A method and system for suppressing boundary effect of TIN encryption based on periodic cubic spline simulation of ground points

Abstract

This invention belongs to the field of terrain modeling technology and discloses a method for suppressing boundary effects in TIN (Terrain Injection) based on periodic cubic splines for simulating ground points. This invention generates high-quality boundary simulation ground points during the initial TIN construction stage by adaptively expanding and smoothing the data boundary, thereby significantly improving the geometry of the TIN. Smoothing complex boundaries using periodic cubic splines effectively fits corridor-shaped and irregular data forms. It avoids generating long and narrow degenerate boundary triangles, significantly improving the geometric quality and stability of the initial TIN. The local orientation estimation based on SVD is insensitive to noise and is applicable to various complex scenarios. It improves the accuracy of ground point discrimination, reduces error accumulation, and enhances the reliability of the final terrain modeling results.

Description

Technical Field

[0001] This invention belongs to the field of terrain modeling technology, and in particular relates to a TIN-based method and system for suppressing boundary effects of simulated ground points using periodic cubic splines. Background Technology

[0002] TIN models are widely used in fields such as lidar point cloud ground filtering, digital elevation model (DEM) construction, and terrain analysis because they can adaptively represent irregular terrain structures. In TIN-based iterative encryption algorithms, it is usually necessary to first construct an initial TIN consisting of a small number of seed points (such as the lowest point or ground seed points), and then gradually introduce candidate points into it to complete terrain reconstruction.

[0003] However, the boundary construction method of the initial TIN has a decisive impact on the subsequent encryption process. In existing technologies, a common practice is to introduce simulated ground points at the four corners of the data range to enclose the initial TIN. However, in practical applications, this method easily generates boundary triangles with excessively large spans and elongated shapes, reducing the geometric reliability of the TIN. To improve this issue, existing research has proposed a method of constructing regular buffers along the data boundaries and uniformly distributing simulated ground points to enhance boundary constraint capabilities.

[0004] While the aforementioned improvements are effective within regular or near-rectangular regions, regular buffer boundaries still struggle to conform to the actual data geometry in corridor-shaped, curved, or highly irregular data regions, and the boundary triangle degradation problem persists. Therefore, there is an urgent need for a boundary simulation point generation method that can adapt to the data boundary shape and balance smoothness and geometric consistency, in order to fundamentally alleviate the boundary effect problem in the TIN encryption process.

[0005] In the existing iterative encryption process of Triangulated Irregular Network (TIN), the boundary effect problem caused by unreasonable boundary handling, especially in the initial TIN construction stage, is prone to producing long and narrow boundary triangles with poor geometric stability in corridor-shaped or complex regions, which leads to the problems of terrain representation distortion, error accumulation and reduced reliability of encryption results.

[0006] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0007] (1) Insufficient boundary geometric constraints

[0008] Using data range corner points or regular buffer boundaries to generate simulation points makes it difficult to accurately describe the true boundary shape of complex or narrow regions, and easily produces long and narrow degenerate triangles.

[0009] (2) Poor adaptability to data format

[0010] For datasets with corridor-like, irregular, or tortuous distributions, regular boundary expansion methods cannot adjust to local geometric changes, resulting in a mismatch between the boundary and the data distribution.

[0011] (3) The initial mass of TIN is unstable.

[0012] Poor quality of boundary triangles will continuously amplify errors during iterative encryption, affecting the accuracy of ground point discrimination and the reliability of the final terrain model.

[0013] (4) Insufficient automation and robustness

[0014] Existing methods lack systematic design in boundary orientation determination, noise suppression, and complex boundary modeling, making it difficult to maintain stable performance under different data scenarios. Summary of the Invention

[0015] To address the problems existing in the prior art, this invention provides a TIN encryption boundary effect suppression method based on periodic cubic spline simulation of ground points.

[0016] This invention is implemented as follows: A method for suppressing TIN-based densification boundary effects using periodic cubic splines to simulate ground points includes:

[0017] Step 1, data boundary extraction;

[0018] Step 2, Local tangent and normal estimation based on SVD;

[0019] Step 3: Boundary expansion and simulation control point generation;

[0020] Step 4: Periodic cubic spline boundary modeling;

[0021] Step 5: Boundary sampling and generation of simulated ground points;

[0022] Step 6: Initial TIN construction and iterative encryption.

