Step terrain segmentation method for enhancing L0 gradient minimization

Abstract

The invention relates to the technical field of three-dimensional point cloud segmentation and terrain feature extraction, and discloses a step terrain segmentation method for enhancing L0 gradient minimization, which comprises the following steps of: calculating point cloud features based on iterative principal component analysis: constructing a dynamic weight distribution mechanism by introducing a robust M estimator; direction self-adaptive neighborhood optimization is carried out on the slope and panel transition area of the original point cloud, the continuity of the normal vector of the slope area is enhanced, and the geometric difference of the transition area is highlighted; multi-scale super voxel segmentation: adopting a normalized spatial metric segmentation method, generating super voxel units by using a distance, normal vector and perpendicularity weighted normalization mechanism, performing planar and non-planar classification on super voxels in combination with a multi-scale strategy, and performing recursive segmentation on non-planar super voxels at a smaller resolution; performing curved surface segmentation based on L0 gradient minimization and global energy optimization; according to the method, the definition of the segmentation boundary and the completeness of slope structure extraction can be remarkably improved, and the slope and the disc table can be accurately distinguished by using the vertical characteristics.

Description

Technical Field

[0001] This invention relates to the field of 3D point cloud segmentation and terrain feature extraction technology, specifically to a stepped terrain segmentation method that enhances L0 gradient minimization. Background Technology

[0002] Stepped terrain is a complex three-dimensional structure composed of multiple horizontal platforms, sloping slopes, and transition zones. Accurate segmentation and step line extraction are core aspects of digital modeling, intelligent mining, and safety monitoring of stepped terrain. With the development of technologies such as LiDAR and UAV mapping, massive amounts of open-pit mine cloud data can be acquired. However, existing technologies still face the following key challenges when processing such data: 1. Insufficient accuracy of normal vector estimation: Normal vectors are the core geometric features for point cloud segmentation, but in open-pit mine transition areas (such as the junction of slopes and platforms), there are problems such as feature ambiguity, noise interference (such as gravel and vegetation points), and scale sensitivity. Traditional principal component analysis (PCA) uses fixed neighborhoods and equal weighting, which can easily lead to smoothing of normal vectors due to excessively large neighborhoods (weakening geometric differences) or cause orientation estimation bias due to excessively small neighborhoods (especially in sharp feature areas), failing to provide a reliable geometric feature basis for subsequent segmentation.

[0003] 2. Blurred Supervoxel Segmentation Boundaries: To handle large-scale point clouds, supervoxel segmentation technology reduces computational complexity by clustering similar points into units. However, existing methods (such as those based on a single scale or considering only distance / normal vector metrics) are prone to blurring of supervoxel boundaries in regions with gentle transitions in normal vectors (such as gently sloping surfaces), leading to the loss of key terrain details in subsequent segmentation. At the same time, multi-scale strategies have not been designed for the "mixed planar and non-planar" characteristics of open-pit mines, making it difficult to balance segmentation efficiency and detail preservation.

[0004] 3. Terrain segmentation is prone to structural fragmentation: Existing point cloud segmentation methods (such as region-based growth and curvature clustering) mostly rely on local geometric features (such as curvature). However, curvature is sensitive to noise and can easily lead to over-segmentation of local areas in complex stepped terrain, causing the complete slope or platform structure to be broken into multiple discontinuous sub-regions (i.e., "fragmentation"). Furthermore, it does not make full use of the vertical feature differences of "steep slopes and gentle platforms" in natural stepped terrain such as open-pit mines, resulting in mis-fusion or mis-segmentation of slopes and platforms.

[0005] 4. Insufficient Completeness and Accuracy of Step Line Extraction: The step line is the boundary between the slope and the platform, and its extraction quality directly affects the planning and stability monitoring. Traditional methods (such as edge detection-based and B-spline fitting) have the following drawbacks: First, the extraction of boundary candidate points is greatly affected by noise, easily introducing false points; second, the candidate point sorting does not integrate distance and angle features, resulting in poor sequence coherence; third, fitting methods (such as single-segment B-splines) are difficult to adapt to areas with abrupt curvature changes, leading to broken step lines and insufficient closure.

[0006] Therefore, it is now necessary to provide a new method for segmenting stepped terrain. Summary of the Invention

[0007] The present invention aims to provide a stepped terrain segmentation method that enhances L0 gradient minimization, so as to achieve accurate and continuous segmentation of stepped terrain.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: Basic Scheme: A stepped terrain segmentation method that enhances L0 gradient minimization, characterized by the following steps: Step 1, Point cloud feature calculation based on iterative principal component analysis: By introducing a robust M estimator to construct a dynamic weight allocation mechanism, the slope and platform transition area of ​​the original point cloud is optimized by orientation-adaptive neighborhood optimization. The goal of the M-estimator is to minimize the weighted residual generalized function:

[0009] in Represents the residual of the i-th sample. It is a robust kernel function with saturation properties; In each iteration, the parameters are first estimated based on the current parameters. Calculate residuals And the weights are dynamically updated through a weighting function: ; The IPCA normal vector estimation algorithm constructs a robust optimization iterative framework, achieving robust handling of sharp features and noise through dynamic weight adjustment and geometric constraints; given the point to be estimated... and its neighborhood point set The algorithm first defines the direction based on the normal vector. The residual function: , And a Geman-McClure type M estimator is introduced to construct the weight function: , scaling factor The dynamic threshold for outlier detection is controlled; when the residual is much larger than... When the residual is small, the weight approaches 0, automatically eliminating outliers; when the residual is small, the weight approaches 1, preserving geometric features. Step 2, Multi-scale Supervoxel Segmentation: A normalized spatial metric segmentation method is adopted, which generates supervoxel units by using a weighted normalization mechanism of distance, normal vector and perpendicularity. The supervoxels are classified as planar and non-planar by combining a multi-scale strategy. Non-planar supervoxels are recursively segmented at a smaller resolution. Among them, normalized spatial metric segmentation: First, the spatial metric of each point in the point cloud is calculated through local neighborhood information to ensure that similar points are clustered in the same supervoxel; , and Used to assess the distance between points , , and yes , and Normalized weights, vertical angular distance Euclidean distance is used to describe the elevation continuity between points. Used to represent the spatial similarity between points in coordinate space, and the similarity of normal vector directions. Used to merge coplanar points: , , and It's about verticality. and It is a spatial vector. and yes , The normal vector; Among them, the generation and classification of multi-scale hypervoxels: The original point cloud is first segmented into parts with an initial resolution of [resolution value missing]. The supervoxel set is then divided into two types: planar supervoxel sets and non-planar supervoxel sets. The supervoxels in the non-planar supervoxel sets are then further subdivided into smaller scales. ), and further classify these into planar and non-planar hypervoxels; repeat the above steps until all points are assigned to planar hypervoxels or the current resolution. Less than Non-planar hypervoxels; all the partitioned hypervoxels of a stepped terrain are grouped into a hypervoxel set. When the supervoxel set The included hypervoxels Covariance matrix generated according to multi-scale partitioning for: , in It is a supervoxel The center of mass, It belongs to a single supervoxel All point clouds, Representative supervoxel set All supervoxes The quantity, thus enabling us to obtain eigenvalues , respectively , and Calculating hypervoxels Linearity, flatness, and divergence; Step 3, Surface segmentation based on L0 gradient minimization and global energy optimization: based on the supervoxel set obtained in Step 2. A voxel scatter hybrid adjacency graph model is constructed. The number of non-zero gradients between adjacent vertices is controlled by the L0 gradient minimization algorithm, and vertical constraints are introduced to suppress the erroneous fusion of platforms and slopes. Then, the surface segmentation results are refined by global energy optimization to avoid structural fragmentation. Before performing segmentation, a graph representing the voxel adjacency structure needs to be created first; the spatial adjacency relationships of supervoxel units are used to establish the topological relationships between supervoxel nodes in the graph model; and the topological relationships between the nodes are defined in the graph model. Sum of edges Basic diagram of composition Above, each node Represents a voxel unit, each edge This represents the spatial relationship between two adjacent nodes, i and j. Represents the edges between adjacent nodes Weights; using Voronoi adjacency to connect the point set with the graph The nodes in the graph are connected to form an adjacency graph that combines voxels and points. .

[0010] Partition the adjacency graph using the L0 gradient minimization algorithm. To obtain the initial segmentation results, the energy function that needs to be minimized is expressed by the formula: , in It is the total energy of the graph model, representing the degree of matching between the segmentation result and the true value; It is the set of reconstructed normal vectors; It is the number of voxel units; It is the first The neighborhood set of a voxel unit; This is used to guide the output normal vector to be as close to the input as possible; Used to constrain sparsity in a local sense, it guides the normal vector of each point to approach its neighboring normal vectors; The number of split faces is used to encourage the merging of adjacent faces; regularization parameter. Used to balance the effects of the two items.

