the above objectives, the technical solution of the present invention is as follows:

[0037] A computer-readable storage medium storing program instructions that, when executed by a processor, are used to implement the binary classification accuracy evaluation method and optimization design based on boundary space offset as described in one of the objectives of this invention.

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

[0039] 1. This invention improves the quantification capability of classification boundary positioning accuracy. By using the BMSI index, the boundary offset is converted into an intuitive value in meters, overcoming the shortcomings of traditional pixel-level indices that cannot reflect spatial position deviation. For example, the average BMSI value of AWEI1 is 0.606 meters, which is significantly better than the 1.256 meters of AWEI0, effectively distinguishing the boundary positioning performance of different algorithms.

[0040] 2. This invention can provide a direction for diagnosing positioning deviations. By analyzing the magnitude and spatial distribution of BMSI values, it can be determined whether the algorithm is affected by terrain shadows or mixed pixel interference. For example, a high BMSI value indicates an overall offset, providing a basis for targeted optimization.

[0041] 3. This invention is decoupled from image resolution. BMSI outputs in meters and is not affected by image resolution. This facilitates comparison of methods between images of different scales and resolutions and avoids evaluation bias caused by resolution differences in traditional indicators.

[0042] 4. This invention improves the credibility of classification results by comparing high-precision reference boundaries (such as vector data interpreted by human visual interpretation) with extracted boundaries, combined with equidistant sampling and shortest distance calculation, reducing human error and improving the objectivity and reliability of evaluation results. Attached Figure Description

[0043] Figure 1 A flowchart illustrating a binary classification accuracy evaluation method based on boundary space offset is provided in this embodiment of the invention.

[0044] Figure 2 This is a schematic diagram of BMSI in a binary classification accuracy evaluation method based on boundary space offset provided in an embodiment of the present invention. NDWI is used to extract the water body boundary and the reference water body boundary interpreted from high-resolution remote sensing images on Google Earth.

[0045] Figure 3Box plots of BMSI results for each index in a binary classification accuracy evaluation method based on boundary space offset are provided in this embodiment of the invention.

[0046] Figures 4-5 This invention provides a comparison diagram of the extraction boundary of typical index results and the boundary of a reference water body in a binary classification accuracy evaluation method based on boundary space offset.

[0047] Figure 6 This invention provides a functional module framework diagram of a binary classification accuracy evaluation system based on boundary space offset. Detailed Implementation

[0048] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0049] To better explain the technical solution, the following technical terms are explained:

[0050] 1. Binary Classification Definition: A classification task that divides the land surface into two categories of target features (e.g., water / non-water bodies, vegetation / non-vegetation). Function: It is the core input of the technical solution, evaluating classification accuracy by comparing the spatial deviation between the extracted boundary and the reference boundary.

[0051] 2. Boundary Mean Offset Index (BMSI) Definition: Quantifies the spatial offset of the classification boundary by calculating the average shortest distance from the sampled points on the extracted boundary to the reference boundary, with the unit being meters. Function: Overcomes the limitations of traditional pixel-level indicators (such as OA and F1), reflecting the boundary positioning accuracy from a spatial location dimension and distinguishing differences in algorithm performance.

[0052] 3. Definition of Equal-Gap Sampling: Sampling points are placed at fixed intervals along the extraction boundary line. The sampling interval is related to the remote sensing image resolution (12 times). Purpose: To ensure coverage of all key areas of the boundary and avoid deviations or omissions due to insufficient sampling density.

[0053] 4. Shortest distance calculation definition: For each sampling point, traverse the reference boundary line segment, calculate the perpendicular distance or endpoint distance to the line segment, and take the minimum value as the shortest distance. Purpose: To accurately quantify boundary offset and solve the error problem caused by geometric complexity in traditional methods.

[0054] 5. Definition of High-Resolution Remote Sensing Imagery: Remote sensing imagery with a spatial resolution better than 1 meter (such as Google Earth, WorldView, QuickBird, etc.), used for visual interpretation of reference boundaries. Purpose: To provide high-precision reference data and ensure the reliability of BMSI calculations.

[0055] 6. Definition of Reference Boundary Vector Data: Boundary data obtained through manual visual interpretation or high-precision methods, serving as a benchmark for comparison of classification results. Purpose: It forms the basis of BMSI calculation, and its accuracy directly affects the evaluation results.