[0023] Furthermore, the data boundary extraction:

[0024] Extracting two-dimensional projected boundaries from the point cloud data to be processed, using... The algorithm generates a closed set of boundary points { } is used to describe the true planar contour of the data.

[0025] Furthermore, the local tangent and normal estimation based on SVD:

[0026] For each boundary point Within its neighborhood, 2w + 1 adjacent boundary points are selected to form a local window. After centering the point set within the window, the local principal direction vector is estimated using singular value decomposition (SVD) as the tangent direction at that point. Based on this, the tangent direction is rotated by 90° and normalized to obtain the corresponding unit normal vector. The normal vector consistency determination mechanism ensures that all normal vectors point to the outside of the data.

[0027] Furthermore, the boundary expansion and simulation control point generation are as follows:

[0028] Along the normal direction For each boundary point Expand the boundary points. Its position is determined by the following formula:

[0029]

[0030] in, The extended distance parameter is used to suppress noise while conforming to local curvature; this forms a closed sequence of extended control points { }

[0031] Furthermore, the periodic cubic spline boundary modeling is as follows:

[0032] Based on the extended control point sequence, the spline parameters are calculated using the centripetal parameterization method (Equation 2); after calculating the cumulative parameters, all Relative to total length Normalized to [0,1] (Equation 3); the periodic cubic spline curve is constructed based on chord length parameterization (Equation 4).

[0033]

[0034]

[0035]

[0036] in , , Indicate control points The second derivative at that point, ;

[0037] In each parameter range Inside, the spline curve passes through the second derivative term. and Constraints, on and Three interpolations are performed between the points to ensure the second-order continuity of the curve across the entire boundary. (Continuous); to satisfy the periodic constraint, it is necessary to ensure , Second derivative coefficients It is obtained by solving the following system of periodic tridiagonal linear equations (Equation 5);

[0038]

[0039] The tridiagonal coefficients are defined as follows: , , Under periodic boundary conditions, subscripts are processed in a cyclic manner, i.e. , , The resulting cyclic tridiagonal matrix contains non-zero terms at the first and last positions to enforce the condition. The periodic constraints ensure that the spline curve remains closed at the boundary. Continuity;

[0040] Solving this system of linear equations will yield all the results. And substitute into formula (4) to construct a complete periodic cubic spline curve.

[0041] Furthermore, the boundary sampling and simulated ground point generation:

[0042] Along the periodic cubic spline curve at fixed arc length intervals Uniform sampling is performed to generate boundary sampling points; by performing three-dimensional nearest neighbor interpolation on the existing seed points on the ground, elevation values ​​are assigned to the sampling points to obtain a set of simulated ground points.

[0043] Initial TIN construction and iterative encryption:

[0044] The generated simulated ground points and ground seed points are used together as input to construct an initial TIN model, and subsequent TIN iterative encryption processes are performed on this basis.

[0045] Another objective of this invention is to provide a TIN-based encrypted boundary effect suppression system for simulated ground points using periodic cubic splines, comprising:

[0046] The extraction module is used for data boundary extraction;

[0047] The estimation module is used for local tangent and normal estimation based on SVD.

[0048] The control point generation module is used for boundary expansion and simulation control point generation.

[0049] The modeling module is used for periodic cubic spline boundary modeling.

[0050] The ground point generation module is used for boundary sampling and simulated ground point generation;

[0051] The iterative encryption module is used for initial TIN construction and iterative encryption.

[0052] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the TIN encryption boundary effect suppression method based on periodic cubic spline simulated ground points.

[0053] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the TIN encryption boundary effect suppression method based on periodic cubic spline simulated ground points.

[0054] Another objective of this invention is to provide an information data processing terminal for implementing the TIN encryption boundary effect suppression system based on periodic cubic spline simulated ground points.

[0055] Based on the above technical solutions and the technical problems solved, please analyze the advantages and positive effects of the technical solution to be protected by this invention from the following aspects:

[0056] First, this invention improves the geometric quality and stability of the initial TIN by introducing an automatic generation method for simulated ground points that combines buffer boundary construction and periodic cubic spline modeling, providing a reliable foundation for subsequent iterative encryption. This invention proposes a TIN encryption boundary effect suppression method based on periodic cubic spline simulated ground points. This method generates high-quality boundary simulated ground points during the initial TIN construction stage by adaptively expanding and smoothly modeling the data boundaries, thereby significantly improving the geometric structure of the TIN.