[0011] Based on the initial segmentation, a global energy optimization method is introduced to relabel surfaces with the same geometric features onto a certain set of surfaces. The global energy function is: , Among them, the super-body surface to be optimized The segmented adjacent segment graph is , C Represents the set of nodes in a segment graph. Indicates the need for optimization of the superbody surface. Adjacent edges between adjacent faces for Features of adjacent surfaces in a segment diagram; Used to measure the similarity of features between segments; Used to penalize inconsistencies in the feature structures between adjacent faces; Represents the weights of the graph; This represents the weighting parameter that balances the two.

[0012] Beneficial effects: In existing technologies, the transition region features are blurred, noise interference is large, and the terrain scale is complex in the segmentation of stepped terrain and the extraction of step lines. This leads to unclear segmentation boundaries, fragmented structure, and insufficient accuracy in the extraction of step lines, and the computational complexity is difficult to control.

[0013] This invention enhances the continuity of normal vectors in slope areas and highlights the geometric differences in transition regions by using point cloud feature calculation based on iterative principal component analysis (IPCA), multi-scale supervoxel segmentation, and energy-optimized stepped terrain segmentation. The dynamic weighting mechanism and iterative scaling strategy of IPCA enhance the robustness of normal vector estimation to noise and cross-surface points. Especially at the junction of slope and platform, the continuity and accuracy of normal vector direction are better than traditional PCA, providing a more reliable geometric basis for subsequent segmentation.

[0014] The robust M-estimator reduces the impact of outliers through a nonlinear loss function, and the iterative reweighting framework ensures stable convergence in noisy environments, further improving the accuracy of normal vector estimation and avoiding orientation deviations caused by local point cloud sparsity or noise. The weighting mechanism of the normalized spatial metric unifies the scale of distance, normal vector, and perpendicularity features, enabling more accurate clustering of similar points in supervoxel units. This solves the boundary blurring problem in regions with smooth normal vector transitions, and its supervoxel boundary preservation capability is superior to single-feature metric methods. The multi-scale supervoxel classification criteria (flatness, orientation difference, distance residual) are specifically adapted to complex stepped terrain, performing fine segmentation only on non-planar regions. This controls computational load while preserving detail, avoiding redundant overhead in global high-resolution segmentation. L0 gradient minimization achieves efficient segmentation by controlling the number of non-zero gradients. The L0 norm constraint of the energy function captures boundaries more accurately than traditional local sparsity constraints, reducing misfusion in transition regions.

[0015] The L0 gradient minimization algorithm controls the number of non-zero gradients between adjacent vertices in the graph model. Point cloud segmentation is achieved through an energy function that includes a normal vector matching term, local sparsity constraints, and adjustment of the number of segmentation faces. This approach can efficiently and accurately complete the segmentation task: the normal vector matching term ensures that the segmentation result fits the original geometric features, the local sparsity constraints promote the consistency of normal vectors between adjacent points to maintain the continuity of local regions, and the L0 norm controls non-zero gradients to reduce redundant boundaries and avoid over-segmentation. At the same time, by balancing the effects of various factors through regularization parameters, adjacent faces with similar features are preferentially fused, which significantly improves the segmentation efficiency and boundary accuracy. Especially in the slope and platform transition areas of stepped terrain such as open-pit mines, it can preserve key geometric details and avoid segmentation chaos caused by noise or complex terrain, laying a high-quality foundation for subsequent surface refinement.

[0016] Vertical constraints utilize the inherent differences between slopes and platforms to physically suppress erroneous fusion, resolving segmentation errors caused by smooth transitions in normal vectors in areas such as slope bottoms and ridges, thus improving the accuracy of distinguishing between slopes and platforms.

[0017] Global energy optimization combined with vertical feature constraints avoids the local fragmentation problem that is easily caused by existing curvature constraint methods, making the segmented slope and platform structures more complete, especially suitable for irregular curved surface areas.

[0018] This invention achieves accurate segmentation of stepped terrain and provides complete and high-precision preparation of the target to be extracted while controlling computational complexity.

[0019] This invention addresses the issues of blurred boundaries, fragmented structures, and excessive computational complexity in stepped terrain segmentation through a collaborative design involving IPCA normal vector estimation, normalized spatial metric supervoxel segmentation, L0 gradient minimization, and global energy optimization. Compared to existing technologies, it significantly improves the clarity of segmentation boundaries and the completeness of boundary structure extraction while controlling computational load. Furthermore, it accurately distinguishes between slopes and terraces using vertical features, making it suitable for complex stepped terrains with vertical characteristics, such as open-pit mines, flood control embankments, and agricultural terraces.

[0020] Preferably, in step one, the IPCA normal vector estimation algorithm constructs a robust optimization iterative framework, achieving robust handling of sharp features and noise through dynamic weight adjustment and geometric constraints. Specific steps include: The first step is to estimate the initial normal vector using classical PCA. And with the largest residual square in the neighborhood Initialize scale parameters; The second step is iterative weighted PCA optimization. In each iteration, an M-estimater is introduced to construct a robust optimization framework, and a weight function based on the Geman-McClure kernel function is established. This function is used to solve for the normal vector direction through weighted PCA after fixing the weights, and the least squares objective function is then used. , By alternately performing weight updates and weighted PCA solutions, adaptive elimination of outliers and gradual optimization of normal vectors are achieved. The third step involves dynamically adjusting the scaling factor by gradually decreasing it by 1.01 increments. until the preset threshold is reached. This strategy retains more neighborhood information in the early stages of iteration and gradually focuses on interior points in the later stages, balancing noise suppression and geometric detail preservation. The fourth step is reference point calibration. To address the reference point offset problem caused by noise, dynamic reference point calibration is introduced.

[0021] In each iteration, along the current normal vector The direction is dynamically adjusted to the reference point position, and repeated optimization is performed to offset the reference point offset caused by noise and improve the stability of the normal vector; In IPCA normal vector estimation, the dynamic weighting mechanism of the M-estimator is embedded in the calculation process of the covariance matrix; by weighting... Correlation with residuals of neighboring points can automatically reduce the contribution of noise points and outliers across edges, making the covariance matrix more accurately reflect the geometric characteristics of the target's local surface.

[0022] Beneficial Effects: This framework, through dynamic weight adjustment and geometric constraints, effectively addresses the challenges of normal vector estimation in stepped terrains such as open-pit mines, particularly in areas with sharp features (e.g., the junction of slopes and platforms) and noise interference (e.g., gravel and vegetation points). On one hand, the dynamic weighting mechanism based on the M-estimator (e.g., the Geman-McClure kernel function) adaptively distinguishes between effective and outlier points within the neighborhood, assigning low weights to noise and cross-surface points to suppress their influence. Simultaneously, it enhances the contribution of geometric feature regions, making the direction estimation of the normal vector more stable in sharp feature areas, avoiding the direction smoothing or deviation caused by fixed neighborhoods and equal weighting in traditional PCA. On the other hand, geometric constraints (e.g., dynamic reference point correction and dual initialization mechanisms) can offset reference point offsets caused by noise, resolving estimation biases caused by uneven neighborhood density, and ensuring accurate normal vector directions are obtained even in complex regions with sparse point clouds and non-uniform sampling.

[0023] The normal vectors output by this framework can preserve the sharp geometric details at the slope junction and resist noise interference, providing a high-precision geometric feature foundation for subsequent super-voxel segmentation, surface segmentation and step line extraction. In particular, it is significantly better than traditional methods in terms of feature discrimination ability in transition regions.

[0024] Preferably, in step two, according to , and The range of values, using , and Normalization is performed; the weights are set as follows, where R is the resolution of the current segmented supervoxel: , Minimum distance between points The median will be used for initialization. This allows for faster iteration.

[0025] Beneficial effects: By specifically limiting the resolution of segmented supervoxels, it is possible to accelerate iteration while ensuring accuracy, thus achieving a balance between computational load and computational accuracy.

[0026] Preferably, in step two, the supervoxel Significant features include: linearity flatness divergence , , For a supervoxel containing some non-planar points, based on the characteristic that the points in such a supervoxel have directional differences, the standard deviation of the angle between the normal of the supervoxel and the normal of the points inside the supervoxel is calculated using the following formula:

[0027] yes Interior point The normal vector, yes The normal vector, Represents supervoxel The number of midpoint clouds, It is the difference in the direction of the hypervoxons.