[0056] 7. Spatial Positioning Accuracy Definition: The degree of spatial matching between the classification boundary and the true boundary, quantified by BMSI. Purpose: To address the shortcomings of traditional indicators that neglect spatial information, providing a clear direction for algorithm optimization.

[0057] 8. Geometric Consistency Definition: The degree of matching between the extracted boundary and the reference boundary in shape and position, reflected by BMSI. Purpose: To distinguish the performance differences of algorithms in scenarios such as boundary blurring, offset, and mixed pixel processing.

[0058] 9. Definition of Mixed Pixel Interference: Classification error caused by a pixel containing multiple land cover types (such as a mixture of water and land). Purpose: When the BMSI value is high, it can be determined that the algorithm is affected by mixed pixel interference, and the boundary demixing capability needs to be optimized.

[0059] 10. Algorithm Optimization Direction Definition: Through spatial distribution analysis of BMSI, identify specific problems in boundary localization of the localization algorithm (such as overall offset and local deviation). Purpose: To provide targeted technical solutions for improving classification models and enhancing boundary extraction accuracy.

[0060] This application provides a binary classification accuracy evaluation method based on boundary spatial offset, which can be widely applied to the binary classification accuracy evaluation of various land features in remote sensing images. For ease of understanding, the following uses water body extraction as an example to describe the specific implementation of the invention in detail. Specifically, it includes the following steps:

[0061] A1. Acquire multispectral remote sensing images of the target area.

[0062] A2. Calculate the water index of the target area based on remote sensing images that have undergone preprocessing such as atmospheric correction;

[0063] The preferred values ​​are MNDWI, NDWI, AWEI0, AWEI1, and WI2015. The calculation formula is as follows:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] In the formula: Blue, Green, Red, SWIR, SWIR1, SWIR2, and NIR are the remote sensing reflectivities of the blue band, green band, red band, shortwave infrared band, shortwave infrared 1 band, shortwave infrared 2 band, and near-infrared band, respectively, corresponding to B2, B3, B4, B8, B11, B12, and B13 in Sentinel-2.

[0070] A3. Based on the water index results after processing such as smoothing filtering, image enhancement or edge suppression, a threshold segmentation method is introduced to extract water bodies.

[0071] The preferred method is the OTU (Otsu method) adaptive threshold segmentation method, which automatically finds the segmentation threshold that maximizes the inter-class variance based on the statistical characteristics of the image histogram.

[0072] A4. High-resolution remote sensing imagery provided by the Google Earth platform was selected as the base map for interpretation. This platform's imagery has a spatial resolution of 0.3 to 0.5 meters, enabling clear identification of surface water body boundaries. Clear images with an imaging date no more than 30 days different from the imaging time of the remote sensing image used to extract the water body to be evaluated, and a cloud cover of less than 5%, were selected. Professional interpreters conducted manual visual interpretation and digital delineation along the visible land-water boundary line in the imagery, using the continuous outer edge of the water body as the boundary. No subjective speculation was made for shaded or obscured areas to ensure the accuracy of the reference water body boundary.

[0073] A5. Sample at equal intervals along the boundary of the extracted water body at 1 times the spatial resolution of the image to obtain a set of sampling points. For each sampling point, traverse all line segments on the reference water body boundary and calculate the shortest distance from the sampling point to each line segment (if the foot of the perpendicular falls within the range of the line segment, take the length of the perpendicular; otherwise, take the shortest distance from the sampling point to the two ends of the line segment). Take the minimum value among all line segment distances as the shortest distance from the sampling point to the reference boundary. Calculate the average of the shortest distances of all sampling points to obtain the BMSI value, in meters. The smaller the BMSI value, the closer the extracted boundary is to the true boundary in spatial location.

[0074] A6. After sampling the extracted water body boundaries at equal intervals using five water body index methods (NDWI, MNDWI, AWEI0, AWEI1, and WI2015), the shortest distance from each sampling point to the reference water body boundary was calculated, yielding the BMSI value for each sample. This data was then compiled into a table, with each sample corresponding to a set of data, ensuring a one-to-one correspondence between the BMSI values ​​of each index method and the reference boundary. The calculated BMSI values ​​for each index were statistically summarized, and the mean, median, standard deviation, minimum, maximum, and interquartile range were calculated for each method to evaluate the overall performance and stability of each method in boundary spatial localization. A smaller BMSI mean indicates that the extracted water body boundary is closer to the true boundary in spatial location; a smaller standard deviation indicates better localization stability of the method across different samples.