[0057] (1) Adaptive boundary modeling

[0058] Complex boundaries are smoothly modeled using periodic cubic splines, effectively fitting corridor-shaped and irregular data forms.

[0059] (2) Significantly suppresses boundary effects

[0060] This avoids generating long and narrow degenerate boundary triangles, significantly improving the geometric quality and stability of the initial TIN.

[0061] (3) High robustness and degree of automation

[0062] Local orientation estimation based on SVD is insensitive to noise and is suitable for a variety of complex scenarios.

[0063] (4) Provide a reliable foundation for iterative encryption

[0064] Improve the accuracy of ground point identification, reduce error accumulation, and enhance the reliability of the final terrain modeling results.

[0065] Secondly, as supporting evidence of the inventiveness of this invention, it is also reflected in the following important aspects:

[0066] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0067] This invention proposes a TIN densification boundary effect suppression method based on periodic cubic spline simulated ground points. It can automatically generate simulated ground points that are highly consistent with the boundary morphology of real data during the initial TIN construction stage, thereby significantly improving the geometric stability and boundary quality of the TIN model.

[0068] This technology has broad application prospects in areas such as lidar point cloud processing, digital elevation model (DEM) construction, 3D terrain modeling, and high-precision maps for smart cities and autonomous driving. By reducing boundary degradation triangles and improving the accuracy of ground point discrimination, this invention can effectively improve the reliability and automation of terrain reconstruction results, thereby reducing the cost of manual intervention and improving data processing efficiency.

[0069] At the industrial application level, this technology can be integrated into point cloud processing software, remote sensing data processing platforms, and geographic information system (GIS) products, providing terrain data processing companies, surveying and mapping institutions, and UAV surveying service providers with more stable and high-precision terrain modeling capabilities. Its commercial value is mainly reflected in: improving the accuracy of point cloud ground filtering and DEM generation, thereby enhancing product competitiveness; reducing the cost of manual correction in processing data from complex terrains or corridor-like areas; enhancing the automated processing capabilities of software systems in complex scenarios; and being integrated as a core algorithm module into surveying software, point cloud processing platforms, and smart city 3D modeling systems.

[0070] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0071] Existing TIN-based iterative encryption algorithms typically construct the initial TIN by placing simulated ground points at the corners of the data range or on the boundaries of regular buffers. However, these methods usually assume that the data boundaries are regular or approximately rectangular structures. When faced with corridor-shaped, curved, or highly irregular data regions, they fail to accurately reflect the shape of the data boundaries and are prone to generating degenerate triangles with large spans and narrow shapes, thus affecting the stability of subsequent encryption processes.

[0072] To address this issue, this invention proposes for the first time to combine α-shape boundary extraction, SVD local orientation estimation, and periodic cubic spline boundary modeling. By adaptively expanding and smoothing the boundary, high-quality simulated ground points are automatically generated for constructing the initial TIN model. This method not only accurately fits complex data boundaries but also avoids boundary triangle degradation while ensuring the second-order continuity of the curve.

[0073] Currently, there is a lack of a unified method that can simultaneously achieve adaptive boundary morphology, geometric smoothness, and automated simulation point generation. This invention introduces periodic cubic splines for boundary modeling, achieving high-quality representation of complex boundary morphologies and significantly improving model stability during the initial TIN construction stage. Therefore, this technology fills the gaps in existing technologies for TIN boundary modeling and simulated ground point generation in complex regions.

[0074] (3) The technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully:

[0075] In TIN-based point cloud ground filtering and terrain reconstruction, the boundary effect has long been a significant technical challenge affecting algorithm stability. Since the initial TIN typically relies on a limited number of seed points for construction, improper boundary construction can easily generate long and narrow degenerate triangles in the boundary region. These unstable structures amplify errors during subsequent iterations and encryption, leading to misjudgments of ground points and distortion of terrain representation.

[0076] Although existing studies have attempted to improve this problem by using regular buffers or adding boundary simulation points, these methods generally lack the ability to adapt to complex boundary morphologies and still struggle to avoid the generation of degenerate triangles in corridor-shaped or curved data regions.

