Track extraction method based on discontinuous surface boundary three-dimensional space constraint intersection line

Abstract

The invention discloses a trace extraction method based on a discontinuous surface boundary three-dimensional space constraint intersection line, and provides an ARCG method based on a three-dimensional point cloud, realizes simultaneous extraction of a single surface and a contour part of a structural surface by dynamically adjusting a parameter threshold value, quantifies and discusses goodness of fit of different structural surface models according to an area ratio, and provides a trace extraction method based on the boundary three-dimensional space constraint intersection line of the discontinuous surface. And finally, selecting a parallelogram as an optimal model. Further searching an intersection line between the contour points of the intersection pairs of the structural surfaces by virtue of a space intersection relation of the model, and dynamically dividing the intersection line to keep the geometric characteristics of the structural surfaces. And finally, connecting the intersecting lines of the same structural plane through a bidirectional weight growth graph theory to form a final trace result. According to the method, the feasibility is verified through data of two slopes, case results show that compared with an existing method and point cloud processing software, the method can achieve extraction of complex traces and keep good connectivity, and the calculation efficiency can be improved by 96.6% while the traces are accurately extracted. Therefore, the method provided by the invention can provide a new method thought for digital characterization of rock mass structural plane parameters.

Description

Technical Field

[0001] This invention relates to the field of geological engineering, specifically to a method for extracting traces of intersection lines based on three-dimensional spatial constraints of discontinuous surface boundaries. Background Technology

[0002] Structural surface traces, as the intersection lines between rock mass structural surfaces and the surface or outcrop, are key basic data for engineering geological surveys, rock mass stability analysis, and underground engineering support design. At the same time, traces are geological interfaces in rock mass with certain directionality and dip, such as fissures, joints, and bedding. Their characteristics determine the mechanical properties of rock mass, so accurate analysis of structural surface traces is the key to studying the mechanical properties of rock mass [3]. Traces can better describe the spatial location and geometric appearance of structural surfaces, and these characterization indices have been improved by subsequent scholars, making the ability to identify structural surface traces gradually improve from qualitative to semi-quantitative to quantitative. However, in terms of the means of obtaining various rock mass indicators, the traditional manual recording method is relatively backward. Although on-site manual measurement can be combined with rich geological experience to make accurate judgments, the subjective inefficiency of collection and the safety of the operation range have always been the biggest limitations and constraints of contact measurement. Therefore, under the needs of scientific research and engineering implementation for efficient, accurate, and automatic acquisition of structural surface parameters, non-contact measurement has gradually entered the vision of the general public and become the main technical means of rock mass structural recording.

[0003] Previously, due to the ease of acquiring and the efficiency of processing digital images, many mature techniques have emerged in the field of trace extraction. Among them, fast line segment detection and image enhancement algorithms were the first to enter the public eye, and subsequently, innovative edge detection operators such as Canny and Sobel have also shown impressive performance in trace segmentation. However, when the target object is a complex trace with gaps, the computational efficiency of these methods will be reduced to some extent. To achieve stable and efficient trace image processing, more scholars have focused on improving existing algorithms and integrating various mathematical theories for complex traces. In addition, with the development of computer technology, the emergence of various machine learning and deep learning methods adapted to image samples has also provided a new approach to trace extraction, but sample collection and training are also important factors affecting the recognition results. Moreover, the various methods mentioned above that use two-dimensional images as data sources require a strictly dust-free environment and controlled lighting conditions.

