Coastline segmentation method, program product and medium for a deep learning model

Abstract

The present application relates to the field of geographic information processing, and more particularly to a coastline segmentation method for deep learning model, program product and medium. The method comprises: obtaining large-scale coastline and corresponding target small-scale coastline; equally sampling the large-scale coastline to obtain each vertex, calculating the corner change amount of each vertex, and the one exceeding the morphological threshold is a candidate morphological breakpoint; constructing a sliding window to calculate the structural energy, and the first-order difference quantity exceeding the superstructure threshold and being the maximum in the neighborhood is a candidate structure breakpoint; mapping the small-scale vertex to the large-scale to obtain a projection point, determining the corresponding index according to the cumulative arc length, and the one satisfying the monotonicity constraint is a candidate scale consistent breakpoint; screening the three types of breakpoints according to the constraint rule to obtain the final breakpoint; incorporating the starting and ending points of the coastline to form boundary vertices; mapping the relative arc length position of the boundary vertices to the small scale to determine the cutting point; and synchronously cutting the two coastlines to obtain a one-to-one corresponding cross-scale coastline segment sample pair.

Description

Technical Field

[0001] This invention relates to the field of geographic information processing, and more particularly to a method, program product, and medium for coastline segmentation oriented towards deep learning models. Background Technology

[0002] Coastlines are the most direct linear geographical elements in the interaction between land and sea, and have important application value in cartography, coastal planning, and ecological monitoring. Multi-scale representation is a core research issue. Coastlines are complex in shape, have rich curvature, and are highly sensitive to scale. Simplification requires balancing detail compression with the preservation of the overall outline and key geomorphic features, which is a key challenge in cartographic generalization. Segmentation is a crucial prerequisite for coastline simplification.

[0003] In the field of online feature simplification (or polyline thinning), classic algorithms such as the Douglas-Peucker algorithm and the Visvaling-Whyatt algorithm laid the foundation for vertex selection and curvature simplification. Subsequently, segmentation approaches based on key points and curvature units have gradually developed. Key point segmentation identifies breakpoints by using curvature extrema and abrupt changes in angle, focusing on local geometric abrupt changes; curvature unit segmentation uses morphological units such as straight lines and continuous curves as the basis for division, focusing on local morphological consistency. Both provide the basic approach for coastline segmentation.

[0004] With the rise of deep learning, sequence models such as Seq2Seq and GRU are used for line simplification, making sample organization a core aspect. Mechanical fixed segmentation has become a common sample processing method, which involves splitting coastlines according to a fixed length or number of points to provide a basic sample format for sequence modeling. However, splitting coastlines according to a fixed length or number of points results in the segmentation location having no correlation with the actual geographical features of the coastline (including geometric shape and structural features). Furthermore, large-scale and small-scale coastlines are mechanically segmented independently, with unrelated segmentation locations. Therefore, it is impossible to establish cross-scale correspondences, and sample pairing is chaotic (i.e., large-scale coastline segments cannot be matched one-to-one with small-scale coastline segments, which is equivalent to low-quality training data to be input into the deep learning model). This seriously affects the model's ability to learn stable mapping patterns, ultimately leading to distorted simplification results. Summary of the Invention

[0005] The purpose of this invention is to provide a method, program product, and medium for coastline segmentation for deep learning models. This addresses the problem that existing technologies segment coastlines at locations that are not related to the actual geographical features of the coastline. This results in the inability to establish cross-scale correspondences after segmentation, making it impossible to establish a one-to-one correspondence between large-scale and small-scale coastline segments. Consequently, this seriously affects the model's ability to learn stable mapping patterns and ultimately leads to distorted simplification results.

[0006] To achieve the above objectives, this invention provides a coastline segmentation method for deep learning models, the method comprising: Obtain large-scale coastlines and their corresponding target small-scale coastlines; Each vertex is obtained by sampling a large-scale coastline at equal intervals, and the change in the angle corresponding to each vertex is determined. If the change in the angle corresponding to any vertex exceeds the preset morphological breakpoint threshold, the vertex is determined to be a candidate morphological breakpoint. The cumulative amount of the rotation angle change within the sliding window corresponding to each pre-constructed vertex is determined as the structural energy of each vertex; if the first-order difference component of the structural energy between any vertex and its neighboring vertices exceeds the preset structural breakpoint threshold, and has the largest first-order difference component among all vertices in the preset neighborhood, then the vertex is determined as a candidate structural breakpoint. Map each vertex of the target small-scale coastline to the large-scale coastline to obtain each projection point; determine the corresponding index of each vertex of the large-scale coastline and each vertex of the target small-scale coastline based on the cumulative arc length of each projection point on the large-scale coastline and the total arc length of the large-scale coastline; if any vertex of the target small-scale coastline and its corresponding index satisfy the monotonic order constraint, then the vertex is determined to be a candidate scale-consistent breakpoint. According to the preset breakpoint constraint rules, some breakpoints are deleted from the candidate morphological breakpoints, candidate structural breakpoints and candidate scale consistent breakpoints to obtain each screening breakpoint; Based on each screening breakpoint, the starting point of the coastline, and the ending point of the coastline, determine each boundary vertex; The relative positions of each boundary vertex along the line are determined based on the total arc length of the large-scale coastline and the cumulative arc length of each boundary vertex on the large-scale coastline. Map the relative positions of each boundary vertex along the line to the total arc length of the target small-scale coastline, determine the target cutting position of each boundary vertex, and determine each cutting point on the small-scale coastline according to the target cutting position. The large-scale coastline is divided into major-scale coastline segments based on the boundary vertices, and the target small-scale coastline is divided into minor-scale coastline segments based on the dividing points.