[0028] Beneficial effects: For supervoxels containing non-planar points, constraints are imposed based on the directional differences of the points, which can optimize the supervoxel segmentation logic through geometric feature constraints. This ensures the directional consistency of points within a supervoxel, avoids erroneous merging caused by the complexity of point clouds in non-planar regions, and prevents supervoxels from becoming "too coarse." It also preserves sharp features and detailed information, preventing key geometric features from being blurred. At the same time, it enhances the robustness and accuracy of subsequent normal vector estimation, surface reconstruction, and other processing, improves adaptability to complex shapes, and provides a more reliable basic unit for the entire point cloud segmentation and feature extraction process.

[0029] Preferably, measuring supervoxel points Distance to the fitted plane The residuals are calculated by averaging the distances to all points. average : , Combining planarity, directional differences, and distance residuals, the criteria for supervoxel plane subdivision can be: , The units of the voxel segmentation are divided into two groups: planar and non-planar. Points in the non-planar region are further segmented at a lower resolution and then further divided into planar or non-planar. This process is repeated until all supervoxels are classified as planar or the resolution is less than a threshold.

[0030] Beneficial Effects: By calculating the average distance residual from the supervoxel point to the fitted plane and constructing a supervoxel plane subdivision standard in conjunction with planarity and directional differences, a multi-scale recursive segmentation strategy is adopted (non-planar regions are iteratively segmented at a smaller resolution until the conditions are met). This approach can accurately distinguish between planar and non-planar supervoxels, ensuring the integrity of planar supervoxels to reduce redundant calculations while preserving complex terrain details through fine segmentation of non-planar regions, effectively balancing segmentation accuracy and computational efficiency. This method avoids misclassification caused by a single standard, making the supervoxel units more closely resemble the real geometric structure of stepped terrain such as open-pit mines. It provides high-quality basic units for subsequent surface segmentation and step line extraction, especially in complex areas such as slopes and platform transition zones, significantly improving the accuracy of segmentation boundaries and the integrity of the structure.

[0031] Preferably, in step three, each supervoxel unit and point corresponds to a node in the graph model. The partitioning of the graph model nodes corresponds to the fusion of large supervoxels and small segments. The graph is partitioned starting from well-structured voxel units, not randomly selected. First, the connectivity fraction of the supervoxels is calculated. Then, based on the connectivity fraction Perform heuristic sorting on the processing groups: , in, The number of points in a voxel unit. For the connectivity fraction of a single point, based on the local connectivity fraction of a voxel. The size of the voxel group to be processed is used for heuristic sorting; voxel units with lower connectivity fractions will be preferentially selected for processing, and voxel units located at the intersection of two faces will have a lower processing order.

[0032] Beneficial effects: In step three, supervoxel units and points are used as nodes in the graph model. The processing groups are heuristically sorted by connectivity fraction (prioritizing voxel units with low connectivity fraction and delaying the processing of units at the interface). The fusion of large supervoxels and small segments is achieved in the segmentation process, which can significantly improve the efficiency and accuracy of segmentation: Prioritizing the processing of well-structured interior point regions can quickly build the initial segmentation framework and reduce the interference of boundary regions on early segmentation; delaying the processing of interface units allows them to more accurately match the features of adjacent surfaces and avoid misfusion; at the same time, the coordinated operation of node division and fusion takes into account the processing efficiency of large-scale point clouds and the preservation of local details, so that the segmentation results not only conform to the overall geometric structure, but also accurately capture the boundary features at the junction of slope and platform, laying a reliable foundation for subsequent energy optimization and step line extraction.

[0033] Preferably, adjacent elements are iteratively merged into a group using a defined fusion criterion to minimize the number of global non-zero gradients; the contribution of each pair of adjacent elements to the total energy E in the figure can be expressed as: , Taking the merging of voxel units as an example, in the formula , This represents the normal vector between two adjacent voxel units; combined with and The solution involves minimizing e in two cases; the fusion criterion is: , Two voxel units , The vertical distance is calculated using the formula: , The fusion criterion after substituting the vertical constraint is: , in The number of points to merge. This represents the updated normal vector after merging nodes. This represents the increase in the total energy of the energy function after merging nodes. The preset vertical distance threshold is set when the energy increment after merging adjacent regions is negative and the vertical distance is less than the threshold. The merger will be accepted at that time.

[0034] Beneficial effects: By formulating fusion criteria to iteratively merge adjacent elements to minimize the number of global non-zero gradients, calculating energy contributions based on the difference in normal vectors of adjacent voxels, and introducing vertical constraints (using the energy increment after merging and the verticality distance threshold as merging conditions), the accuracy and rationality of segmentation can be significantly improved. On the one hand, the calculation of energy contributions based on the difference in normal vectors and the goal of minimizing non-zero gradients ensure that the fusion of adjacent nodes conforms to the consistency of geometric features, reducing erroneous merging. On the other hand, the vertical constraints utilize the inherent feature differences between slopes and platforms in open-pit mines to restrict unreasonable fusion from a physical perspective, avoiding erroneous merging in the boundary areas such as slope bottoms and ridges due to unstable normal vectors. At the same time, the energy increment judgment ensures the global optimality of the segmentation results after fusion, ultimately making the segmented surface retain both local geometric details and conform to the overall structural laws of stepped terrain such as open-pit mines, providing a more reliable foundation for subsequent step line extraction.

[0035] Preferably, spatially adjacent regions with approximately vertical characteristics and high connectivity scores are merged; to determine whether to merge regions, the vertical characteristics and connectivity scores of the two regions are defined. : , Post-processing for surface refinement allows segmented surfaces to be aggregated into a complete surface.

[0036] Beneficial effects: Given a standard voxel adjacency graph G, and a voxel-point mixed adjacency graph G, then... Through all processes of this invention After processing, through the merging operation of the L0 gradient, here... There are no scattered points within. Based on the initial segmentation, a global energy optimization method (combining an energy function that penalizes feature similarity and structural consistency) is used, along with a region merging criterion defined based on vertical features and connectivity scores, to refine and aggregate the piecewise surfaces. This effectively solves the surface fragmentation problem in the initial segmentation: the global energy function balances inter-segment feature similarity and structural consistency, ensuring that the merged regions have inherent geometric uniformity; while the merging criterion based on vertical features and connectivity scores fully utilizes the inherent vertical properties and spatial connectivity patterns of slopes and platforms in open-pit mine terrain, enabling accurate aggregation of surfaces with similar structures. This post-processing preserves local geometric details while ensuring the integrity and coherence of the overall structure. Especially in complex stepped terrain, it significantly improves the global consistency of surface segmentation, providing a more complete and reliable geometric foundation for subsequent step line extraction.

[0037] The advantages of this invention are: 1. Phased iterative segmentation to balance efficiency and accuracy: By adopting the strategy of "global coarse segmentation → fine iterative segmentation of non-planar regions", high-resolution processing is only performed on key regions, achieving a balance between efficiency and accuracy, and improving the boundary recall score by 18.3%.

[0038] 2. Precise utilization of vertical features: From L0 gradient minimization of region fusion to global energy optimization of surface refinement, vertical feature constraints are embedded throughout the process, rather than just used as classification thresholds. This improves the segmentation accuracy of slopes and platforms by 15.5% compared to the Global-L0 method, solving the problem of insufficient utilization of vertical features in existing methods.

[0039] 3. L0 gradient and global optimization avoid structural fragmentation: Compared with existing curvature-based methods, L0 gradient minimization reduces excessive segmentation through non-zero gradient control. Combined with global energy optimization with vertical feature constraints, the structural accuracy exceeds 86.7%, and the continuous morphology of the slope and platform is fully preserved.

[0040] 4. Optimization of the entire process for step line extraction: The combination of 3D concave hull edge detection, weighted sorting and NURBS fitting solves the problems of step line breakage and insufficient closure in traditional methods. The extraction accuracy (positional deviation ≤0.35m) and completeness (92%) are both superior to existing technologies.

[0041] The non-obviousness of the comparison document is as follows: 1. Innovation in Normal Vector Estimation: Comparative documents only mention "point-by-point calculation of the normal vector," without disclosing the iterative weighting mechanism of IPCA and the dynamic weight allocation of the M-estimator. This invention enhances the continuity of the normal vector through IPCA, representing a substantial improvement over traditional PCA, rather than a simple parameter adjustment.

[0042] 2. The essential difference between the segmentation algorithms: The comparison file uses energy optimization with "gradient descent + local sparsity constraint", while the L0 gradient minimization of this invention controls non-zero gradients through the L0 norm. They are different in both mathematical principle and effect - the L0 norm more directly suppresses redundant boundaries, while the local sparsity constraint of the comparison file is prone to over-smoothing. The two do not have an obvious substitution relationship.

[0043] 3. In-depth application of vertical features: The comparative documents only use verticality as the screening threshold for the candidate set of slopes, while this invention embeds vertical features into the L0 gradient fusion criterion and global energy optimization to form a full-process control of "local constraint → global optimization". This systematic utilization of vertical features is not disclosed in the comparative documents and cannot be derived from its "regular constraints".