[0004] Meanwhile, with the continuous development of 3D model building technology, modern research has long since moved towards methods for extracting geological information elements at a higher dimensional level. Thanks to the ability of 3D point cloud data to finely characterize the geometric properties of rock mass surfaces, in addition to the automatic extraction of planar target point clouds such as structural surfaces, automatic detection algorithms for linear and convex target point clouds, such as traces, are also relatively mature. Currently available methods can roughly achieve trace extraction in three aspects: firstly, using a triangular mesh model constructed from point clouds as the basic unit, and quantifying the spatial dimension of the triangular mesh through principal curvature, normal vectors, and other indicators. Existing technologies propose methods to directly identify traces from the DSM using principal curvature values. Another representative method is to obtain trace feature points through normal tensor voting and introduce Laplacian contraction to aggregate scattered feature points into the trace skeleton, significantly improving trace smoothness and noise resistance (compared to the coarse results caused by direct connection of feature points in traditional methods). However, the trace recognition results of this method are highly dependent on the smoothness and resolution of the DSM mesh, and the effect is not ideal in low-density or data-deficient areas. On the other hand, some researchers start directly from the spatial location and local features of the point cloud, automatically connecting trace segments by manually determining the starting point, or integrating the RGB values ​​of the point cloud and proposing multiscale spatial local binary. The pattern (MS-LBP) algorithm eliminates the influence of shadows, or the region growing method can be used to extract point clouds of both planes and cracks simultaneously. In addition, a new trend has emerged of using machine learning to process multi-scale features of trace point clouds in batches and learn from samples, which may be a new digital approach to rock mass structure characterization. However, due to the massive amount and lack of topology of point clouds, such methods are prone to misclassifying noise, such as anomalous protrusions, as trace points, and are still in their early stages, lacking a mature theoretical framework. Finally, the third approach, starting from the definition of traces, determines the intersection relationship between pairs of structural surfaces and uses the intersection line as the detection target, which is more in line with reality. Some scholars have used fitting single-plane projection of structural surfaces to two dimensions to find contour traces, extracting the structural surface contours in the image as linear traces using Canny edge detection, and supplementing three-dimensional geometric data with LiDAR. However, relying on the combination of two-dimensional and three-dimensional data for extraction results in relatively fragmented contour lines between surfaces and poor connectivity. Furthermore, the fitting accuracy of structural surfaces is also a significant limiting factor for the extraction effect of this method, and the intersection relationship between surfaces in three-dimensional space is also quite complex, which is difficult to clarify using only two-dimensional projection.

[0005] Therefore, methods based on the intersection of structural surfaces have not been widely applied due to limitations in the accuracy of structural surface fitting and contour fragmentation. This invention primarily addresses the issue of structural surface identification accuracy in such methods by proposing an adaptive region contour growing algorithm (ARCG) based on 3D point cloud data. This algorithm prioritizes acquiring individual structural surfaces while also extracting their contour points. Furthermore, given the complexity of actual intersection relationships among large-scale structural surfaces, this invention discusses various structural surface distribution models and selects a superior category to represent the spatial location of the structural surfaces. After determining the intersecting structural surfaces, the intersection lines of the contour points are extracted and connected using a bidirectional weighted growth method to form the final trace result. Summary of the Invention

[0006] To address the aforementioned shortcomings in the prior art, this invention provides a method for extracting traces based on the intersection lines of three-dimensional spatial constraints on discontinuous surface boundaries.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: A method for extracting traces based on the intersection lines of three-dimensional spatial constraints on discontinuous surface boundaries includes the following steps: S1. Perform single-face segmentation and contour extraction on the three-dimensional point cloud data to obtain the contour point cloud of each structural surface. S2. Based on the spatial geometric relationship of the point cloud of the structural surface contour, determine the intersection relationship between structural surfaces and identify the intersection pairs; S3. Extract the intersection lines between structural surfaces based on the intersection pairs, and perform fitting and vectorization processing on the intersection lines; S4. Connect the intersection segments of the same structural surface using the bidirectional weighted growth graph theory method to form the final trace result.

[0008] Furthermore, the specific method for single-face segmentation and contour extraction of the structural surface in S1 is as follows: S11. Calculate the normal vector and curvature of each point in the point cloud. The normal vector is calculated by random Hough transform, and the curvature is quantized by the neighborhood difference of the normal vector. S12. The adaptive region contour growth algorithm ARCG is adopted. The point with the minimum curvature is used as the initial seed point. The normal vector and curvature threshold are dynamically adjusted to simultaneously complete the single-sided segmentation of the structural surface and the extraction of contour points.