[0007] Beneficial Effects: This invention provides a coastline segmentation method for deep learning models. First, starting from the geometric features of a large-scale coastline, this method calculates the change in angle at each vertex and identifies candidate morphological breakpoints. A sliding window is constructed to calculate the structural energy and its first-order difference component to identify candidate structural breakpoints. Finally, the mapping relationship between the vertices of the target small-scale coastline and the large-scale coastline is used to identify candidate scale-consistent breakpoints. This achieves comprehensive identification of candidate breakpoints from three levels: local morphology, regional structure, and scale consistency. This fundamentally avoids the shortcomings of relying solely on a single feature to identify breakpoints, enabling the segmentation results to closely match the real geographical features of the coastline and effectively adapt to various complex coastline morphologies.

[0008] After identifying each candidate breakpoint, the three types of candidate breakpoints are screened based on the preset breakpoint constraint rules, and some breakpoints are deleted to obtain the screened breakpoints (i.e. the final determined breakpoints). This effectively suppresses the problems of excessive breakpoint density and excessively short shore segments, avoids segmentation fragmentation, preserves the integrity of certain key landforms (such as headlands, bays, etc.), and improves the geometric rationality and structural stability of the segmentation results.

[0009] This method establishes a one-to-one correspondence between the boundary vertices of a large-scale coastline and the cutting points of the target small-scale coastline based on their relative arc length along the line. This enables cross-scale backhaul and synchronous cutting of the breakpoints, solving the core problems of existing technologies that cannot establish cross-scale correspondences and suffer from chaotic sample pairing. It enables large-scale and small-scale coastline segments to form structurally consistent and scale-corresponding data pairs, providing a high-quality sample foundation for deep learning models to learn stable cross-scale mapping patterns.

[0010] In summary, the method proposed here for coastline segmentation not only avoids the sample feature mixing and information interference caused by forcibly merging straight and complex curved coastlines, but also enables deep learning models to learn cross-scale simplification rules more effectively, thereby improving the stability and naturalness of the simplification results and reducing distortion.

[0011] Furthermore, based on preset breakpoint constraint rules, some breakpoints are deleted from the candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints to obtain each selected breakpoint, including: The candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints are sorted according to their corresponding indices, and the cumulative arc length between each adjacent breakpoint after sorting is calculated. When the cumulative arc length between any two adjacent breakpoints is less than the preset minimum breakpoint spacing threshold, including: If the breakpoint types are different, the lower-priority breakpoint is deleted from two adjacent breakpoints according to the preset priority order, while the higher-priority breakpoint is retained; the priority order from high to low is as follows: candidate scale-consistent breakpoint, candidate structure breakpoint, and candidate morphology breakpoint. If the breakpoints are of the same type, delete the breakpoint with the lower strength value among two adjacent breakpoints and keep the breakpoint with the higher strength value. Divide the shoreline into sections based on the preserved breakpoints and calculate the arc length of each section; If the arc length of any shore segment is less than the preset minimum shore segment length threshold, then the breakpoints with lower strength values ​​are deleted at both ends of that shore segment, while the breakpoints with higher strength values ​​are retained. Each shore segment whose arc length is less than the preset minimum shore segment length threshold is merged into the corresponding adjacent shore segment to obtain each reconstructed shore segment. When the arc length of each reconstructed shoreline is greater than or equal to the preset minimum shoreline length threshold, each screening breakpoint is determined.

[0012] Furthermore, based on the total arc length of the large-scale coastline and the cumulative arc length of each boundary vertex on the large-scale coastline, the relative positions of each boundary vertex along the line are determined, including: The total arc length of a large-scale coastline is determined by summing the Euclidean distances between adjacent vertices. The cumulative arc length of each boundary vertex on a large-scale coastline is determined by the sum of the Euclidean distances between adjacent vertices from the starting point of the coastline to each boundary vertex. The ratio of the cumulative arc length of each boundary vertex on the large-scale coastline to the total arc length of the large-scale coastline is used to determine the relative position of each boundary vertex along the line.

[0013] Furthermore, the relative positions of each boundary vertex along the line are mapped onto the total arc length of the target small-scale coastline to determine the target cutting position of each boundary vertex, including: The target cutting position of each boundary vertex is determined by multiplying the relative position of each boundary vertex along the line with the total arc length of the target small-scale coastline.

[0014] Furthermore, determine the angle change corresponding to each vertex, including: Substitute the vertical and horizontal increments between any two adjacent vertices into the preset direction angle function to determine the direction angle corresponding to each vertex, and calculate the change in rotation angle corresponding to each vertex based on the direction angle corresponding to each vertex.

[0015] Furthermore, the change in rotation angle corresponding to each vertex is calculated based on the orientation angle corresponding to each vertex, including: ; in, This represents the change in angle corresponding to the i-th vertex; The direction angle corresponding to the i-th vertex; It is the direction angle corresponding to the (i-1)th vertex.

[0016] Furthermore, based on the cumulative arc length of each projection point on the large-scale coastline and the cumulative arc length of each vertex of the large-scale coastline, the corresponding indices of each vertex of the large-scale coastline and each vertex of the target small-scale coastline are determined, including: ; in, The i-th vertex of the large-scale coastline and the vertex of the target small-scale coastline The corresponding index; Let be the cumulative arc length of the i-th vertex of a large-scale coastline; small scale vertex The cumulative arc length of the projection point on a large-scale coastline.

[0017] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described coastline segmentation method for deep learning models.

[0018] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described coastline segmentation method for deep learning models.