[0044] In summary, this invention solves the problems of blurred boundaries and fragmented structures that the comparison documents failed to address through innovative algorithm combination and feature utilization. Its technical solution is not a simple superposition of existing technologies and has significant non-obviousness. Attached Figure Description

[0045] Figure 1 This is the 2D projection of the normal vector on the intersecting surface in this invention.

[0046] Figure 2 This is a comparison diagram of multi-scale supervoxel generation examples in this invention.

[0047] Figure 3 This is a schematic diagram of the slope structure features in this invention.

[0048] Figure 4 This is a flowchart of the method of the present invention. Detailed Implementation

[0049] The following detailed description illustrates the specific implementation method: This invention belongs to the interdisciplinary technical field of surveying and mapping science and technology, computer vision and mining engineering. Specifically, it involves three-dimensional point cloud segmentation and terrain feature extraction technology, which is particularly suitable for segmentation of terraced terrain such as open-pit mines, flood control dikes and agricultural terraces, and slope structure identification. It can be applied to scenarios such as digital modeling of terraced terrain, slope stability monitoring, intelligent mining planning and safe production decision-making.

[0050] This invention improves the clarity of segmentation boundaries and ensures structural integrity while controlling computational complexity by optimizing normal vector estimation, designing multi-scale supervoxel segmentation, introducing energy optimization with vertical feature constraints, and employing a precise step line extraction strategy. This provides a prerequisite for improving the accuracy of step line extraction and recognition in the future.

[0051] like Figure 4 As shown, the stepped terrain segmentation method of the present invention, which enhances L0 gradient minimization, includes the following steps: (1) Point cloud feature calculation based on iterative principal component analysis (IPCA): By introducing a robust M-estimator to construct a dynamic weight allocation mechanism, the slope and platform transition area of ​​the original point cloud is optimized by direction-adaptive neighborhood optimization, which enhances the continuity of the normal vector of the slope area and highlights the geometric differences of the transition area. The IPCA dynamically adjusts the weight of each point in the neighborhood through the kernel function to suppress noise and cross-surface points, while enhancing the contribution of the geometric feature area. During the iteration process, the scaling factor is gradually reduced to focus on the in-point area. The robust M-estimator adopts a Geman-McClure type loss function to map the residuals to weights, so that large residuals correspond to low weights. The stable estimation of the normal vector is achieved through the iterative reweighted least squares framework.

[0052] (2) Multi-scale supervoxel segmentation: A normalized spatial metric segmentation method is adopted, which generates supervoxel units using a weighted normalization mechanism of distance, normal vector, and perpendicularity. A multi-scale strategy is combined to classify supervoxels as planar or non-planar, with non-planar supervoxels recursively segmented at a lower resolution. The metric for the normalized spatial metric segmentation method is:

[0053] in, For Euclidean distance For the similarity of normal vector directions, Vertical distance , and For normalized weights.

[0054] The criteria for classifying hypervoxel planes include flatness, difference in normal vector direction, and residual distance from the point to the fitted plane. When a hypervoxel meets the following conditions, it is determined to be a planar hypervoxel: flatness threshold ≥ 0.8, direction difference ≤ 15°, and residual distance ≤ 0.3m.

[0055] (3) Surface segmentation based on L0 gradient minimization and global energy optimization: Construct a voxel scatter point hybrid adjacency graph model, control the number of non-zero gradients of adjacent vertices through the L0 gradient minimization algorithm, introduce vertical constraints to suppress the erroneous fusion of platforms and slopes; and refine the surface segmentation results through global energy optimization to avoid structural fragmentation. The energy function of the L0 gradient minimization algorithm is: , in, For the input normal vector, To reconstruct the normal vector, For balancing parameters, It is the L0 norm.

[0056] The vertical constraint is controlled by a verticality distance threshold. When the verticality distance between two supervoxels exceeds 30°, merging is prohibited to avoid erroneous fusion of the platform and the slope.

[0057] The global energy optimization is solved using the L0-cut pursuit algorithm. The energy function introduces vertical feature similarity constraints, prioritizing the fusion of adjacent regions with consistent vertical features.

[0058] Specifically, 1. Hypervoxel segmentation based on spatial metrics: For example, in the segmentation and extraction of stepped terrain such as open-pit mines, flood control dikes, and agricultural terraces, there are problems such as unclear features, large noise interference, and complex terrain scale variations in the transition areas between slopes and platforms. This invention employs a point cloud feature calculation method based on Iterative Principal Component Analysis (IPCA). Through directional adaptive neighborhood optimization, it enhances the continuity of normal vectors in slope areas and highlights the geometric differences in transition areas, thereby obtaining more detailed and accurate normal vector directions at slope boundaries. Simultaneously, to quickly obtain accurate segmentation models from large-scale point cloud data in open-pit mine scenes, this invention uses multi-scale supervoxel segmentation technology to segment the open-pit mine point cloud into supervoxel units. To further address the problem of blurred supervoxel unit boundaries in areas with smooth transitions in normal vectors in open-pit mine scenes, this invention designs a normalized spatial metric segmentation method. Utilizing a weighted normalization mechanism based on distance, normal vector, and verticality, it better reduces the distance between boundary points and supervoxel centers, generating supervoxel units that retain the boundary features of the point cloud. This paper proposes a multi-scale supervoxel method to generate voxel structures with appropriate resolution, thereby reducing the number of computational units and mitigating the impact of point cloud density variations and outliers. This chapter will detail the implementation process of the proposed method and its advantages in improving the accuracy of stepped terrain segmentation and the reliability of step line extraction.

[0059] 1.1 Estimation of Normal Vectors in Sharp Boundary Regions As a core parameter representing the three-dimensional geometric features of stepped terrain in open-pit mines, accurate normal vector estimation is fundamental to point cloud segmentation and step line extraction. The accuracy of normal vector calculation directly affects the reliability of key processes such as slope identification, topology reconstruction, and feature line generation. Traditional Principal Component Analysis (PCA) obtains the local geometric principal direction through eigenvalue decomposition of the covariance matrix, but it is susceptible to scale effects in complex transition regions. A larger neighborhood radius leads to smoothing of the normal vector, weakening geometric differences; a smaller neighborhood causes direction estimation bias due to local sparsity of the point cloud and noise interference, especially at the boundary between the step edge and the slope.

[0060] To address the challenges of feature ambiguity, noise interference, and scale sensitivity in the transition area between slopes and platforms, this invention introduces a point cloud feature calculation method based on Iterative Weighted Principal Component Analysis (IPCA). This method constructs a dynamic weight allocation mechanism by introducing a robust M-Estimator, adaptively distinguishing between in-neighbor points and outliers during the iteration process. Unlike traditional fixed-neighborhood PCA, IPCA dynamically adjusts the weights of each point through a kernel function, suppressing noise and cross-surface points while enhancing the contribution of geometric feature regions. Compared to traditional methods, IPCA significantly improves the stability of normal vector direction estimation in sharp feature regions such as the boundary between open-pit mine steps. The iterative weight update mechanism weakens the influence of non-uniform sampling and anisotropy, providing feature representations with significant geometric discriminative power for subsequent supervoxel segmentation.

[0061] 1.1.1 Robust Weight Assignment Based on M Estimator The M-estimater is a robust statistical tool that reduces the impact of outliers on parameter estimation by replacing the squared loss of least squares with a nonlinear loss function. Its core idea is to design a loss function that is insensitive to outliers, thus minimizing the impact of residuals on parameter estimation. (For example, the orthogonal distance from data points to the hyperplane) is mapped to weights, so that large residuals correspond to low weights. The squared loss of the traditional least squares method is replaced with a robust kernel function with saturation properties. This reduces the excessive influence of large residual samples on the objective function. The goal of the M estimator is to minimize the weighted residual functional, as shown in Equation (1-1).

[0062] (1-1) in The kernel function represents the residual of the i-th sample (e.g., the orthogonal distance from the midpoint of the point cloud normal vector estimation to the local plane), while the kernel function represents the residual of the i-th sample. The design dictates the outlier suppression strategy. The M-estimator employs an Iterative Reweighted Least Squares (IRLS) framework, transforming the nonlinear optimization into a series of weighted least squares problems. In each iteration, the current parameter estimates are first... Calculate residuals The weights are dynamically updated through a weight function, as shown in formula (1-2).

[0063] (1-2) Then, the weighted least squares problem is solved as shown in Equation (1-8), and the parameters are updated using numerical methods such as Gauss-Newton or Levenberg-Marquardt. The essence of this process is to iteratively adjust the weights, gradually shrinking the optimization focus from the global data distribution to the interior-dominant region, thereby achieving stable convergence in an environment where noise and outliers coexist.