[0075] In this embodiment, to systematically test the universality and robustness of the boundary mean offset index, this study selected 50 representative reservoirs in China as the study area. The selection strictly adhered to the principle of diversity across five dimensions: climate, geomorphology, environmental background, season, and reservoir type. The study area covers major climate zones including humid, semi-humid, semi-arid, and arid, and is distributed across various geomorphic units such as plains, hills, basins, plateaus, and mountains. The shoreline environment encompasses typical land surface types such as urban areas, cultivated land, forest land, bare land, and snow and ice. Image acquisition spans spring, summer, autumn, and winter to reflect phenological changes. The reservoir samples include both large and medium-sized reservoirs, and different morphological types such as riverine and lacustrine reservoirs. Through this multi-dimensional system design, the validation set can simulate complex scenarios in real-world applications to the greatest extent possible, providing a solid geographical empirical foundation for method evaluation.

[0076] To further analyze the extraction effect of the boundary areas, three 100m×100m (1 hectare) square quadrats were manually identified and determined on key sections of the shoreline boundary of each reservoir (such as inlets, convex banks, concave banks, and shaded areas). The selection criteria for the quadrats were: (1) containing a clear water-land boundary; (2) covering a major interference background (such as building shadows, mountain shadows, and mixed vegetation areas); and (3) being stably identifiable on 10-meter resolution images. A total of 150 boundary quadrats constituted the basic spatial unit for the accuracy evaluation of this study.

[0077] Figure 2 This is a schematic diagram of BMSI, using NDWI to extract the water body boundary and the reference water body boundary interpreted from high-resolution remote sensing imagery on Google Earth.

[0078] Figure 3Box plots of the BMSI results for each index are shown. Based on the mean, the accuracy ranking of the five methods is: AWEI1 (0.606 m) < NDWI (0.642 m) < WI2015 (0.667 m) < MNDWI (0.881 m) < AWEI0 (1.256 m). AWEI1 performed best, with an average offset of only 0.606 meters; NDWI and WI2015 were next, with mean values ​​of 0.642 meters and 0.667 meters respectively; MNDWI performed poorly, with a mean value of 0.881 meters; AWEI0 performed worst, with a mean value as high as 1.256 meters, 2.07 times that of AWEI1, indicating a serious spatial positioning bias in the water body boundary extracted by this method.

[0079] The median ranking is largely consistent with the mean: AWEI1 (0.559 m), NDWI (0.515 m), WI2015 (0.576 m), MNDWI (0.735 m), and AWEI0 (1.151 m). The median for each method is less than the mean, indicating that the BMSI distribution is right-skewed, with a few large-biased samples inflating the overall mean. The NDWI median shows the largest difference between its mean and median (0.642 vs 0.515), suggesting it is significantly affected by extremely high values.

[0080] Standard deviation reflects the stability of the method. AWEI1 has the smallest standard deviation (0.310 m), indicating that its spatial localization is the most stable; WI2015 is next (0.373 m); AWEI0 and MNDWI have relatively large standard deviations, at 0.715 m and 0.538 m, respectively; NDWI has the largest standard deviation (0.562 m), but its mean is low. Combined with the large difference between its mean and median, this indicates that although NDWI performs well overall, it has a large localization bias on some samples.

[0081] The interquartile range (IQR) reflects the error distribution range of the middle 50% of the samples. AWEI1 has the smallest IQR (0.388 m), followed by NDWI (0.431 m) and WI2015 (0.446 m), indicating that the offset distance distribution of these three methods is the most concentrated. MNDWI has an IQR of 0.572 m, which is more dispersed. AWEI0 has the largest IQR (0.993 m), which is 2.56 times that of AWEI1, further confirming its instability.

[0082] In summary, the BMSI accuracy ranking of the five methods is: AWEI1 > NDWI > WI2015 > MNDWI > AWEI0. AWEI1 performs best in terms of mean, median, standard deviation, IQR, and maximum value. NDWI and WI2015 perform well overall, but attention should be paid to the extreme bias of NDWI on some samples. MNDWI performs poorly. AWEI0 has a large positioning bias and poor stability.

[0083] Figures 4-5 A comparison chart showing the effect of extracting the boundary from the typical index results and the boundary of the reference water body.

[0084] This application provides a binary classification accuracy evaluation system based on boundary space offset. The system includes a data acquisition module 21, a sampling module 22, a distance calculation module 23, and a BMSI calculation module 24.