[0077] This invention constructs a boundary modeling mechanism based on periodic cubic splines, combined with local orientation information estimated by SVD, to provide a smooth and continuous geometric representation of the real data boundary and generate simulated ground points along the boundary, thereby significantly improving the quality of boundary triangles in the initial TIN construction stage. This method fundamentally alleviates the long-standing boundary effect problem in TIN encryption, making ground point discrimination and terrain modeling results more stable and reliable. Therefore, this invention effectively solves a key technical problem that has long existed and is difficult to completely resolve in TIN iterative encryption algorithms.

[0078] (4) The technical solution of the present invention overcomes technical bias:

[0079] In traditional TIN construction methods, it is generally believed that the initial TIN construction requirements can be met simply by expanding the boundaries or setting a few simulated ground points at the corners of the data range. This approach assumes that the data boundaries are relatively regular, and therefore usually uses rectangular boundaries or regular buffers. However, this approach often leads to severe degradation of boundary triangles in complex data regions, affecting the stability of subsequent algorithms.

[0080] This invention breaks through the traditional technical approach mentioned above. By introducing periodic cubic spline curves to model the boundary and combining it with SVD to estimate the local geometric direction, the generation of boundary simulation points can adapt to the real contour of the data, rather than relying on fixed regular boundaries. This method shows that modeling the boundary with high-order continuous curves and generating simulation points can significantly improve the initial structure quality of TIN, thereby effectively suppressing boundary effects.

[0081] Therefore, this invention breaks through the traditional technical understanding that "a reliable initial TIN can be constructed simply by using simple rule boundaries," and proposes a more reasonable and stable boundary modeling mechanism, which to some extent overcomes the technical bias in the existing technical approach. Attached Figure Description

[0082] Figure 1 This is a flowchart of the TIN encryption boundary effect suppression method based on periodic cubic spline simulation of ground points provided in an embodiment of the present invention.

[0083] Figure 2 This is a set of simulated ground point maps provided in the embodiments of the present invention.

[0084] Figure 3 This is a block diagram of the TIN encryption boundary effect suppression system based on periodic cubic spline simulated ground points provided in an embodiment of the present invention.

[0085] Figure 4 This is a degenerate boundary triangle diagram provided in an embodiment of the present invention.

[0086] Figure 5 This is a schematic diagram of initial TIN densification provided in an embodiment of the present invention.

[0087] Figure 6 This is a data overview diagram of the power transmission corridor provided in an embodiment of the present invention.

[0088] Figure 7 This is a schematic diagram of the global shape preservation analysis of the Fourier descriptor of the power transmission corridor dataset provided in the embodiments of the present invention. Detailed Implementation

[0089] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0090] like Figure 1 As shown, the TIN-based densification boundary effect suppression method for simulated ground points using periodic cubic splines provided by this invention includes the following steps:

[0091] S101, Data Boundary Extraction;

[0092] S102, Local tangent and normal estimation based on SVD;

[0093] S103, Boundary expansion and simulation control point generation;

[0094] S104, periodic cubic spline boundary modeling;

[0095] S105, Boundary sampling and simulated ground point generation;

[0096] S106, Initial TIN Construction and Iterative Encryption.

[0097] Data boundary extraction provided in this embodiment of the invention:

[0098] Extracting two-dimensional projected boundaries from the point cloud data to be processed, using... The algorithm generates a closed set of boundary points { } is used to describe the true planar contour of the data.

[0099] The local tangent and normal estimation based on SVD provided in this embodiment of the invention:

[0100] For each boundary point Select within its neighborhood A local window is formed by two adjacent boundary points. After centering the set of points within the window, the local principal direction vector is estimated using singular value decomposition (SVD) as the tangent direction at that point. Based on this, the tangent direction is rotated by 90° and normalized to obtain the corresponding unit normal vector. The normal vector consistency determination mechanism ensures that all normal vectors point to the outside of the data.

[0101] The boundary extension and simulation control point generation provided in this embodiment of the invention:

[0102] Along the normal direction For each boundary point Expand the boundary points. Its position is determined by the following formula:

[0103]

[0104] in, The extended distance parameter is used to suppress noise while conforming to local curvature; this forms a closed sequence of extended control points { }

[0105] Periodic cubic spline boundary modeling provided in this embodiment of the invention:

[0106] Based on the extended control point sequence, the spline parameters are calculated using the centripetal parameterization method (Equation 2); after calculating the cumulative parameters, all Relative to total length Normalized to [0,1] (Equation 3); the periodic cubic spline curve is constructed based on chord length parameterization (Equation 4).