[0064] (1-3) The IPCA normal vector estimation algorithm constructs a robust optimization iterative framework, achieving robust handling of sharp features and noise through dynamic weight adjustment and geometric constraints. Given the current point to be estimated... and its neighborhood point set The algorithm first defines the direction based on the normal vector. The residual function is shown in Equation (1-4), and a weight function is constructed by introducing a Geman-McClure type M estimator, as shown in Equation (1-5).

[0065] (1-4) (1-5) scaling factor The dynamic threshold for outlier detection is controlled. When the residual is much larger than... When the residual is small (e.g., the neighborhood contains different surface points), the weight approaches 0, automatically excluding outliers; when the residual is small (e.g., in smooth surface areas), the weight approaches 1, preserving geometric features. This mechanism significantly improves the noise resistance of sharp areas at the junction of slopes and platforms.

[0066] 1.1.2 Normal Vector Estimation Based on IPCA Weighted PCA is an extension of traditional PCA. It adjusts the contribution of data points to the covariance matrix through a dynamic weighting mechanism, thereby enhancing the algorithm's robustness to noise and outliers. Traditional PCA assumes all data points have equal importance and obtains the principal component directions through eigenvalue decomposition of the covariance matrix. However, this assumption can lead to estimation bias when faced with noise or outliers. Weighted PCA optimizes the robustness of traditional PCA by introducing a dynamic weighting mechanism, effectively suppressing noise interference and enhancing geometric sensitivity to sharp feature regions. Specifically, the point cloud data is... The weight is The weighted covariance moments are defined as follows: (1-6) in This is the weighted mean. The estimated normal vector. Is The eigenvector associated with the minimum eigenvalue is the local principal direction of the weighted PCA estimate. This corresponds to the optimization function of the least squares minimization solution, which is the normal vector: (1-7) This process is similar to the classic weighted principal component analysis performed by Pauly et al. (2002), through... This is used to modify the PCA reference point (neighborhood centroid). Introducing a suitable robust estimator can reflect the reliability of data points or their local geometric contributions, thereby improving robustness to noise and outliers.

[0067] The IPCA algorithm first extracts the target point and its neighborhood point set, adjusts the covariance contribution of each point through a residual-driven weight function, then constructs a weighted covariance matrix and performs eigenvalue decomposition, finally using the eigenvector corresponding to the smallest eigenvalue as the normal vector. The specific implementation steps are as follows: (1) Initial estimation of normal vector: The initial normal vector is calculated using classical PCA. And with the largest residual square in the neighborhood Initialize the scale parameters.

[0068] (2) Iterative weighted PCA optimization: In each iteration, an M-estimater is introduced to construct a robust optimization framework, and a weight function based on the Geman-McClure kernel function is established, as shown in formula (1-5). This is used to solve for the normal vector direction after fixing the weights, i.e., minimizing the weighted residual sum of squares, as shown in formula (1-7). By alternately performing weight updates and weighted PCA solutions, adaptive elimination of outliers and gradual optimization of the normal vector are achieved.

[0069] (3) Dynamic parameter adjustment, gradually reduce (Scaling factor 1.01 / time), until the preset threshold is reached. This strategy retains more neighborhood information in the early stages of iteration, and gradually focuses on interior points in later stages, balancing noise suppression and geometric detail preservation.

[0070] (4) Reference point correction: To address the reference point offset problem caused by noise, dynamic reference point correction is introduced, as shown in formula (1-8). In each iteration, along the current normal vector... The direction is dynamically adjusted to the reference point position, and repeated optimization is performed to offset the reference point offset caused by noise and improve the stability of the normal vector.

[0071] (1-8) In IPCA normal vector estimation, the dynamic weighting mechanism of the M-estimator is embedded in the calculation process of the covariance matrix. This is achieved by weighting... Associating the residuals with neighboring points (i.e., the distance from a point to the local plane) automatically reduces the contribution of noise points and outliers across edges, allowing the covariance matrix to more accurately reflect the geometric characteristics of the target's local surface. In sharp feature regions of the point cloud, the weights of large residual points are significantly attenuated, thus avoiding the smoothing bias of the normal vector caused by equal weighting in traditional PCA. Figure 1As shown. This data-adaptive weight allocation strategy ensures that the feature vector (i.e., normal vector) corresponding to the smallest extracted feature value retains local geometric details while also being robust to complex noise.

[0072] 1.2 Multiscale Supervoxel Segmentation To quickly obtain accurate segmentation models from large-scale point cloud data of stepped terrain such as open-pit mine scenes, a key step is to perform super-voxel segmentation to reduce the number of computational units and mitigate the impact of point cloud density variations and outliers. Preserving object boundaries as much as possible in the created voxel edges is a major problem that super-voxel segmentation needs to address. The resolution of the voxel structure determines the granularity of fragments or marker points; different resolution voxel structures can describe object boundary details at different levels. This invention designs a normalized spatial metric segmentation method to solve the boundary blurring problem in regions with smooth transitions in the normal vectors of open-pit mine scenes, using a multi-scale super-voxel method to generate voxel structures of appropriate resolution.

[0073] 1.2.1 Normalized Spatial Metric Partition The core objective of normalized spatial metric segmentation is to construct supervoxel units that preserve the boundary features of the point cloud to resist noise interference and reduce computational complexity. The introduction of normalized spatial metrics allows features at different scales to be compared under a unified standard, thereby improving segmentation accuracy. Specifically, the spatial metric of each point in the point cloud is first calculated using local neighborhood information to ensure that similar points are clustered in the same supervoxel. To this end, this invention extends the previously studied supervoxel segmentation method NSSS. However, unlike NSSS, which incorporates the spectral information of the point cloud as the metric function for supervoxel segmentation, this invention employs a normalized spatial metric-based supervoxel segmentation method with a weighted mechanism of distance, normal vector, and perpendicularity to better reduce the distance between boundary points and supervoxel centers, particularly in regions where the normal vector angle changes gently.

[0074] , and Used to assess the distance between points . , and yes , and Normalized weights. Vertical angular distance. Used to describe the elevation continuity between points. Euclidean distance. Used to represent the spatial similarity between points in coordinate space, and the similarity of normal vector directions. Used to merge coplanar points.

[0075] (1-9) (1-10) and It's about verticality. and It is a spatial vector. and yes , The normal vector. This definition is similar to NSSS, VCCS, and TBBS, but differs in that NSSS deals with MPC point cloud data, utilizing SAM to establish spectral similarity of the point cloud and incorporating it into the segmentation metric; VCCS deals with RGB-D point cloud data, evaluating color distances in the CIELab space; and TBBS uses only spatial and normal vector features. To map distance factors from different distance ranges to the same range, according to... , and The range of values, using , and Normalization is performed; the weights are set as follows, where R is the resolution of the current segmented supervoxel.

[0076] (1-11) 1.2.2 Generation and classification of multiscale supervoxels A normalized spatial metric-based supervoxel segmentation method will be used for multi-scale supervoxel generation. Employing adaptive resolution supervoxels ensures that the segmented supervoxels cover the vast majority of planar regions while preserving boundary information at different granularities. The original point cloud is first segmented into segments with an initial resolution of [resolution value missing]. The supervoxel set is then divided into two types: planar supervoxel sets and non-planar supervoxel sets. The supervoxels in the non-planar supervoxel sets are then further subdivided into smaller scales. ), and further classify these into planar and non-planar hypervoxels; repeat the above steps until all points are assigned to planar hypervoxels or the current resolution. Less than Non-planar hypervoxels; all the partitioned hypervoxels of a stepped terrain are grouped into a hypervoxel set. A detailed description of multi-scale supervoxel generation is as follows: The hypervoxel is calculated using formula (1-12). covariance matrix .

[0077] (1-12) in It is a supervoxel The center of mass, It belongs to the category of supervoxels All point clouds, Represents supervoxel The size, so that we can obtain eigenvalues Use them separately , and Calculating hypervoxels Linearity, flatness, and divergence.

[0078] Unlike urban buildings and interior structures, which are primarily planar with strong directional constraints, the Manhattan model, open-pit mine scenes often feature irregular curved surface structures. This invention aims to over-subdivide the stepped terrain point cloud into a greater number of planar voxel units to preserve the boundary information of complex curved surface structures. Referring to planar indices introduced in related research, this invention uses a more stringent subdivision standard to further reduce the curved surface structure to a smaller scale of planar elements.

[0079] supervoxel Significance characteristics: linearity flatness divergence Calculated using the corresponding existing formula.

[0080] (1-13) For supervoxels containing some non-planar points, the resolution of the supervoxels is limited by applying normal vector constraints. Specifically, the constraint is based on the characteristic that the points in these supervoxels have directional differences, and the standard deviation of the angle between the normal of the supervoxel and the normal of the points inside the supervoxel is calculated using formula (1-14).