[0009] Furthermore, the calculation methods for the adaptive normal vector threshold and curvature threshold in S12 are as follows:

[0010] In the formula, For adaptive normal vector thresholding, , These represent the maximum and minimum values ​​within a given threshold range, respectively. There are already points in the current area. A scaling factor to control the growth rate;

[0011]

[0012] In the formula, For adaptive curvature threshold, It is the set of curvature values ​​within the current region. , This represents the absolute deviation of the median curvature of the region. Given a lower limit for the curvature threshold, It is the curvature growth sensitivity coefficient.

[0013] Furthermore, the specific method for determining the intersection relationship of structural surfaces in S2 is as follows: S21. Select a parallelogram as the structural surface fitting model and calculate the minimum circumscribed parallelogram for each structural surface. S22. Filter potentially intersecting structural faces based on spatial distance; S23. Calculate the line of intersection of the planes containing the two parallelograms, and determine whether the line of intersection intersects both parallelograms at two points. If so, it is considered a true intersection.

[0014] Furthermore, the area ratio AR of the parallelogram model in S21 is defined as:

[0015] In the formula, This represents the area of ​​the fitted model. This represents the actual area of ​​the minimum convex hull of the structural surface.

[0016] Furthermore, the specific method for intersection line extraction and vectorization in S3 is as follows: S31. Using the contour points of one intersecting structural surface as the search set, search the contour points of the other structural surface through the KD tree neighborhood to obtain two sets of nearly linear points. S32. After denoising the point set, calculate the centroid and principal direction, and fit it as a straight line in three-dimensional space. S33. Divide the straight line into segments and take the centroid of each segment, then connect them to form a broken line segment as the trace segment.

[0017] Furthermore, the specific method for connecting the trace segments in S4 is as follows: S41. Construct an undirected graph using trace segments involved in the same structural plane, and use the longest trace segment as the seed segment to search for neighboring points in both directions. S42. Expand the path based on the positional relationship of the trace segments to which the point belongs, and construct a weighted undirected graph; S43. Calculate the weight score based on path length, number of nodes and angle deflection, and select the optimal path as the final trace.

[0018] Furthermore, the weighted score in S43 is calculated as follows:

[0019] In the formula, To select the final weighted score, This indicates the path length. Indicates the length of all nodes. This indicates the number of nodes in the path. Indicates the total number of nodes. This indicates the maximum angle deflection of the node on the path. These are the weight coefficients for the three features.

[0020] The present invention has the following beneficial effects: 1. The adaptive region contour growth algorithm (ARCG) proposed in this invention achieves simultaneous single-face segmentation and contour extraction of structural surfaces by dynamically adjusting the normal vector and curvature threshold, effectively avoiding the undersegmentation or oversegmentation problems caused by fixed thresholds in traditional region growth algorithms.

[0021] 2. By comparing various structural surface fitting models such as disks, ellipses, rectangles, and parallelograms, this invention selects the parallelogram as the better model, which achieves the best balance in terms of area ratio (AR) distribution and running time.

[0022] 3. This invention uses point density adaptive division of intersection segments to better preserve the geometric characteristics of the structural surface edge; and adopts a two-way weighted growth graph theory method to connect trace segments. By comprehensively considering multiple weight indicators such as path length, number of nodes and angle deflection, the true trace path is effectively selected.

[0023] 4. Starting from the essential definition of structural plane intersection, the method of this invention can clarify the relationship between the trace line and the structural plane through precise intersection pair discrimination and intersection line extraction, which is beneficial to subsequent attitude grouping and rock mass stability analysis. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the trace extraction method based on the intersection line of three-dimensional spatial constraints of discontinuous surface boundaries according to the present invention.

[0025] Figure 2 This is a schematic diagram of the parallel process of region growth and contour point extraction in an embodiment of the present invention.

[0026] Figure 3 The above are violin diagrams showing the area ratios of different structural surface models in embodiments of the present invention.

[0027] Figure 4 This is a schematic diagram illustrating five types of structural surface intersection pairs in an embodiment of the present invention.

[0028] Figure 5 This is a schematic diagram of the fitting trace line segment of the structural surface intersection pair in an embodiment of the present invention.

[0029] Figure 6 This is a schematic diagram of the bidirectional weighted growth graph theory algorithm according to an embodiment of the present invention.

[0030] Figure 7 This is a schematic diagram showing the comparison results between the embodiments of the present invention and existing methods for Case A.