[0107]

[0108]

[0109]

[0110] in , , Indicate control points The second derivative at that point, ;

[0111] In each parameter range [ Within, the spline curve passes through the second derivative term. and Constraints, on and Three interpolations are performed between the points to ensure the second-order continuity of the curve across the entire boundary. (Continuous); to satisfy the periodic constraint, it is necessary to ensure , Second derivative coefficients It is obtained by solving the following system of periodic tridiagonal linear equations (Equation 5);

[0112]

[0113] The tridiagonal coefficients are defined as follows: , , Under periodic boundary conditions, subscripts are processed in a cyclic manner, i.e. , , The resulting cyclic tridiagonal matrix contains non-zero terms at the first and last positions to enforce the condition. The periodic constraints ensure that the spline curve remains closed at the boundary. Continuity;

[0114] Solving this system of linear equations will yield all the results. And substitute into formula (4) to construct a complete periodic cubic spline curve.

[0115] The boundary sampling and simulated ground point generation provided in this embodiment of the invention:

[0116] Along the periodic cubic spline curve at fixed arc length intervals Uniform sampling is performed to generate boundary sampling points; by performing three-dimensional nearest neighbor interpolation on existing seed points on the ground, elevation values ​​are assigned to the sampling points to obtain a set of simulated ground points. Figure 2 );

[0117] Initial TIN construction and iterative encryption:

[0118] The generated simulated ground points and ground seed points are used together as input to construct an initial TIN model, and subsequent TIN iterative encryption processes are performed on this basis.

[0119] like Figure 3 As shown, an embodiment of the present invention provides a TIN-based densification boundary effect suppression system for simulated ground points using periodic cubic splines, comprising:

[0120] The extraction module is used for data boundary extraction;

[0121] The estimation module is used for local tangent and normal estimation based on SVD.

[0122] The control point generation module is used for boundary expansion and simulation control point generation.

[0123] The modeling module is used for periodic cubic spline boundary modeling.

[0124] The ground point generation module is used for boundary sampling and simulated ground point generation;

[0125] The iterative encryption module is used for initial TIN construction and iterative encryption.

[0126] This invention systematically analyzes the geometric degradation mechanism of point cloud boundary regions and constructs an overall suppression mechanism that combines boundary perception, periodic modeling, and structural constraints. This fundamentally solves the problems of elongated triangles, collapse, and topological instability that easily occur at the boundaries of triangular irregular networks.

[0127] In the specific implementation process, the boundary of the point cloud data is first extracted to obtain a sequence of closed boundary points that truly reflect the data coverage. Then, the tangent direction of the boundary points is determined through local neighborhood principal direction analysis, and a consistent normal direction pointing outwards from the data is obtained accordingly. This normal direction does not exist independently but serves as a unified geometric reference for subsequent boundary expansion and spline modeling, ensuring that the expanded control points maintain an overall outward extension trend consistent with the original boundary, avoiding structural deviations caused by traditional random point addition or simple translation.

[0128] Building upon this foundation, cubic splines satisfying periodic constraints are introduced to model the extended control points holistically. By simultaneously applying constraints of consistent function values ​​and consistent second derivatives at the beginning and end of the splines, the boundary curves maintain curvature continuity at closure points, thus forming a complete, smooth, and seamless external constraint boundary. This periodic continuity characteristic cannot be achieved by a single interpolation method but directly determines the stability of the boundary simulation points in terms of geometry and topology.

[0129] Finally, uniform arc-length sampling is performed along the boundary of the periodic spline to generate simulated ground points, which participate in topological constraints during the initial triangular irregular network construction stage. Due to the combined effect of the simulated ground points and the original ground points, the triangular structure of the boundary region is constrained by the external stable boundary in the early stages of network construction, effectively suppressing boundary triangle degradation and providing a reliable structural foundation for subsequent iterative encryption. This overall mechanism is achieved through multi-stage synergy and cannot be obtained through simple splicing or replacement using existing technologies.