[0081] (1-14) yes Interior point The normal vector, yes The normal vector, Represents supervoxel Size, It is the difference in the direction of the hypervoxons.

[0082] Since a planar model can be described using the centers of hypervoxels and normal vectors, the residuals of all points can be calculated when fitting the planar model, thus taking into account the inconsistencies between the points and the fitted plane. Specifically, the hypervoxel points are measured. Distance to the fitted plane The residuals are calculated by averaging the distances to all points. As shown in formula (1-15).

[0083] (1-15) Combining planarity, directional differences, and distance residuals, the criteria for subdividing a hypervoxel plane can be expressed as shown in formula (1-16).

[0084] (1-16) Figure 2 Examples representing multi-scale hypervoxel generation and classification. Figure 2 (a) represents the original point cloud. Figure 2 (b) shows the results of multi-scale supervoxel segmentation. The units of the voxel segmentation are divided into two groups: planar and non-planar. Points in non-planar regions are further segmented at a lower resolution and then further divided into planar or non-planar regions. This process is repeated until all supervoxels are classified as planar or the resolution is less than a threshold. In this invention, the centroid of each planar supervoxel represents the entire voxel, while non-planar voxels are broken down into scattered points. Figure 2 (c) shows the basic unit used for subsequent processing.

[0085] This invention addresses the challenges of blurred transition region features, noise interference, and massive terrain data in the segmentation and extraction of stepped terrain in open-pit mines. It proposes a method based on IPCA and multi-scale supervoxel segmentation. First, in the normal vector estimation stage, an M-estimator is introduced through the IPCA algorithm to construct a dynamic weight allocation mechanism, adaptively suppressing noise and outliers across surfaces. Combined with directional adaptive neighborhood optimization, the continuity and geometric differences of the normal vector direction at slope boundaries are enhanced, overcoming the smoothing bias problem of traditional PCA in sharp feature regions. Second, to address the need for efficiency in large-scale point cloud segmentation and boundary preservation, a multi-scale supervoxel segmentation framework is designed: a normalized spatial metric method is used to integrate distance, normal vector, and verticality weighted indices to solve the problem of blurred supervoxel boundaries in gently transitioning regions; a hierarchical recursive segmentation strategy dynamically adjusts the voxel resolution, reducing computational complexity while preserving terrain details. Experimental results show that the proposed method outperforms mainstream algorithms in terms of boundary recall and undersegmentation error. It exhibits stronger boundary capture capabilities in areas with noise interference and abrupt terrain changes, and can accurately express multi-scale structures such as stepped facades, gentle slopes, and gravel transition zones.

[0086] 2. Energy-optimized stepped terrain segmentation: Point cloud segmentation is a key task in the digital processing of stepped terrain with steep slopes, such as in open-pit mines. Its purpose is to divide massive point cloud data acquired through 3D laser scanning or UAV mapping into subsets with different geometric features and semantic attributes. Stepped terrain in open-pit mines is complex and diverse, containing various structures such as horizontal steps, sloping sides, and irregular rock surfaces. Point cloud segmentation can separate these different types of surfaces, enabling refined modeling and analysis of the mine's terrain. The original point cloud segmentation method for stepped terrain mainly consists of two steps: planar segmentation with basemap optimization and structural refinement. First, based on the original point cloud being divided into multi-scale supervoxels, this method uses individual points corresponding to planar and non-planar supervoxels as the basic unit of operation. Second, using the adjacency relationship of voxels in space, a voxel scatter point hybrid adjacency graph model is constructed, and an efficient energy optimization framework is used to segment the graph model to generate an initial planar set. Then, a global energy optimization method is used to fuse and refine the initial planar set to obtain the surface segmentation result.

[0087] 2.1 Point Cloud Segmentation Based on L0 Gradient Minimization In Section 1.2, the original point cloud of the stepped terrain is converted into a supervoxel set and a point set. The supervoxel set CS and the point set extracted from the original point cloud of the stepped terrain according to existing techniques are used together as input for this step, serving as the basis for constructing a voxel-point hybrid adjacency graph model. This invention will use a graph model to describe the neighborhood feature relationships between these units. A voxel-point hybrid adjacency graph is designed to describe the neighborhood relationships of the supervoxel set and the point set, where each supervoxel basic unit is a set of point clouds with similar local primitive features. Therefore, both supervoxel units and points are treated as nodes in the adjacency graph, transforming the point cloud segmentation problem into a graph model construction and partitioning problem. Based on the connectivity propagation mechanism of the adjacency graph and the vertical region fusion strategy, this chapter proposes an improved gradient minimization algorithm to cluster disjoint supervoxel subsets with common local features into an initial segment graph, thereby obtaining the main planar structure of the open-pit mine stepped terrain. In Section 2.2, a global optimization method will be used to obtain the complete slope structure from the initial segment graph.

[0088] 2.1.1 Graph Model Construction and Propagation Mechanism Each supervoxel is a set of point clouds with similar local primitive features. To map supervoxel units and scattered points to an optimal surface regularization constraint model, this invention transforms the point cloud segmentation problem into the construction and partitioning problem of a global graph model. The main advantage of using a graph model is that it can explicitly depict points with a mathematically reasonable structure and infer potential information from known observations. The goal of supervoxel graph optimization is to use a local graph structure to cluster disjoint supervoxel subsets with common local features into segments, where each segment node represents a clustered planar structure.

[0089] Before segmentation, a graph representing the voxel adjacency structure needs to be created. Many methods exist for constructing graphs, each with its own advantages. Voronoi adjacency is suitable for capturing long-distance relationships between supervoxels, but may lead to inaccurate descriptions of adjacency relationships in boundary regions. k-nearest neighbor adjacency avoids links between objects separated by small gaps, but may generate many small connected components. To ensure that local voxels can establish direct relationships with candidate merging objects and to suppress cross-region merging phenomena, this invention uses the spatial adjacency relationships of supervoxel units to establish the topological relationships between supervoxel nodes in the graph model. Defined on a set of nodes... Sum of edges Basic diagram of composition Above, each node Represents a voxel unit, each edge This represents the spatial relationship between two adjacent nodes, i and j. Represents the edges between adjacent nodes Weights; using Voronoi adjacency to connect the point set with the graph The nodes in the graph are connected to form an adjacency graph that combines voxels and points. .

[0090] Each supervoxel unit and point corresponds to a node in the graph model. Point cloud segmentation is essentially the partitioning of graph model nodes, and the segmentation process corresponds to the fusion of large supervoxels and small segments. Unlike the segmentation process in existing technologies, this invention introduces a more robust propagation mechanism, starting the graph segmentation from well-structured voxel units, rather than randomly selecting them. First, the connectivity fraction of the supervoxels is calculated. As shown in formula (2-1), then, based on the connectivity fraction Perform heuristic sorting on the processing groups.

[0091] (2-1) in, The number of points in a voxel unit. For the connectivity fraction of a single point, based on the local connectivity fraction of a voxel. The size of the voxels is used to heuristically sort the groups to be processed. Voxels with lower connectivity fractions are more likely to be inside faces and will be preferentially selected for processing. Voxels located at the intersection of two faces have a lower processing order, ensuring they can be correctly added to the existing face set. This ensures greater efficiency and robustness when using segmentation graph models.

[0092] 2.1.2 L0 Gradient Minimization Algorithm The L0 gradient minimization algorithm is widely used in image denoising and mesh denoising. Due to its performance under high noise and its speed in solving graphical models, this invention uses the L0 gradient minimization algorithm to control the number of non-zero gradients between adjacent vertices in the graphical model, thereby achieving point cloud segmentation. The energy function to be minimized using the L0 gradient minimization algorithm is expressed as shown in equation (2-2).

[0093] (2-2) in It is the total energy of the graph model, representing the degree of matching between the segmentation result and the true value; It is the set of reconstructed normal vectors; It is the number of voxel units; It is the first The neighborhood set of a voxel unit; This is used to guide the output normal vector to be as close to the input as possible; Used to constrain sparsity in a local sense, it guides the normal vector of each point to approach its neighboring normal vectors; The number of split faces is used to encourage the merging of adjacent faces; regularization parameter. Used to balance the effects of the two items.

[0094] The L0 gradient minimization algorithm solves the np-hard problem of equation (2-2) using a region fusion method. It iteratively merges adjacent elements into a group using a defined fusion criterion to minimize the number of global non-zero gradients. The contribution of each pair of adjacent elements to the total energy E in the diagram can be expressed as: (2-3) Taking the merging of voxel units as an example, in the formula , This represents the normal vector between two adjacent voxel units; combined with and The solution involves minimizing e in two cases; the fusion criterion is: (2-4) Two voxel units , The vertical distance is calculated using the formula: (2-5) The fusion criterion after substituting the vertical constraint is: (2-6) in The number of points to merge. This represents the updated normal vector after merging nodes. This represents the increase in the total energy of the energy function after merging nodes. The preset vertical distance threshold is set when the energy increment after merging adjacent regions is negative and the vertical distance is less than the threshold. The merger will be accepted at that time.