[0031] Figure 8 This is a schematic diagram showing the comparison results between the embodiments of the present invention and existing methods for Case B. Detailed Implementation

[0032] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0033] A method for extracting traces based on the intersection lines of three-dimensional spatial constraints on discontinuous surface boundaries, such as... Figure 1 As shown, it includes the following steps: S1. Perform single-face segmentation and contour extraction on the 3D point cloud data to obtain the contour point cloud of each structural face. In this embodiment, the specific steps include: S11. Calculate the normal vector and curvature of each point in the point cloud. The normal vector is calculated by random Hough transform, and the curvature is quantized by the neighborhood difference of the normal vector. The core elements of region growing are the selection of seed points and the selection of growth criteria. These parameters must be quantified in terms of three-dimensional spatial features. Therefore, this invention selects normal vector and curvature as their characterization parameters.

[0034] (1) Calculation of normal vector PCA measures the main trend direction of data using eigenvalues ​​and is often used for efficient normal vector calculation of large-scale point clouds. However, due to its computational characteristics of constructing neighborhood matrices, it often smooths the normal vectors at the sharp edges of rock mass structures, leading to distorted results. Therefore, this invention uses stochastic Hough transform, which can greatly enhance the robustness of normal vector acquisition at abrupt changes in structural surfaces.

[0035] The stochastic Hough transform is also calculated starting from a neighborhood point, but its characteristic, as shown in the figure, is that it is calculated from a given center point. Within the neighborhood, any two other non-collinear points are randomly selected. , Form a triplet and define it as a computational unit, then cross-product the internal edge vectors. , As the normal vector of this unit ,in , To record the distribution of normal vectors, and considering different accumulators, a spherical accumulator is chosen here for ease of statistical analysis. As triples are constructed, the more normal vector results generated during this process, the closer they are to a normal distribution. However, in the constructed point set, the number of triples that can be generated is approximately the cube of the number of points. Therefore, when the normal vector distribution "tends" to a certain interval without changing, we assume that a correct normal vector has been generated, stop generating triples, and continue calculating the next target point. For this purpose, the following definition is given: Assume the number of accumulator grids is... The number of triples is So the current grid and the current triplet Both satisfy the independent correlation distribution in mathematical statistics. ,when Vote for hour Otherwise, it is 0. Furthermore, we use... This represents the empirical mean of current grid voting. That is the actual value. The difference between the two is the value. The confidence value is... Let's define the minimum number of triples, i.e., the stopping threshold. We'll first describe this using an empirical probability formula. and The relationship between them: (1) Then, by substituting Hoeffding's inequality into Equation 1, we obtain... The relationship between the variables mentioned above: (2) When the number of triples is satisfied The construction can be stopped immediately, and the mean of the grid with the most votes from the current accumulator is selected as the final normal vector of the target point. In addition, during the voting process, grid discrepancy may occur, causing the peak of the normal distribution to be located at the grid boundary. Therefore, this effect is quickly counteracted by rotating the accumulator. Experiments have shown that 5 rotations and a rotation range of 5° are sufficient.

[0036] (2) Curvature calculation Curvature is typically calculated by fitting a surface polynomial. However, to more accurately represent the three-dimensional curvature of a point and establish a relationship with the normal vector, this invention chooses to quantify curvature using the neighborhood difference of the normal vector. As shown in Equations 3 and 4: (3) (4) in Let be the normal vector of the target point. Let be the normal vector of any point in the neighborhood. Indicates the angle between the two. The number of neighboring points.

[0037] S12. The adaptive region contour growth algorithm ARCG is adopted. The point with the minimum curvature is used as the initial seed point. The normal vector and curvature threshold are dynamically adjusted to simultaneously complete the single-sided segmentation of the structural surface and the extraction of contour points.