[0130] Example 1: Suppression of boundary effects under regular rectangular point cloud boundaries

[0131] In a set of ground laser point cloud data with a regular rectangular outer contour, a sequence of two-dimensional projected boundary points is first extracted, ensuring that the boundary points form a closed loop. For each boundary point, the local tangent direction is determined based on the distribution of its adjacent boundary points, and the normal direction pointing outwards from the tangent direction is determined by the tangent direction. The boundary points are then expanded outwards at a uniform distance along the normal direction to generate an extended control point sequence. Based on the extended control points, a periodic cubic spline boundary is constructed, ensuring that the spline maintains second-order continuity at the closure point. Arc length is uniformly sampled along the spline boundary and elevation information is assigned to generate simulated ground points. These simulated ground points are used together with the original ground seed points to participate in the initial triangular irregular network construction. The results show that the elongated triangle phenomenon at the rectangular boundary is significantly reduced, and the boundary undulations are smoother.

[0132] Example 2: Curvature stability modeling under irregular concave polygon boundaries

[0133] For point cloud data of irregular terrain with obvious concave structures, after extracting the closed boundaries, a tangent estimation method based on neighborhood principal direction analysis is introduced for each boundary point to ensure that the normal direction adaptively adjusts with local geometric changes. Control points generated through normal expansion are denser in high-curvature regions. Periodic cubic splines are constructed using a centripetal parameterization method, correlating parameter distribution with geometric distance, thereby suppressing oscillations in high-curvature regions. Experimental results show that, compared to directly using linear interpolation to expand the boundaries, this scheme generates simulated ground points at concave boundaries that better reflect the actual terrain trend, avoiding structural breaks in the TIN at concave corners.

[0134] Example 3: Robust Boundary Spreading in Scenarios with Strong Noise Interference

[0135] In point cloud data with significant measurement noise, directly using the original boundary points can easily lead to amplified boundary jitter. In this embodiment, by introducing a principal direction constraint of the local tangent direction before the boundary point normal expansion, the normal direction is not affected by individual outliers. After the expanded control points are generated, global modeling using periodic cubic splines ensures that the boundary curve maintains second-order continuity globally. The results show that even in noisy regions, the generated spline boundary remains generally smooth, and the generated simulated ground points form stable constraints in the TIN, effectively suppressing the structural amplification of noise at the boundary.

[0136] Example 4: Assigning Simulated Ground Points under Complex Terrain Elevation Conditions

[0137] In mountainous terrain data with significant slope variations, uniform sampling is performed along the boundary of periodic cubic splines. Elevation information is then assigned to the sampled points using three-dimensional nearest neighbor interpolation, ensuring that the elevation changes of the simulated ground points align with the actual terrain trend. This method avoids interference from abrupt elevation changes at the boundary simulation points on the initial structure of the TIN. The constructed triangular irregular network maintains a continuous slope morphology in the boundary region, reducing the occurrence of edge collapses and anomalous elevation triangles.

[0138] Example 5: Adaptability under different sampling densities

[0139] Experiments were conducted within the same region using both sparse and high-density point clouds. By maintaining the arc-length sampling interval of the periodic cubic spline matching the average point distance of the original point cloud, the number of simulated ground points adaptively varied with the boundary scale. The results show that under sparse point cloud conditions, the proposed method can supplement boundary structure constraints; under high-density point cloud conditions, the method does not introduce redundant constraint points, and the TIN structure of the boundary region remains stable, demonstrating good scale adaptability.

[0140] Example 6: Comparison and Verification with Traditional Aperiodic Spline Methods

[0141] This method is compared with a method using aperiodic cubic splines for boundary modeling. Aperiodic splines exhibit first- or second-order discontinuities at boundary closures, leading to significant structural abrupt changes near the closure points during initial TIN construction. Using periodic cubic splines ensures curvature continuity at boundary closures, resulting in a natural transition of simulated ground points at the closure positions. Comparative results demonstrate that this method exhibits significant advantages in overall boundary smoothness, TIN structural stability, and consistency of subsequent iterations.

[0142] Evidence related to the technical effects obtained by the embodiments of the present invention.