[0019] Both the computer program product and the computer-readable storage medium provided by this invention can execute the coastline segmentation method for deep learning models provided by this invention, and have the corresponding functional modules and beneficial effects of the execution method. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating the coastline segmentation method for deep learning models in the implementation of the coastline segmentation method of the present invention. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0023] Implementation of a coastline segmentation method for deep learning models; This implementation presents a technical solution for a coastline segmentation method oriented towards deep learning models. The core innovation of this solution lies in: In this embodiment, the method includes: Obtain large-scale coastlines and their corresponding target small-scale coastlines; Each vertex is obtained by sampling a large-scale coastline at equal intervals, and the change in the angle corresponding to each vertex is determined. If the change in the angle corresponding to any vertex exceeds the preset morphological breakpoint threshold, the vertex is determined to be a candidate morphological breakpoint. The cumulative amount of the rotation angle change within the sliding window corresponding to each pre-constructed vertex is determined as the structural energy of each vertex; if the first-order difference component of the structural energy between any vertex and its neighboring vertices exceeds the preset structural breakpoint threshold, and has the largest first-order difference component among all vertices in the preset neighborhood, then the vertex is determined as a candidate structural breakpoint. Map each vertex of the target small-scale coastline to the large-scale coastline to obtain each projection point; determine the corresponding index of each vertex of the large-scale coastline and each vertex of the target small-scale coastline based on the cumulative arc length of each projection point on the large-scale coastline and the cumulative arc length of each vertex of the large-scale coastline; if any vertex of the target small-scale coastline and its corresponding index satisfy the monotonic order constraint, then the vertex is determined to be a candidate scale-consistent breakpoint. According to the preset breakpoint constraint rules, some breakpoints are deleted from candidate morphological breakpoints, candidate structural breakpoints and candidate scale consistent breakpoints to obtain each selected breakpoint; Based on each screening breakpoint, the starting point of the coastline, and the ending point of the coastline, determine each boundary vertex; The relative positions of each boundary vertex along the line are determined based on the total arc length of the large-scale coastline and the cumulative arc length of each boundary vertex on the large-scale coastline. Map the relative positions of each boundary vertex along the line to the total arc length of the target small-scale coastline, determine the target cutting position of each boundary vertex, and determine each cutting point on the small-scale coastline according to the target cutting position. The large-scale coastline is divided into major-scale coastline segments based on each boundary vertex, and the target small-scale coastline is divided into minor-scale coastline segments based on each dividing point.

[0024] Figure 1 This is a flowchart of the method. Figure 1As shown, to ensure that the segmentation results reflect the local geometric features of the coastline, maintain the integrity of the overall structure, and establish a clear correspondence with the target scale, this method first identifies candidate breakpoints from three levels: local morphology, regional structure, and scale consistency. These are defined as candidate morphological breakpoints R1, candidate structural breakpoints R2, and candidate scale consistency breakpoints R3, respectively. R1 and R2 are identified from the geometric and structural features of the large-scale coastline itself, while R3 is constructed from the cross-scale constraints of the small-scale true coastline on the large-scale true coastline. These three types of breakpoints correspond to local geometric abrupt changes, mesoscale structural switching, and the mapping positions of the target scale-preserved vertices, respectively, and together form the candidate boundary set for coastline segmentation.

[0025] First, let the large-scale coastline be: ; in, Represents a large-scale coastline; Represents the coordinates of the i-th vertex; Let x be the x-coordinate of the i-th vertex; Let be the ordinate of the i-th vertex.

[0026] Let the corresponding target small-scale coastline be: ; in, Represents a small-scale coastline of the target; This represents the coordinates of the s-th vertex; For the first The x-coordinates of the vertices; For the first The ordinates of each vertex.

[0027] Large-scale coastline It can be obtained from existing standard nautical charts, topographic map data, remote sensing image extraction results, or field measurement data. Target small-scale coastline True data can be obtained from published authoritative small-scale nautical charts or map products, or pseudo-true data can be generated by classic simplification algorithms, or drawn by professional cartographers.

[0028] In a preferred embodiment, the coastline is expressed sequentially at a fixed interval of 100m (i.e., equal-distance resampling), which ensures that the calculation of local turning angles of different shore sections is based on a consistent sampling step size, so that the morphological breakpoint threshold can be set at a uniform scale.

[0029] To quantify the local orientation change of the coastline at the i-th vertex, we first define the orientation angle at the i-th vertex, representing the change in orientation from vertex i. Point to the next vertex The azimuth angle of the line segment relative to the horizontal direction: ; in, This represents the orientation angle at the i-th vertex; Let x be the x-coordinate of the (i+1)th vertex; Let be the ordinate of the (i+1)th vertex; The function can reliably calculate the orientation angle across the entire angular range, avoiding issues such as quadrant ambiguity. Specifically, the function automatically determines the quadrant based on the vertical and horizontal increments of adjacent vertices and returns (-). The azimuth angle within the range.

[0030] Based on the change in the direction angle of adjacent line segments, the change in the rotation angle at the i-th vertex can be further defined. , used to characterize the intensity of local directional abrupt changes.

[0031] In this embodiment, determining the angle change corresponding to each vertex includes: Substitute the vertical and horizontal increments between any two adjacent vertices into the preset direction angle function to determine the direction angle corresponding to each vertex, and calculate the change in rotation angle corresponding to each vertex based on the direction angle corresponding to each vertex.

[0032] Calculate the change in rotation angle for each vertex based on the orientation angle corresponding to each vertex, including: ; in, This represents the change in angle corresponding to the i-th vertex; The direction angle corresponding to the i-th vertex; It is the direction angle corresponding to the (i-1)th vertex.

[0033] Specifically, considering the periodicity of the angle, the change in angle is defined as follows:

[0034] ; in, This represents the change in angle at the i-th vertex; Let represent the orientation angle at the (i-1)th vertex; this definition ensures that the change in angle always takes the minimum equivalent angle difference, and its value range is... This can objectively reflect the true degree of inflection of the shoreline at that apex. The change in angle is essentially equivalent to the curvature intensity in a discrete sense. In fact, when A significant increase indicates that the shoreline has undergone a clear geometric bend at that location, and there may be a candidate morphological breakpoint at that location.

[0035] In this embodiment, the candidate morphological breakpoint set is defined as: ; in, This is a set of candidate morphological breakpoints; The preset threshold for determining morphological breaks (i.e., morphological break threshold) emphasizes identifying significant turning points of the coastline from a local geometric perspective to ensure that key features such as headlands and sharp bends at bay mouths are preferentially preserved during the segmentation process.