[0038] In single-face segmentation, region growing and single-face fitting methods are widely used. Region growing algorithms were initially used for image segmentation, aiming to extract different regions of interest based on manually determined conditions. Rock mass structural surfaces, with their obvious discontinuous planar features, exhibit high adaptability to this algorithm. Furthermore, manually set growth criteria preserve the geometric details of the structural surface better than the static iterative formulas of single-face fitting. Therefore, in addition to the numerous threshold selections required in traditional region growing algorithms, this invention proposes an adaptive thresholding method to address the issue of repeated parameter adjustments. This method automatically identifies single-face structural surfaces simply by setting the range of normal vector and curvature threshold values. Another improvement in this invention is that traditional point cloud planar contour point extraction methods have many limitations in handling concave structural surfaces with complex shapes. Currently used methods include Alpha Shape, Convex Hull, Delaunay triangulation, and latitude / longitude scanning, but these methods cannot simultaneously solve the problems of manual parameter adjustment and the coexistence of concave and convex contours. Moreover, the contour extraction step is usually only performed after single-face segmentation is completed. In summary, this invention addresses the low adaptability of fixed thresholds and the cumbersome post-processing of structural surface contours by proposing a moving spatial contour scanning method combined with adaptive region growing. This method can extract contour point clouds while recognizing complex structural surfaces of arbitrary geometries, avoiding the entire surface from participating in subsequent structural surface intersection calculations, thus improving computational efficiency. The method is as follows: First, the curvatures calculated according to this invention are sorted by size. Growth begins with the point of smallest curvature as the initial seed point, using the angle between the normal vectors and the curvature difference as growth criteria. The growth process is as follows: [Identifying neighborhood points] With the initial seed point The angle between the normal vectors If it is greater than the normal vector threshold Then the point Classified as pending processing point If the value is less than the normal vector threshold, then add the initial seed point. Queue. And re-evaluate the curvature difference. If less than the threshold Then this point Defined as a secondary growth point If it exceeds the threshold, the point will be... Defined as boundary point At the same time, when the boundary point When it appears, record it as the current contour point. And calculate its relationship with the initial seed point. Projection direction vector (The projection plane is composed of) (Determined by the normal vector), when the new boundary point When it appears, project its vector With existing vectors In comparison, if Model length greater than If the angle between the two vectors is less than a given projection angle threshold, then... Record as new contour point And delete the original outline points. If the above conditions are not met, then only record it as a new contour point. The parallel process of specific region growing and contour point extraction is as follows: Figure 2 As shown.

[0039] To handle complex concave polygons, after the contour points are scanned, the current region points are projected onto the 2D projection plane centered on the initial seed point, and then randomly divided into subspaces. If the contour points are discontinuous within a certain subspace (i.e., two projection vectors have a small angle but a large difference in magnitude), the contour point set is considered defective. Since the current structural surface has actually completed single-face segmentation, K-means++ is then used to select a cluster size of 2 to divide the current structural surface point cloud into a dual-cluster point set. The cluster center farther from the initial seed point is taken as the new scan point. After obtaining the new round of contour points, they are merged with the original contour points to remove duplicates and become the final contour points of the structural surface.

[0040] It should be noted that, in order to enable the normal vector threshold to be dynamically adjusted, an adaptive normal vector threshold is set. Equation 5: (5) In the formula , These represent the maximum and minimum values ​​within a given threshold range, respectively. This indicates that the current area already has points. This represents the scaling factor that controls the growth rate; here it is set to 1000.

[0041] Simultaneously, Equations 6 and 7 are used as adaptive curvature thresholds. : (6) (7) In the formula It is the set of curvature values ​​within the current region. , This represents the absolute deviation of the median curvature of the region. Given a lower limit for the curvature threshold, The curvature growth sensitivity coefficient is set to 1.5 here.

[0042] During the growth process, the normal vector determines whether to add a point to the region, while the curvature determines whether it serves as a seed point for continued growth. Therefore, the normal vector decision actually has higher priority. Adaptive normal vector threshold. Core part It is a classic asymptotic growth function. When the target region just begins to grow and the number of points is small, this function maintains a strict angle tolerance to ensure the accuracy of the initial planar growth. As growth continues and the number of points in the region becomes sufficiently large... The restrictions will be relaxed appropriately to allow for minor fluctuations in growth.

[0043] Adaptive curvature threshold The core is This ensures that it is not excessively affected by abnormal protrusions or noise on the structural surface.