[0143] (1) Experimental data

[0144] Airborne lidar data was collected over a 500 kV and 220 kV transmission corridor along the Dongguan-Boluo border in Guangdong, China, using sensors mounted on a DJI Zenmuse L1 UAV. Flights were conducted at an altitude of 100 meters and a speed of 10 m / s, employing dual-echo scanning, a 240 kHz pulse rate, and a non-repeating flight path. Point clouds were downsampled to 13.97 points / m² for analysis. The dataset comprises 15 segments—13 from 500 kV (samples 01-13) and 2 from 220 kV (samples 14-15)—covering a wide range of terrain features common in the transmission corridor. Instead of categorizing the terrain into predefined classes, we described the samples using qualitative terms to capture their inherent variability, including rugged terrain, steep elevation changes, fragmented ground surfaces, and dense vegetation. These features appeared in different combinations across the 15 samples (e.g., sample 02 is rugged terrain with dramatic elevation changes, while sample 08 is a fragmented surface with dense vegetation), reflecting the natural heterogeneity of the corridor environment. Figure 6 An overview of all transport corridor samples is presented, and the detailed characteristics of each sample are summarized in Table 1.

[0145] Table 1. Characteristics of Transmission Corridor Samples

[0146]

[0147] (2) Experimental Design

[0148] Fifteen power transmission corridor samples were subjected to simulated ground point interpolation based on periodic cubic splines. The evaluation of the experimental results mainly focused on the shape preservation of the buffer boundary and the original point cloud boundary. Regarding parameter settings, and Take 10 m and 5 m respectively.

[0149] Specifically, buffers based on periodic cubic splines better preserve the boundary geometry of the processed data, thereby reducing the generation of elongated triangles and improving the quality of the initial TIN. The shape preservation of the buffer boundary from the original data boundary is evaluated using a two-layer evaluation strategy: a Fourier descriptor is used to represent its overall shape, while a shape context algorithm is used to represent its local details.

[0150] In global shape analysis, periodic cubic splines are fitted to both the original boundary point set and the point set after boundary expansion to obtain a smooth closed contour. Subsequently, each contour is reparameterized by arc length and uniformly sampled within the normalized parameter domain to obtain an isoparametric point sequence suitable for Fourier analysis. Next, a Fast Fourier Transform (FFT) is performed on the resulting ordered sampled point sequence to obtain a normalized low-order Fourier descriptor, where Fk represents the complex Fourier coefficient corresponding to the k-th harmonic component. The amplitude of each descriptor is defined as... , representing the amplitude of the corresponding frequency component. Subsequently, these amplitudes of the two boundary profiles were compared using the Pearson correlation coefficient (r) and the Lin's Concordance Correlation Coefficient (CCC):

[0151]

[0152]

[0153] The superscripts (1) and (2) represent two curves respectively. and This represents the mean and standard deviation. High correlation and consistency indicate strong preservation of the overall shape.

[0154] In local shape analysis, each boundary is first uniformly resampled within the arc-length domain, and a shape context descriptor is calculated at each sampling point. Then, the Hungarian algorithm is used to establish pairwise correspondences between the original and extended boundaries, with chi-square distance as the matching cost. The final average cost is mapped to a similarity score Ssc through an exponential transformation.

[0155]

[0156] A higher Ssc value (closer to 1) indicates stronger local geometric consistency, meaning that the deformation introduced during spline fitting is smaller.

[0157] (1) Experimental Results

[0158] At the global comparison level, the top 20 low-frequency Fourier coefficients were selected ( ), calculate the normalized amplitude And based on this, correlation and consistency analysis were performed (see Figure 7 All samples showed strong consistency (r > 0.96, CCC > 0.95), with samples 01, 08, and 12 reaching a high level of consistency (r = 0.99, CCC = 0.99). Slight biases were observed in individual samples (e.g., sample 14: MaxAD = 0.038; sample 15: r = 0.94, CCC = 0.93), resulting in slightly lower precision for individual samples, but the overall results still validated high global shape preservation.

[0159] At the local comparison level, the shape context-based similarity index Ssc was used for quantitative evaluation (see Table 2). All samples maintained a high Ssc value, ranging from 0.862 to 0.964, with a mean (Avg) of 0.934 and a standard deviation (SD) of 0.029. Specifically, samples 05, 06, 11, and 14 all had Ssc values ​​exceeding 0.958; sample 15 had an Ssc of 0.862... Although relatively low, it still indicates that its local structure has a moderate to acceptable level of consistency.

[0160] These results demonstrate that the buffer boundary maintains good consistency with the original boundary contour shape at both global and local scales, thus verifying the structural reliability of the initial TIN model.