[0095] 2.2 Structural Refinement The L0 gradient minimization algorithm yields segmentation results covering almost all potential surfaces. However, this segmentation result can only be considered as the initial segmentation result of the open-pit mine surface. Because the generated adjacent surface normals differ significantly and do not merge, the complete slope surface becomes segmented. Furthermore, the L0 gradient minimization algorithm does not consider the spatial connectivity of the segmentation, dividing some surfaces in the open-pit mine scene into multiple coplanar but unconnected sub-regions. To ensure the structural integrity of the surface, a global energy optimization method is introduced based on the initial segmentation to relabel surfaces with the same geometric features to a certain surface set, thereby overcoming the above problems. The global energy function is shown in Equation (2-7).

[0096] (2-7) Formula (2-7) defines the surface of the superbody to be optimized. Undirected segment graph generated by segmentation with existing technology Superbody surface to be optimized This refers to the surface corresponding to the supervoxel after fusing scatter points and neighborhood feature relationships represented by the graph model, where C represents the set of nodes in the segment graph. Indicates the need for optimization of the superbody surface. Adjacent edges between adjacent faces for Features of adjacent surfaces in a segment diagram; Used to measure the similarity of features between segments; Used to penalize inconsistencies in the feature structures between adjacent faces; Represents the weights of the graph; This represents the weighting parameter that balances the two.

[0097] Surface segmentation based on coordinate information is difficult and inevitably results in fragmented surfaces. Considering the vertical continuity of surfaces in mining areas, regions with approximately perpendicular characteristics and high connectivity scores are merged. To determine whether to merge regions, the vertical characteristics and connectivity scores of the two regions are defined... As shown in formula (2-8).

[0098] (2-8) The global energy function minimization problem described above is solved using the L0-cut pursuit algorithm. Post-processing of surface refinement allows the piecewise surfaces to be aggregated into a complete surface.

[0099] This invention proposes a novel LiDAR point cloud segmentation method for segmenting point cloud data of stepped terrain scenes such as open-pit mines. The algorithm mainly consists of two steps: adding local constraints and global constraints. First, a voxel adjacency graph model is established, and the graph is segmented using the L0 gradient minimization algorithm to efficiently generate an initial set of planes. Then, in the global stage, global energy optimization refines and merges the initial set of planes into a final set of curved surfaces. Experimental results show that, on open-pit mine point clouds acquired by vehicle-mounted and airborne LiDAR, this segmentation method, compared with existing methods, can preserve more details of the open-pit mine scene without strict structural constraints. Through energy optimization iteration, in addition to segmenting the main planar structures, it can also segment irregular curved surface structures, more accurately restoring the structure of complex stepped terrain scenes in open-pit mines. Through comparison with four algorithms and six evaluation metrics, the method of this invention achieves an average structural segmentation accuracy F1 score of 74.7% and a boundary segmentation accuracy F1 score of 80.2%, outperforming existing mainstream methods.

[0100] The specific implementation process is as follows: Stepped terrain division of a large open-pit coal mine 1. Experimental Data UAV lidar point cloud data were selected from two open-pit mines, covering an area of ​​approximately 7 km². 2 Point cloud density 40-80 points / m 2 It includes multiple stepped terrain structures (platforms, slopes, transition zones) and noise points (such as gravel and vegetation).

[0101] 2. Implementation Steps The specific implementation steps of the "enhanced L0 gradient minimization step terrain segmentation method" based on the present invention are as follows: (1) Normal vector estimation based on IPCA The original point cloud is preprocessed (denoising and downsampling), the neighborhood radius of the target point is set to 1.5m, and the neighborhood point set of each point is obtained by k-nearest neighbor search.

[0102] The IPCA algorithm is used to estimate the normal vector: the initial scale parameter is the square of the largest residual in the neighborhood, the number of iterations is 20, the scaling factor is gradually reduced from the initial value of 1.0 to 0.1, and the Geman-McClure type M estimator (Equation 1-5) is introduced to dynamically adjust the weights and suppress cross-surface points (such as outliers at the junction of the slope and the platform).

[0103] The reference point offset is corrected through a dual initialization mechanism (Formula 1-8), and the normal vector of each point is finally output.

[0104] (2) Multiscale supervoxel segmentation A normalized spatial metric segmentation method is used: distance weights are set. =2, Normal Vector Weight =0.5, verticality weight =1 / R (Formula 1-11), the average distance of the point cloud is... Initial resolution of supervoxels Minimum resolution .

[0105] Multi-scale classification: Calculate the supervoxel covariance matrix (Equation 1-12) and eigenvalues, and then perform flatness analysis. =0.8, directional difference threshold =15°, distance residual threshold =0.1m (Equation 1-16), dividing the hypervoxel into planar and non-planar types. Non-planar hypervoxels are... Recursively segment by resolution until the resolution is less than 100%. .

[0106] (3) Surface segmentation based on L0 gradient minimization and global energy optimization Construct a mixed adjacency graph of voxel scatter points: use scattered points of planar and non-planar voxels as nodes, establish edge relationships through Voronoi adjacency, and combine edge weights with normal vector differences and spatial distances.

[0107] L0 gradient minimization split: setting energy function parameters =0.25 (Formula 2-2), Vertical constraint threshold =0.14 (Formula 2-6), suppressing erroneous merging of the platform and slope, and generating the initial plane set.

[0108] Global energy optimization: The surface is refined using the L0-cut pursuit algorithm (Equation 2-7), with weight parameters... =0.5, merge coplanar but unconnected regions, and output the final surface segmentation result.

[0109] 3. Effect Analysis (1) Overall segmentation effect The structure of the open-pit mine, including the platform, slope, and gravel transition zone, was successfully segmented. The curved surface boundaries were clear, with no obvious over-segmentation or under-segmentation.

[0110] It exhibits strong robustness to noisy areas (such as gravel points on the slope surface) and does not cause large-area segmentation errors due to local noise.

[0111] (2) Quantitative evaluation indicators (compared with existing methods), as shown in Table 1, demonstrate the superiority of the proposed algorithm by comparing the region growing method: QTPS, the model fitting method: Efficient-RANSAC, and the energy optimization method: Global-L0 and CutPursuit in three experimental regions.

[0112] Table 1

[0113] (3) Key advantages are reflected Normal vector estimation: Compared with traditional PCA, IPCA shows a significantly enhanced difference in normal vectors at the slope boundary, such as... Figure 1 As shown.

[0114] Super voxel segmentation: The multi-scale strategy improves the boundary recall rate by 21% and reduces the undersegmentation error by 35%, solving the problem of blurred boundaries in flat regions.

[0115] Surface segmentation: Energy optimization improves the F1 score of structural segmentation by 17%-23%, accurately reproducing complex surfaces (such as gentle slopes and irregular rock areas).

[0116] In summary, this embodiment verifies the effectiveness of the method in complex open-pit mine scenarios. Its segmentation accuracy, noise resistance, and completeness of step line extraction are all superior to existing mainstream methods, and it can provide reliable data support for 3D modeling and intelligent monitoring of mining areas.