[0044] Because this method requires setting a threshold range, the normal vector threshold is set to 5°-20° based on empirical values ​​from existing research. The curvature threshold is set through the curvature distribution. Then, K-means++ is used to cluster the one-dimensional curvature, selecting a cluster size of 2 to initially distinguish between trace points and planar points. Points with lower curvature in the first category are tentatively called planar points, while points with higher curvature in the second category are called non-planar points. The curvature distribution after clustering is shown in the figure; therefore, the curvature range is set to 0.01-0.16.

[0045] Here, the original region growing algorithm is selected for single-face segmentation (since the ARCG algorithm performs two steps simultaneously, stopping the contour point extraction step can also complete single-face segmentation), and the widely used Alpha-shape algorithm is selected for contour point extraction of the structural surface. The results are compared with those of the method of this invention. The comparison results are shown in the figure. The original region growing algorithm requires multiple parameter trials, which can easily lead to undersegmentation or oversegmentation of the structural surface. Correspondingly, post-processing operations such as re-segmentation or re-merging are required. In addition, the parameters of Alpha-shape also need to be adjusted multiple times to find the optimal value. However, the method of this invention can dynamically adjust the threshold adaptively to the current region and extract contour points simultaneously, balancing the accuracy and efficiency of automatic extraction.

[0046] S2. Based on the spatial geometric relationship of the point cloud of the structural surface contour, determine the intersection relationship between structural surfaces and identify the intersection pairs.

[0047] After extracting the point cloud of the structural surface contours, the next step is to determine the intersection relationships between the surfaces, and then find the intersection by using the point clouds of adjacent surfaces. However, due to the massive amount of point clouds and their lack of topology, it is difficult to automatically search using coordinates alone. Therefore, a spatially representative model is needed to characterize the three-dimensional distribution range of each structural surface. A classic approach is the Beacher disk model assumption, based on the patterns summarized by Robertson from statistical data of approximately 9,000 trace lengths on the slopes of an open-pit mine in Debeer, South Africa. Thanks to the ease of construction and computation of the disk model, which only requires three parameters—center coordinates, radius, and normal vector—to obtain simulation results, it has been widely used in clarifying intersection relationships and in the construction of DFN networks and blocks. In addition, other models are used to simulate structural surfaces. For example, the orthogonal model of 1955 assumes that structural surfaces are two or three sets of infinitely extending mutually perpendicular planes, but this is clearly not suitable for finding tangent relationships. Some scholars have defined structural surfaces as polygonal models to make them fit the actual situation and used intersection relationships to find blocks. The concept of similar elliptical models was actually proposed at the same time as the disk model, but due to its limitations, it has not been widely accepted compared to the disk model. Later scholars found that structural surfaces can also be simulated by elliptical disk models when considering trace length distribution, and in some cases where structural surfaces are exposed, ellipses fit the structural surface type better. The above-mentioned studies show that structural surfaces can be simulated by different geometric models, but the optimal model is still undetermined and needs to be determined according to specific circumstances. Therefore, when judging the spatial intersection relationship of structural surfaces, this invention chooses to select a better category by discussing several different structural surface models and quantitatively describes the simulation effect of the model by the area ratio AreaRatio. It is worth noting that the above models for calculating structural surfaces are actually based on the minimum convex hull polygon of the structural surface contour point cloud, so Area Ratio is defined as follows: (8) In the formula This represents the area of ​​the fitted model. This represents the actual area of ​​the minimum convex hull of the structural surface.

[0048] S21. Select a parallelogram as the structural surface fitting model and calculate the minimum circumscribed parallelogram for each structural surface. This section selects circles, ellipses, rectangles, parallelograms, parallel hexagons, and arbitrary trapezoids as models to be discussed (all calculated using the least bounded form). Given the existing research models, the reason for choosing other models considering geological conditions is that actual rock mass structural surfaces often exhibit polygonal, irregular quadrilateral, or banded shapes, especially structural surfaces formed by tectonic stress, which often have directional extensions (such as conjugate joint systems). Parallelograms or hexagons can better simulate this anisotropic characteristic. From a mathematical and geometric perspective, the reason is that point cloud data is discrete when depicting the outline of structural surfaces, which is actually a complex polygon in a geometric sense. The more complex the model used, the closer it is to the structural surface in theory, but the computational efficiency will be significantly reduced. Therefore, simple parallel polygons can represent the main extension direction while also ensuring fast calculation. A total of 1260 structural surfaces were obtained. After calculating the area using the obtained outline points, the AR distribution was obtained by fitting different models, as shown below. Figure 3 As shown: S22. Filter potentially intersecting structural faces based on spatial distance; S23. Calculate the line of intersection of the planes containing the two parallelograms, and determine whether the line of intersection intersects both parallelograms at two points. If so, it is considered a true intersection.