[0085] The data acquisition module 21 is configured to: acquire the binary classification result of the target region and obtain the extracted classification boundary vector data, and acquire the reference classification boundary vector data of the same target region;

[0086] Sampling module 22 is configured to perform equidistant sampling on the extraction boundary;

[0087] Distance calculation module 23 is configured to calculate the shortest distance from each sampling point to the reference boundary;

[0088] The BMSI calculation module 24 is configured to calculate the Boundary Average Offset Index (BMSI) based on the distance between sampling points and output the evaluation results.

[0089] This embodiment provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement a binary classification accuracy evaluation method based on boundary space offset.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions 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 can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications should be covered within the scope of the claims of the present invention.

Claims

1. A method for evaluating the accuracy of binary classification based on boundary space offset, characterized in that, Includes the following steps: S1. Obtain the binary classification result of the target region and extract the classification boundary vector data; S2. Obtain reference classification boundary vector data for the same target region; S3. Perform equidistant sampling on the extraction boundary to obtain a set of sampling points; S4. Calculate the shortest distance from each sampling point to the reference boundary; S5. Calculate the Boundary Mean Offset Index (BMSI); S6. Determine the extraction error type based on the magnitude and spatial distribution of the BMSI value.

2. The binary classification accuracy evaluation method based on boundary space offset as described in claim 1, characterized in that: The binary classification results divide the land surface into two categories: target features and non-target features.

3. The binary classification accuracy evaluation method based on boundary space offset as described in claim 2, characterized in that: The reference classification boundary vector data is obtained through manual visual interpretation of high-resolution remote sensing images, including Google Earth platform images, WorldView images, QuickBird images, or Jilin-1 images, and the image imaging time differs from the classification result image by no more than 30 days, with a cloud cover rate of less than 5%.

4. The binary classification accuracy evaluation method based on boundary space offset as described in claim 3, characterized in that: The equal-interval sampling is set according to the spatial resolution of the remote sensing image. The sampling interval is 1 to 2 times the spatial resolution of the image. The sampling points are arranged at fixed intervals along the total length of the boundary line, and the starting point and the ending point are both included in the sampling point set.

5. The binary classification accuracy evaluation method based on boundary space offset as described in claim 4, characterized in that, When calculating the shortest distance from each sampling point to the reference boundary, all line segments on the reference boundary are traversed: If the foot of the perpendicular falls within the range of the line segment, then the distance is the length of the perpendicular. If the foot of the perpendicular falls outside the endpoints of the line segment, then the distance is the shortest distance from the sampling point to the two endpoints of the line segment. The minimum value among all line segment distances is taken as the shortest distance of the sampling point.

6. The binary classification accuracy evaluation method based on boundary space offset as described in claim 5, characterized in that, The formula for calculating the Boundary Average Offset Index (BMSI) is as follows: Where N is the number of sampling points, pi is the i-th sampling point, Sr is the reference boundary, D(pi, Sr) is the shortest Euclidean distance from point pi to boundary Sr, and BMSI unit is meters.

7. The binary classification accuracy evaluation method based on boundary space offset as described in claim 6, characterized in that, Based on the magnitude and spatial distribution of BMSI values, the extraction error type is determined: when the BMSI value is high, it is determined that the algorithm is severely affected by terrain shadows or mixed pixels, and the classification strategy is adjusted to optimize the boundary positioning accuracy.

8. The binary classification accuracy evaluation method based on boundary space offset as described in claim 7, characterized in that: The method is not limited to water body extraction; it can be applied to the binary classification accuracy evaluation of various land features in remote sensing images. Only the reference boundary and the extraction boundary need to be input to achieve a quantitative evaluation of the boundary positioning accuracy.

9. A binary classification accuracy evaluation system based on boundary space offset, characterized in that, It includes a data acquisition module, a sampling module, a distance calculation module, and a BMSI calculation module. The data acquisition module is configured to: acquire the binary classification result of the target region and obtain the extracted classification boundary vector data, and acquire the reference classification boundary vector data of the same target region; The sampling module is configured to perform equidistant sampling on the extraction boundary; The distance calculation module is configured to calculate the shortest distance from each sampling point to the reference boundary. The BMSI calculation module is configured to calculate the Boundary Average Offset Index (BMSI) based on the distance between sampling points and output the evaluation results.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program instructions that, when executed by a processor, implement the method as described in any one of claims 1 to 8.

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