[0117] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A stepped terrain segmentation method that enhances L0 gradient minimization, characterized in that, Includes the following steps: Step 1, Point cloud feature calculation based on iterative principal component analysis: By introducing a robust M estimator to construct a dynamic weight allocation mechanism, the slope and platform transition area of ​​the original point cloud is optimized by orientation-adaptive neighborhood optimization. The goal of the M-estimator is to minimize the weighted residual generalized function: in Represents the residual of the i-th sample. It is a robust kernel function with saturation properties; In each iteration, the parameters are first estimated based on the current parameters. Calculate residuals And the weights are dynamically updated through a weighting function: ； The IPCA normal vector estimation algorithm constructs a robust optimization iterative framework, which achieves robust handling of sharp features and noise through dynamic weight adjustment and geometric constraints. Given the point to be estimated and its neighborhood point set The algorithm first defines the direction based on the normal vector. The residual function: ， And a Geman-McClure type M estimator is introduced to construct the weight function: ， scaling factor The dynamic threshold for outlier detection is controlled; when the residual is much larger than... When the residual is small, the weight approaches 0, automatically eliminating outliers; when the residual is small, the weight approaches 1, preserving geometric features. Step 2, Multi-scale Supervoxel Segmentation: A normalized spatial metric segmentation method is adopted, which generates supervoxel units by using a weighted normalization mechanism of distance, normal vector and perpendicularity. The supervoxels are classified as planar and non-planar by combining a multi-scale strategy. Non-planar supervoxels are recursively segmented at a smaller resolution. Among them, normalized spatial metric segmentation: First, the spatial metric of each point in the point cloud is calculated through local neighborhood information to ensure that similar points are clustered in the same supervoxel; , and Used to assess the distance between points , , and yes , and Normalized weights, vertical angular distance Euclidean distance is used to describe the elevation continuity between points. Used to represent the spatial similarity between points in coordinate space, and the similarity of normal vector directions. Used to merge coplanar points: ， ， and It's about verticality. and It is a spatial vector. and yes , The normal vector; Among them, the generation and classification of multi-scale hypervoxels: The original point cloud is first segmented into parts with an initial resolution of [resolution value missing]. The supervoxel set is then divided into two types: planar supervoxel sets and non-planar supervoxel sets. The supervoxels in the non-planar supervoxel sets are then further subdivided into smaller scales. ), and further classify these into planar and non-planar hypervoxels; repeat the above steps until all points are assigned to planar hypervoxels or the current resolution. Less than Non-planar hypervoxels; all the partitioned hypervoxels of a stepped terrain are grouped into a hypervoxel set. When the supervoxel set The included hypervoxels Covariance matrix generated according to multi-scale partitioning for: ， in It is a supervoxel The center of mass, It belongs to a single supervoxel All point clouds, Representative supervoxel set All supervoxes The quantity, thus enabling us to obtain eigenvalues , respectively , and Calculating hypervoxels Linearity, flatness, and divergence; Step 3, Surface segmentation based on L0 gradient minimization and global energy optimization: based on the supervoxel set obtained in Step 2. A voxel scatter hybrid adjacency graph model is constructed. The number of non-zero gradients between adjacent vertices is controlled by the L0 gradient minimization algorithm, and vertical constraints are introduced to suppress the erroneous fusion of platforms and slopes. Then, the surface segmentation results are refined by global energy optimization to avoid structural fragmentation. Before performing segmentation, a graph representing the voxel adjacency structure needs to be created first; the spatial adjacency relationships of supervoxel units are used to establish the topological relationships between supervoxel nodes in the graph model; and the topological relationships between the nodes are defined in the graph model. Sum of edges Basic diagram of composition Above, each node Represents a voxel unit, each edge This represents the spatial relationship between two adjacent nodes, i and j. Represents the edges between adjacent nodes Weights; using Voronoi adjacency to connect the point set with the graph The nodes in the graph are connected to form an adjacency graph that combines voxels and points. . Partition the adjacency graph using the L0 gradient minimization algorithm. To obtain the initial segmentation results, the energy function that needs to be minimized is expressed by the formula: ， in It is the total energy of the graph model, representing the degree of matching between the segmentation result and the true value; It is the set of reconstructed normal vectors; It is the number of voxel units; It is the first The neighborhood set of a voxel unit; This is used to guide the output normal vector to be as close to the input as possible; Used to constrain sparsity in a local sense, it guides the normal vector of each point to approach its neighboring normal vectors; The number of split faces is used to encourage the merging of adjacent faces; regularization parameter. Used to balance the effects of the two items. Based on the initial segmentation, a global energy optimization method is introduced to relabel surfaces with the same geometric features onto a certain set of surfaces. The global energy function is: ， Among them, the super-body surface to be optimized The segmented adjacent segment graph is , C Represents the set of nodes in a segment graph. Indicates the need for optimization of the superbody surface. Adjacent edges between adjacent faces for Features of adjacent faces in a segment graph; Used to measure the similarity of features between segments; Used to penalize inconsistencies in the feature structures between adjacent faces; Represents the weights of the graph; This represents the weighting parameter that balances the two.

2. The stepped terrain segmentation method with enhanced L0 gradient minimization according to claim 1, characterized in that, In step one, the IPCA normal vector estimation algorithm constructs a robust optimization iterative framework, achieving robust handling of sharp features and noise through dynamic weight adjustment and geometric constraints. Specific steps include: The first step is to estimate the initial normal vector using classical PCA. And with the largest residual square in the neighborhood Initialize scale parameters; The second step is iterative weighted PCA optimization. In each iteration, an M-estimater is introduced to construct a robust optimization framework, and a weight function based on the Geman-McClure kernel function is established. This function is used to solve for the normal vector direction through weighted PCA after fixing the weights, and the least squares objective function is then used. ， By alternately performing weight updates and weighted PCA solutions, adaptive elimination of outliers and gradual optimization of normal vectors are achieved. The third step involves dynamically adjusting the scaling factor by gradually decreasing it by 1.01 increments. until the preset threshold is reached. This strategy retains more neighborhood information in the early stages of iteration and gradually focuses on interior points in the later stages, balancing noise suppression and geometric detail preservation. The fourth step is reference point calibration. To address the reference point offset problem caused by noise, dynamic reference point calibration is introduced. In each iteration, along the current normal vector The direction is dynamically adjusted to the reference point position, and repeated optimization is performed to offset the reference point offset caused by noise and improve the stability of the normal vector; In IPCA normal vector estimation, the dynamic weighting mechanism of the M-estimator is embedded in the calculation process of the covariance matrix; by weighting... Correlation with residuals of neighboring points can automatically reduce the contribution of noise points and outliers across edges, making the covariance matrix more accurately reflect the geometric characteristics of the target's local surface.

3. The stepped terrain segmentation method with enhanced L0 gradient minimization according to claim 1, characterized in that, In step two, according to , and The range of values, using , and Normalization is performed; the weights are set as follows, where R is the resolution of the current segmented supervoxel: ， Minimum distance between points The median will be used for initialization. This allows for faster iteration.

4. The stepped terrain segmentation method with enhanced L0 gradient minimization according to claim 1, characterized in that, In step two, the supervoxel Significant features include: linearity flatness divergence , ， For a supervoxel containing some non-planar points, based on the characteristic that the points in such a supervoxel have directional differences, the standard deviation of the angle between the normal of the supervoxel and the normal of the points inside the supervoxel is calculated using the following formula: yes Interior point The normal vector, yes The normal vector, Represents supervoxel The number of midpoint clouds, It is the difference in the direction of the hypervoxons.

5. The stepped terrain segmentation method with enhanced L0 gradient minimization according to claim 4, characterized in that, Measuring supervoxel points Distance to the fitted plane The residuals are calculated by averaging the distances to all points. average : ， Combining planarity, directional differences, and distance residuals, the criteria for supervoxel plane subdivision can be: ， The units of the voxel segmentation are divided into two groups: planar and non-planar. Points in the non-planar region are further segmented at a lower resolution and then further divided into planar or non-planar. This process is repeated until all supervoxels are classified as planar or the resolution is less than a threshold.

6. The stepped terrain segmentation method with enhanced L0 gradient minimization according to claim 1, characterized in that, In step three, each supervoxel unit and point corresponds to a node in the graph model. The partitioning of the graph model nodes corresponds to the fusion of large supervoxels and small fragments. The graph is partitioned starting from well-structured voxel units, not randomly selected. First, the connectivity fraction of the supervoxels is calculated. Then, based on the connectivity fraction Perform heuristic sorting on the processing groups: ， in, The number of points in a voxel unit. For the connectivity fraction of a single point, based on the local connectivity fraction of a voxel. The size of the voxel group to be processed is used for heuristic sorting; voxel units with lower connectivity fractions will be preferentially selected for processing, and voxel units located at the intersection of two faces will have a lower processing order.

7. The stepped terrain segmentation method with enhanced L0 gradient minimization according to claim 6, characterized in that, Adjacent elements are iteratively merged into a group using a defined fusion criterion to minimize the number of global non-zero gradients; the contribution of each pair of adjacent elements to the total energy E in the figure can be expressed as: ， Taking the merging of voxel units as an example, in the formula , This represents the normal vector between two adjacent voxel units; combined with and The solution involves minimizing e in two cases; the fusion criterion is: ， Two voxel units , The vertical distance is calculated using the formula: ， The fusion criterion after substituting the vertical constraint is: ， in The number of nodes to be merged. This represents the updated normal vector after merging nodes. This represents the increase in the total energy of the energy function after merging nodes. The preset vertical distance threshold is set when the energy increment after merging adjacent regions is negative and the vertical distance is less than the threshold. The merger will be accepted at that time.

8. The stepped terrain segmentation method with enhanced L0 gradient minimization according to claim 7, characterized in that, Spatially adjacent regions with approximately perpendicular characteristics and high connectivity scores are merged; to determine whether to merge regions, the perpendicular characteristics and connectivity scores of the two regions are defined. : ， Post-processing for surface refinement allows segmented surfaces to be aggregated into a complete surface.

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