[0036] Because this implementation uses a fixed 100-m interval to represent the coastline sequentially, and the calculation of local turning angles in different shore sections is based on a consistent sampling step size, the morphological breakpoint threshold can be set at a uniform scale. Based on this, the morphological breakpoint threshold... The threshold is fixed at 0.35 rad. This threshold can effectively distinguish between local abrupt changes in the true shape and minor perturbations caused by high-density vertices, thus ensuring that key features such as headlands and sharp bends at bay mouths are preferentially preserved during the segmentation process.

[0037] By introducing breakpoints at vertices with significant local turns, it is possible to effectively prevent segments from crossing different morphological units, ensuring that each shoreline segment has a relatively consistent orientation and curvature characteristics in terms of geometry.

[0038] In complex coastal geomorphological environments, shoreline morphology often exhibits multi-layered structural characteristics. While some shoreline sections may show relatively gentle directional changes at a local scale, their overall geometry undergoes significant transformations within a larger spatial neighborhood. These structural changes may not necessarily result in abrupt changes at a single point; therefore, candidate morphological breakpoint R1 cannot guarantee that such points will not be missed. Based on this understanding, this implementation introduces candidate structural breakpoint R2 to characterize the switching of the mesoscale structural state of the coastline.

[0039] The candidate structural breakpoint R2 focuses on the overall curvature behavior of the shoreline within a certain spatial window, rather than the local directional differences at a single vertex. This is to describe the shoreline at the vertex... To assess the overall structural complexity, a sliding window of length k is introduced. The changes in the rotation angle within the window are accumulated to construct the structural energy function.

[0040] ; in, represents the cumulative change in angle within the sliding window corresponding to the i-th vertex; j represents the vertex index within the sliding window; k represents the half-window length, i.e., the number of vertices extending from the sliding window to both sides of the central vertex; n represents the total number of vertices on the large-scale coastline. This represents the change in angle at the j-th vertex; The lower bound of the starting index of the sliding window is indicated: to ensure that it does not go out of bounds (starting from the second vertex, because the first vertex has no angle change). The upper limit of the sliding window's end index is indicated to ensure that it does not go out of bounds (it ends at the (n-1)th vertex, because the nth vertex has no angle change).

[0041] According to the above formula, if the corner changes within the window are relatively gentle, then The value is relatively small; if the shoreline exhibits high-frequency fluctuations or significant curvature within this neighborhood, then The value increases accordingly.

[0042] To identify the transition points of the structural states, the first-order difference component of the structural energy is further defined: ; in, This represents the first-order difference component of the structural energy between the i-th vertex and the (i-1)-th vertex; This represents the cumulative amount of the angle change within the sliding window corresponding to the (i-1)th vertex.

[0043] According to the above formula, when Exceeding the preset structural breakpoint threshold At that time, it indicates that the coastline was in the [number]th [year]. The structural complexity changes significantly near each vertex. These locations typically correspond to a transition from a low-complexity region to a high-complexity region on the shoreline, or a transition from a high-complexity region to a relatively flat area. Vertex Therefore, they can be marked as candidate structural breakpoints. Thus, the set of candidate structural breakpoints can be initially defined as follows:

[0044] ; in, This is the set of candidate structural breakpoints; The preset structural breakpoint determination threshold (i.e., structural breakpoint threshold).

[0045] To avoid continuous multi-point triggering caused by local noise, further restrictions are imposed. The maximum extremum point within a local area is considered a candidate structural breakpoint (the maximum extremum point represents the area with the largest structural energy change intensity within a given neighborhood). This constraint ensures reasonable control over the number of candidate breakpoints and makes their locations more geometrically meaningful. Let the local extremum detection radius be... Then the final set of candidate structural breakpoints can be written as:

[0046] ; in, Large-scale coastlines ; This represents the local neighborhood range of the i-th vertex; Indicates the scope of the field The largest first-order difference component among all vertices within the range.

[0047] The above formula means that the following two conditions must be met simultaneously to determine the candidate structural breakpoint: Condition one: If the first-order difference component of the structural energy between the i-th vertex and the (i-1)-th vertex exceeds the threshold, it can be confirmed that there is a significant structural state transition at this position. Condition two: , representing the range of the i-th vertex in the neighborhood. The largest first-order difference component among all vertices within the region is a local maximum point.

[0048] In essence, by introducing candidate structural breakpoints, the segmentation results can respond to local directional abrupt changes, while ensuring that the structural state transitions between straight and continuously curved sections, and between low-complexity and high-complexity sections, can be identified. This achieves the task of explicitly maintaining the structural integrity of the shoreline morphology at the segmentation level, providing quantifiable structural change indicators for the intensity measurement and priority selection of breakpoint types.

[0049] In the actual target scale, some points that have a controlling significance on the overall shape will still be retained in the simplified result. These nodes often correspond to the geometric transitions or structural features of the coastline that must be clearly expressed at the target scale, and their spatial location largely determines the overall orientation of the simplified coastline. Based on the above understanding, a candidate scale-consistent breakpoint R3 is proposed.

[0050] Candidate scale-consistent breakpoints R3 are key nodes that can be preserved at the target scale and have a clear geometrical correspondence on large-scale coastlines. Unlike candidate morphological breakpoints, which focus on local geometric abrupt changes at a single scale, the core of candidate scale-consistent breakpoints lies in establishing the correspondence between coastlines at different scales, so that the segmentation results can directly reflect the constraints brought about by the associated points in the multi-scale representation.

[0051] In this embodiment, the relative position of each boundary vertex along the line is determined based on the total arc length of the large-scale coastline and the cumulative arc length of each boundary vertex on the large-scale coastline, including: The total arc length of a large-scale coastline is determined by summing the Euclidean distances between adjacent vertices. The cumulative arc length of each boundary vertex on a large-scale coastline is determined by the sum of the Euclidean distances between adjacent vertices from the starting point of the coastline to each boundary vertex. The ratio of the cumulative arc length of each boundary vertex on the large-scale coastline to the total arc length of the large-scale coastline is used to determine the relative position of each boundary vertex along the line.