[0161] Table 2 Local shape preservation quantified by shape context

[0162]

[0163] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0164] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for suppressing the boundary effect of TIN (Temporal Intensity Refinement) based on periodic cubic spline simulation of ground points, characterized in that, This method constructs a closed spline boundary that satisfies periodic second-order continuous constraints, and generates simulated ground points based on the closed spline boundary to participate in the construction of a triangular irregular network, thereby suppressing structural distortion in the boundary region during the initial network construction stage. The method includes the following mechanistic steps: Based on the two-dimensional boundary point sequence of point cloud data, a set of extended control point sequences is constructed along the outer direction of the boundary. Using the extended control point sequence as periodic nodes, a parameter sequence is established through centripetal parameterization, and the parameters are normalized. Construct a periodic cubic spline boundary curve in the parameter space that satisfies the same function values ​​at the beginning and end positions and the same second derivative, so that the spline maintains second-order continuity at the boundary closure. Sampling is performed along the boundary of the periodic cubic spline at fixed arc length intervals to generate a set of boundary simulation plane points; Elevation information is assigned to the boundary simulated plane points to form simulated ground points, and the simulated ground points and ground seed points are used together to construct an initial triangular irregular network to weaken the abnormal extension of the triangular structure at the boundary.

2. The method as described in claim 1, characterized in that, The construction of the periodic cubic spline boundary introduces a second derivative constraint at each control point, ensuring that the curve segment between any two adjacent extended control points is continuously controlled by the second derivative, thereby guaranteeing the continuity and consistency of the entire closed boundary at the curvature level.

3. The method as described in claim 1, characterized in that, The periodic constraint is achieved by setting the function values ​​and second derivatives to be the same at the beginning and end of the parameter positions, so that the spline curve does not have abrupt curvature changes at the boundary closure point.

4. A method for generating control points and coordinating parameters for periodic cubic spline boundary modeling, characterized in that, This method achieves stable extrapolation of boundary curvature trends through a collaborative design between boundary point normal expansion and periodic spline parameter construction. The method includes the following mechanism steps: In the closed boundary point sequence, a normal direction pointing outwards from the data is determined for each boundary point; The boundary points are expanded outward along the normal direction to generate a closed sequence of extended control points; Based on the spatial distance between adjacent extended control points, a centripetal parameterization method is used to generate cumulative parameters, and the cumulative parameters are normalized to a unified interval. Periodic cubic splines are constructed based on normalized parameters, so that the extended control points form a continuous closed spline constraint structure in the parameter space.

5. The method as described in claim 4, characterized in that, The normal direction is obtained by performing principal direction analysis on the set of points in the neighborhood of the boundary point to obtain the tangent direction, and then rotating based on the tangent direction to obtain the corresponding normal direction.

6. The method as described in claim 4, characterized in that, The centripetal parameterization method makes the parameter distribution more sensitive to local curvature changes by exponentially accumulating the distance between adjacent control points, thereby avoiding spline oscillations in high curvature regions.

7. A TIN-reinforced boundary effect suppression system based on periodic cubic spline simulation of ground points, characterized in that, The system includes: The control point generation module is used to generate a closed extended control point sequence in the direction outside the boundary points; The spline modeling module is used to construct a periodic cubic spline boundary that satisfies a periodic second-order continuous constraint based on the extended control point sequence. A boundary sampling module is used to sample the arc length along the boundary of the periodic cubic spline and generate boundary simulation plane points; The elevation assignment module is used to generate corresponding elevation information for the boundary simulation plane points; The TIN construction module is used to involve the simulated ground points and ground seed points in the initial construction and subsequent encryption of the triangular irregular network.

8. The system as described in claim 7, characterized in that, The spline modeling module includes a periodic constraint unit, which is used to enforce the constraint relationship of consistent function values ​​and consistent second derivatives at the first and last nodes of the spline.

9. The system as described in claim 7, characterized in that, The boundary sampling module performs uniform sampling of the spline boundary at fixed arc length intervals to ensure the consistency of the spatial distribution of simulated ground points.

10. The system as described in claim 7, characterized in that, The TIN construction module introduces the simulated ground points during the initial network construction phase, so that the triangular structure of the boundary region forms a stable constraint before iterative densification, thereby reducing the impact of boundary effects on the overall terrain modeling results.

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