[0052] Map each vertex of the target small-scale coastline to the large-scale coastline (i.e., the original coastline), and then map the original vertex set... For each vertex, its optimal corresponding point is found. Based on this theory, this implementation method uses the nearest neighbor projection mapping method to find the accurate corresponding vertex on the original scale A through arc length matching constraints. Taking the s-th vertex on the target small-scale coastline as an example, this vertex is on the large-scale coastline. Projection point on for:

[0053] ; in, The s-th vertex of the target small-scale coastline; Let s be the projection point of the s-th vertex on the small-scale coastline onto the large-scale coastline. This represents the projection operator, which projects a point onto the coastline. Mapping functions on; Point Time Euclidean distance (straight-line distance in space).

[0054] The essence of the above formula is: among all points on a large-scale coastline, find the distance from the small-scale vertex. The closest point (i.e., the point with the smallest Euclidean distance).

[0055] Let the cumulative arc length of the i-th vertex of the large-scale coastline be . And the projection point The arc length position on a large-scale coastline is Based on the cumulative arc length of each projection point on the large-scale coastline and the cumulative arc length of each vertex of the large-scale coastline, determine the corresponding indices of each vertex of the large-scale coastline and each vertex of the target small-scale coastline, including:

[0056] ; in, The i-th vertex (or vertex i) of the large-scale coastline and the vertex of the target small-scale coastline The corresponding index; Let be the cumulative arc length of the i-th vertex of a large-scale coastline; small scale vertex The cumulative arc length of the projection point on a large-scale coastline. In addition, Indicates the traversal range, which covers all vertices of a large-scale coastline; indicates the projection point. The cumulative arc length position on a large-scale coastline.

[0057] The essence of the above formula is: among all vertices of a large-scale coastline, find the position where the cumulative arc length is closest to the arc length of the projected point. The index of that vertex.

[0058] To avoid cross-shore mismatches in complex shoreline sections, the mapping results are required to satisfy a monotonic order constraint along the coastline direction. This is further defined by... Then there should be .

[0059] This yields a set of candidate scale-consistent breakpoints (where... , ): ; in, Represents the set of candidate scale-consistent breakpoints; Represents the first large-scale coastline vertices (i.e., corresponding indices are ) The vertex); represents the vertex index on a small-scale coastline (traversal variable); The total number of vertices on a small-scale coastline; The traversal range excludes the start and end points of small-scale coastlines.

[0060] According to the above formula, This set represents the set of vertices on the large-scale coastline corresponding to the vertices within the small-scale coastline (excluding the start and end points) after projection mapping. It encodes the structural locations that must be preserved in the target-scale representation. Candidate scale-consistent breakpoints have the highest information level among the three types of candidate breakpoints. This set represents the candidate breakpoint locations on the original-scale coastline that correspond one-to-one with key nodes of the target scale. By segmenting at these locations, it can be ensured that subsequent segmentation results directly reflect the true representation requirements of the target-scale coastline, thereby enhancing the consistency between segmentation boundaries and the scale transformation task.

[0061] After introducing three types of candidate breakpoints—candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints—local areas of the coastline may simultaneously satisfy multiple breakpoint criteria, leading to a high spatial concentration of candidate breakpoints. In sequence modeling scenarios, excessively short shorelines can also introduce instability in sample distribution, affecting the convergence behavior of subsequent model training. Therefore, it is necessary to introduce a spatial constraint mechanism after the breakpoint set is generated to control the spacing between candidate breakpoints.

[0062] Based on the above requirements, this method provides two constraint rules as follows: minimum breakpoint spacing constraint C1 and minimum shoreline length C2: 1) Minimum breakpoint spacing constraint; The minimum breakpoint spacing constraint C1 is introduced. Its core principle is that when the arc length distance between adjacent candidate breakpoints along the shoreline is less than a given threshold, only the more important or stronger breakpoints are retained to avoid local breakpoint redundancy. This constraint mainly aims at point-level sparsity of the candidate breakpoint set, with the goal of suppressing breakpoint clustering caused by the superposition of multiple rules, so that the final segmentation maintains a reasonable breakpoint density in space.

[0063] In this embodiment, according to preset breakpoint constraint rules, some breakpoints are deleted from candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints to obtain each selected breakpoint, including: Sort the candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints according to their corresponding indices, and calculate the cumulative arc length between each adjacent breakpoint after sorting. When the cumulative arc length between any two adjacent breakpoints is less than the preset minimum breakpoint spacing threshold, including: If the breakpoint types are different, the lower-priority breakpoint will be deleted from two adjacent breakpoints according to the preset priority order, while the higher-priority breakpoint will be retained; the priority order from high to low is as follows: candidate scale-consistent breakpoint, candidate structure breakpoint, and candidate morphology breakpoint. If the breakpoints are of the same type, delete the breakpoint with the lower strength value among two adjacent breakpoints and keep the breakpoint with the higher strength value. Divide the shoreline into sections based on the preserved breakpoints and calculate the arc length of each section; If the arc length of any shore segment is less than the preset minimum shore segment length threshold, then the breakpoints with lower strength values ​​are deleted at both ends of that shore segment, while the breakpoints with higher strength values ​​are retained. Each shore segment whose arc length is less than the preset minimum shore segment length threshold is merged into the corresponding adjacent shore segment to obtain each reconstructed shore segment. When the arc length of each reconstructed shoreline is greater than or equal to the preset minimum shoreline length threshold, each screening breakpoint is determined.

[0064] Specifically, let the set of candidate breakpoints obtained after filtering by rules R1, R2, and R3 be: ; in, These represent the corresponding indices on large-scale coastlines. , , The vertex, and Define any adjacent candidate breakpoints. and The arc length distance between them is:

[0065] ; in, express and The cumulative arc length along the original broken line is used to ensure that the distance measurement is consistent with the actual geometry of the shoreline, thus avoiding underestimation of the true spatial interval due to the approximation of a straight line.

[0066] Given a minimum breakpoint spacing threshold When there are adjacent candidate breakpoints that satisfy: ; If the above conditions are met, then the two breakpoints are considered too close spatially and should not be retained simultaneously. In this case, one breakpoint needs to be deleted from the breakpoint pair. That is, the deletion strategy is based on a comparison of breakpoint strength, retaining the breakpoint with greater strength while removing the one with less strength. Based on this, the updated set of breakpoints is denoted as From Remove weak breakpoints The results obtained later.

[0067] The above process is executed iteratively in the order of the vertex sequence until the following conditions are met between any two adjacent breakpoints: ; In this embodiment, considering the difference between the point spacing and the target scale, the minimum breakpoint spacing threshold is determined. The fixed setting is 2000 m, which corresponds to 20 sampling points. This value is used to control the clustering of local breakpoints, preserving key turning points and structural boundaries while avoiding excessive repetition of breakpoints within a short distance.

[0068] Without changing the type determination result of the breakpoint, C1 globally adjusts the spatial density at the candidate breakpoint set level, so that the segmentation result avoids too many short segments due to local geometric disturbances, and ensures that each segment has a basic length in the spatial scale, thereby maintaining the stability of the morphological features within the segment. It plays an important control role between connection breakpoint identification and final segmentation output.

[0069] 2) Minimum shoreline length constraint; Since candidate breakpoints arise from the superposition of multiple criteria, short shoreline segments may still form in local areas. These extremely short segments often lack complete geographic semantic information in their geometric structure, which negatively weakens the overall stability of the segmentation results and makes it difficult to guarantee the consistency of sample units in subsequent sequence modeling. Therefore, a minimum shoreline length constraint C2 is introduced.

[0070] The core of this constraint lies in controlling the minimum spatial scale of the final shoreline segment at the segmented structural level, ensuring that each segment has a basic length requirement in the sense of arc length. C1 is a point-level control for the set of breakpoints, while C2 applies to the shoreline segment formed after segmentation, and is a segment-level structural constraint.

[0071] Let the set of breakpoints after C1 processing still be denoted as: ; shoreline formed by adjacent discontinuities Defined as: ; shoreline The arc length is defined as: ; Given a minimum shoreline length threshold When a shoreline exists that satisfies: ; If the breakpoint is too short to constitute an independent unit on a spatial scale, then the breakpoints at both ends of the breakpoint are not simply deleted. Instead, the breakpoints at both ends of the breakpoint are filtered. By deleting the weaker breakpoints at both ends of the short breakpoint, the short breakpoint is incorporated into the adjacent breakpoints. Then, the set of breakpoints is reconstructed, and the reconstructed breakpoints are recalculated until all breakpoints satisfy the following condition:

[0072] ; Compared to C1, the constraint object of C2 has shifted from candidate breakpoints to the initial segmentation result. The former belongs to the point-level sparsity constraint at the breakpoint set level, while the latter belongs to the segment-level stabilization constraint at the segmentation result level. The two are logically independent, but sequentially connected in the process. C1 first controls the local clustering of breakpoints, and then C2 controls the minimum structural scale of the final shoreline segment. Through the collaborative constraints of C1 and C2, the geometric rationality of the breakpoints can be guaranteed, while ensuring that the final segmentation result has a stable structural expression capability in spatial scale.

[0073] Breakpoint Priority Decision Rules: The information levels carried by the three types of candidate breakpoints differ fundamentally. Candidate morphological breakpoints reflect local geometric abrupt changes and are mainly used to identify local morphological features such as headlands and sharp bends. Candidate structural breakpoints reflect changes in structural complexity at the neighborhood scale and characterize the boundaries of coastline morphological units. Candidate scale-consistent breakpoints directly originate from the mapping of the true-value coastline vertices at the target scale to the large-scale coastline, encoding the structural positions that must be retained in the target-scale representation. Considering that the task objective is to serve the true-value scale conversion from large to small scales, scale consistency information should take precedence over mesoscale structural information, and structural information should take precedence over local geometric details. Based on the differences in the above information levels, the priority between breakpoint types is defined as follows:

[0074] ; To further filter when breakpoints of the same type conflict, intensity functions for three types of breakpoints are defined.

[0075] The intensity of the candidate morphological breakpoint is represented by the change in single-point rotation angle: ; Since these candidate breakpoints reflect local geometric information, they can be filtered by intensity ranking, provided that scale semantics and overall structural boundaries are guaranteed.

[0076] The set of candidate structural breakpoints reflects the geometric state changes of the shoreline at the neighborhood scale, and its intensity is represented by the structural energy difference: ; These candidate breakpoints carry mesoscale structural information and determine the boundary positions of shoreline morphological units. Segmenting the coastline needs to conform to the principle of integration from the whole to the part, so its constraint strength is weaker than that of scale semantic information, but still higher than that of local geometric details.

[0077] For a candidate scale-consistent breakpoint, its strength is represented by the reciprocal of the mapping residual. Let the vertex of the true value at a small scale be... Mapped to the corresponding vertex of a large-scale coastline The projected residual is The intensity is expressed as:

[0078] ; in, The smallest constant to prevent the denominator from being zero is 10. -6 . The smaller the value, the more stable the correspondence between the target-scale vertex and the original-scale vertex, and the greater the intensity.

[0079] Record candidate breakpoints The type function is If a vertex belongs to a set of multiple candidate breakpoints, its type is defined as the one with the highest priority, i.e.: ; When a breakpoint is deleted due to a C1 or C2 constraint, the breakpoint types are compared first, and the one with higher priority is retained. If the types are the same, their strength function values ​​are compared, and the breakpoint with the greater strength is retained.

[0080] The breakpoint selection process can be described as follows: prioritizing scale semantics, followed by structural boundaries, and then local geometric details, the strength of breakpoints at the same level is compared and selected. This hierarchical decision-making mechanism helps to maintain the consistency between the target scale semantics and the overall structure of the coastline to the greatest extent possible under spatial constraints, while preserving necessary local morphological information.

[0081] After identifying candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints, the final set of internal breakpoints on a large-scale coastline is obtained through minimum breakpoint spacing constraints, minimum shoreline length constraints, and breakpoint priority rules. This set is denoted as […]. : ; in, To facilitate complete data segmentation, the start and end points of the coastline are incorporated into the boundary set as natural boundary points, denoted as... : ; in, .

[0082] Final breakpoint set The identification is entirely based on large-scale coastlines, while the construction of training samples requires further data pairs that correspond one-to-one between large-scale and small-scale coastlines. Therefore, in obtaining... Then, the relative position of the final breakpoint at the large scale along the coastline is transmitted back to the small scale coastline, thereby constructing a consistent split boundary across scales and ensuring the consistency of the corresponding positions of the two scales of the coastline.

[0083] In this embodiment, the relative position of each boundary vertex along the line is determined based on the total arc length of the large-scale coastline and the cumulative arc length of each boundary vertex on the large-scale coastline, including: The total arc length of a large-scale coastline is determined by summing the Euclidean distances between adjacent vertices. The cumulative arc length of each boundary vertex on a large-scale coastline is determined by the sum of the Euclidean distances between adjacent vertices from the starting point of the coastline to each boundary vertex. The ratio of the cumulative arc length of each boundary vertex on the large-scale coastline to the total arc length of the large-scale coastline is used to determine the relative position of each boundary vertex along the line.

[0084] Specifically, establish a large-scale coastline. The total arc length is: ; Boundary points The cumulative arc length position on a large-scale coastline is defined as: ; Normalize it to the proportion of relative positions along the line, the normalization formula is as follows: ; in, Represents boundary vertices Located at the relative arc length position along the entire large-scale coastline (i.e., relative position along the line). The boundary point indices satisfy a strict increasing relationship to ensure that the segmentation order is not disordered when subsequently transmitted back to the target small-scale coastline. The increasing relationship is expressed as:

[0085] ; In this embodiment, the relative positions of each boundary vertex along the line are mapped to the total arc length of the target small-scale coastline to determine the target cutting position of each boundary vertex, including: The target cutting position of each boundary vertex is determined by multiplying the relative position of each boundary vertex along the line with the total arc length of the target small-scale coastline.

[0086] Specifically, set a target small-scale coastline The total arc length is: ; Then the boundary point with large scale The corresponding target segmentation position for a small scale is defined as follows: ; in, Indicates the boundary point between the small-scale coastline and the large-scale coastline. The target arc length has the same relative position along the line. Therefore, a small-scale coastline of the target can be obtained. Determine the corresponding split point. ,definition Parameters along the arc length of a small-scale coastline The corresponding linear reference position:

[0087] ; The set of corresponding dividing points for the target at a small scale is as follows: ; in, The original apex of the small-scale coastline There is no necessary connection, when When a point falls within a certain broken line segment, a new dividing point can be inserted at that location to segment the small-scale coastline. This approach can better maintain the consistency of the scale along the line and reduce the impact of differences in the density of the original vertex distribution on the dividing point.

[0088] Based on large-scale boundary sets Set of dividing points corresponding to the target small scale Then, the two-scale coastlines are divided. The large-scale coastline is defined by adjacent boundary points. and The defined first Each section of the shore is , is represented as:

[0089] ; Divided by adjacent points on a small scale and Between Each section of the shore is The expression is: ; This leads to the construction of a set of cross-scale, one-to-one correspondence coastal segment data pairs. : ; In summary, by using relative arc lengths along the coastline as a medium, the segmented boundaries identified on a large-scale coastline are stably transferred to the target small-scale coastline, thus ensuring a one-to-one correspondence between the two scales. This segmentation method achieves comprehensive utilization of information on the local morphology, overall structure, and scale consistency of the coastline, and also enhances the ability of the segmentation results to preserve key geographical features.

[0090] This invention also provides a computer program product.

[0091] Various embodiments of the methods and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementation in one or more computer program products, which may include one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be an application-specific or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0092] This invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements a method for predicting wireless communication medium parameters and path loss as provided in all embodiments of this invention. The method includes: acquiring a large-scale coastline and a corresponding target small-scale coastline; obtaining vertices by equidistant sampling of the large-scale coastline and determining the angle change corresponding to each vertex; determining a vertex as a candidate morphological breakpoint if the angle change of any vertex exceeds a preset morphological breakpoint threshold; determining the accumulated angle change within a pre-constructed sliding window corresponding to each vertex as the structural energy of each vertex; determining a vertex as a candidate structural breakpoint if the first-order difference of the structural energy between any vertex and its neighboring vertices exceeds a preset structural breakpoint threshold and has the largest first-order difference among all vertices in a preset neighborhood; mapping each vertex of the target small-scale coastline to the large-scale coastline to obtain projection points; and calculating the cumulative arc of each projection point on the large-scale coastline. The total arc length of the large-scale coastline is used to determine the corresponding indices of each vertex of the large-scale coastline and each vertex of the target small-scale coastline. If any vertex of the target small-scale coastline and its corresponding index satisfy the monotonic order constraint, then the vertex is determined as a candidate scale-consistent breakpoint. According to the preset breakpoint constraint rules, some breakpoints are deleted from the candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints to obtain each selected breakpoint. Based on each selected breakpoint, the start point of the coastline, and the end point of the coastline, each boundary vertex is determined. Based on the total arc length of the large-scale coastline and the cumulative arc length of each boundary vertex on the large-scale coastline, the relative position along the line of each boundary vertex is determined. The relative position along the line of each boundary vertex is mapped to the total arc length of the target small-scale coastline to determine the target cutting position of each boundary vertex, and each cutting point is determined on the small-scale coastline based on the target cutting position. Based on each boundary vertex, the large-scale coastline is divided into large-scale coastline segments, and based on each cutting point, the target small-scale coastline is divided into small-scale coastline segments.

[0093] A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electronic device, apparatus, or device that is electrical, magnetic, optical, electromagnetic, infrared, or semiconductor, or any combination thereof. More specific examples of a computer-readable storage medium (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an electronic device, apparatus, or device that can be executed by instructions.

[0094] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in conjunction with an electronic device, apparatus, or device that executes instructions.

[0095] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0096] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0097] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A coastline segmentation method for deep learning models, characterized in that, include: Obtain large-scale coastlines and their corresponding target small-scale coastlines; Each vertex is obtained by sampling a large-scale coastline at equal intervals, and the change in the angle corresponding to each vertex is determined. If the change in the angle corresponding to any vertex exceeds the preset morphological breakpoint threshold, the vertex is determined to be a candidate morphological breakpoint. The cumulative amount of the rotation angle change within the sliding window corresponding to each pre-constructed vertex is determined as the structural energy of each vertex; if the first-order difference component of the structural energy between any vertex and its neighboring vertices exceeds the preset structural breakpoint threshold, and has the largest first-order difference component among all vertices in the preset neighborhood, then the vertex is determined as a candidate structural breakpoint. Map each vertex of the target small-scale coastline to the large-scale coastline to obtain each projection point; determine the corresponding index of each vertex of the large-scale coastline and each vertex of the target small-scale coastline based on the cumulative arc length of each projection point on the large-scale coastline and the cumulative arc length of each vertex of the large-scale coastline; if any vertex of the target small-scale coastline and its corresponding index satisfy the monotonic order constraint, then the vertex is determined to be a candidate scale-consistent breakpoint. According to the preset breakpoint constraint rules, some breakpoints are deleted from the candidate morphological breakpoints, candidate structural breakpoints and candidate scale consistent breakpoints to obtain each screening breakpoint; Based on each screening breakpoint, the starting point of the coastline, and the ending point of the coastline, determine each boundary vertex; The relative positions of each boundary vertex along the line are determined based on the total arc length of the large-scale coastline and the cumulative arc length of each boundary vertex on the large-scale coastline. Map the relative positions of each boundary vertex along the line to the total arc length of the target small-scale coastline, determine the target cutting position of each boundary vertex, and determine each cutting point on the small-scale coastline according to the target cutting position. The large-scale coastline is divided into major-scale coastline segments based on the boundary vertices, and the target small-scale coastline is divided into minor-scale coastline segments based on the dividing points.

2. The coastline segmentation method for deep learning models according to claim 1, characterized in that, According to preset breakpoint constraint rules, some breakpoints are deleted from the candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints to obtain the selected breakpoints, including: The candidate morphological breakpoints, candidate structural breakpoints, and candidate scale-consistent breakpoints are sorted according to their corresponding indices, and the cumulative arc length between each adjacent breakpoint after sorting is calculated. When the cumulative arc length between any two adjacent breakpoints is less than the preset minimum breakpoint spacing threshold, including: If the breakpoint types are different, the lower-priority breakpoint is deleted from two adjacent breakpoints according to the preset priority order, while the higher-priority breakpoint is retained; the priority order from high to low is as follows: candidate scale-consistent breakpoint, candidate structure breakpoint, and candidate morphology breakpoint. If the breakpoints are of the same type, delete the breakpoint with the lower strength value among two adjacent breakpoints and keep the breakpoint with the higher strength value. Divide the shoreline into sections based on the preserved breakpoints and calculate the arc length of each section; If the arc length of any shore segment is less than the preset minimum shore segment length threshold, then the breakpoints with lower strength values ​​are deleted at both ends of that shore segment, while the breakpoints with higher strength values ​​are retained. Each shore segment whose arc length is less than the preset minimum shore segment length threshold is merged into the corresponding adjacent shore segment to obtain each reconstructed shore segment. When the arc length of each reconstructed shoreline is greater than or equal to the preset minimum shoreline length threshold, each screening breakpoint is determined.

3. The coastline segmentation method for deep learning models according to claim 1, characterized in that, Based on the total arc length of the large-scale coastline and the cumulative arc length of each boundary vertex on the large-scale coastline, determine the relative position of each boundary vertex along the line, including: The total arc length of a large-scale coastline is determined by summing the Euclidean distances between adjacent vertices. The cumulative arc length of each boundary vertex on a large-scale coastline is determined by the sum of the Euclidean distances between adjacent vertices from the starting point of the coastline to each boundary vertex. The ratio of the cumulative arc length of each boundary vertex on the large-scale coastline to the total arc length of the large-scale coastline is used to determine the relative position of each boundary vertex along the line.

4. The coastline segmentation method for deep learning models according to claim 1, characterized in that, Mapping the relative positions of each boundary vertex along the line to the total arc length of the target small-scale coastline determines the target cutting position of each boundary vertex, including: The target cutting position of each boundary vertex is determined by multiplying the relative position of each boundary vertex along the line with the total arc length of the target small-scale coastline.

5. The coastline segmentation method for deep learning models according to claim 1, characterized in that, Determine the angle change corresponding to each vertex, including: Substitute the vertical and horizontal increments between any two adjacent vertices into the preset direction angle function to determine the direction angle corresponding to each vertex, and calculate the change in rotation angle corresponding to each vertex based on the direction angle corresponding to each vertex.

6. The coastline segmentation method for deep learning models according to claim 5, characterized in that, Calculate the change in rotation angle for each vertex based on the orientation angle corresponding to each vertex, including: ； in, This represents the change in angle corresponding to the i-th vertex; The direction angle corresponding to the i-th vertex; It is the direction angle corresponding to the (i-1)th vertex.

7. The coastline segmentation method for deep learning models according to claim 1, characterized in that, Based on the cumulative arc length of each projection point on the large-scale coastline and the cumulative arc length of each vertex of the large-scale coastline, determine the corresponding indices of each vertex of the large-scale coastline and each vertex of the target small-scale coastline, including: ； in, The i-th vertex of the large-scale coastline and the vertex of the target small-scale coastline The corresponding index; Let be the cumulative arc length of the i-th vertex of a large-scale coastline; small scale vertex The cumulative arc length of the projection point on a large-scale coastline.

8. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements a coastline segmentation method for a deep learning model according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements a coastline segmentation method for a deep learning model as described in any one of claims 1-7.

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