[0049] Because there are too many structural surfaces in three-dimensional space and they are randomly distributed, determining the intersection between them by directly calculating each one using a simple enumeration method would incur a significant computational burden. Therefore, it is necessary to filter the spatial distances before calculation. The distance between the center points of any pair of structural surfaces is used as the basis for this filtering. Is it smaller than both? The sum is used as a selection criterion, where different models... The methods for determining the values ​​differ: for a circle, the radius; for an ellipse, half its major axis; and for a rectangle, parallelogram, parallel hexagon, or any trapezoid, half its longest diagonal. After spatial filtering, the number of objects to be judged for each structural surface will be significantly reduced. The next step is to determine the authenticity of intersection pairs. The same method is used for different models (using an elliptical model as an example): directly calculate the intersection line of the planes containing the two models. If neither model intersects the line with two points, it is directly determined as a false intersection pair; if both models intersect the line with two points, connect the points to form line segments. If the two line segments overlap in space, it is a true intersection pair. Figure 4As shown, the positional relationships of intersecting pairs after spatial filtering are of five types.

[0050] S3. Extract the intersection lines between structural surfaces based on the intersection pairs, and perform fitting and vectorization processing on the intersection lines; After determining the intersection of two structural surfaces in space, it is necessary to extract their intersection lines, i.e., traces. However, at this point, the structural surfaces have already been segmented, and the position of the trace cannot be correctly determined from a single structural surface. Furthermore, if the trace results are connected in units of point clouds, the issue of assigning connection points is also difficult to resolve. Therefore, this invention uses the spatial geometric center of the contour points of two structural surfaces as the connection unit to achieve trace connection. The steps are as follows: Step 1: First, using the contour point set of one face as the search set, construct the KD tree neighborhood relationship for each point. Then, search for points in another contour point set with a given radius (if the point density of the searched point set is significantly lower than that of the search point set, the search radius can be appropriately increased according to the density difference). Then, swap the search point sets, resulting in two similar linear point sets (due to the massive discreteness of the point cloud, DBSCAN is needed to denoise each point set before extracting the traces. Based on the point density and actual needs, the eps and minpts parameters in DBSCAN are set to 0.04 and 4, respectively). Step 2: Next, obtain the centroids of the two denoised point sets respectively (assuming the point data is...). (Equation 9) and use PCA (Principal Component Analysis) to perform eigenvalue decomposition on the covariance matrix of the point set, taking the largest eigenvalue as the direction vector of the point set. Taking the centroid of the point set as a point on the direction vector, the linear point set can be represented by a straight line in three-dimensional space.

[0051] (9) Step 3: Using the direction vector of the two point sets and the mean of the centroids as the two points of the union point set, project all points onto this line and cut it into segments using the two farthest points. Then, divide this line segment into several sub-segments at equal intervals, the number of which is... Based on bus segment length and the density of points within the line segment range The determination is made using equations 9 and 10: (10) (11) In the formula It is optimized and adjusted based on the number of segments with differences in point density. The global average point density is 0.04, which is the minimum segment length determined by humans in meters. In order to preserve the basic geometric features of the trace, this formula guarantees that the minimum number of segments is 4.

[0052] Step 4: After obtaining the appropriate number of segments based on the length and point density, take the length of each segment as... The centroids of the segmented point set are then connected sequentially to form the trace between the two structural surfaces, which is represented in three-dimensional space as a broken line segment. A schematic diagram of the line segmentation is shown below. Figure 5 As shown.

[0053] S4. Connect the intersection segments of the same structural surface using the bidirectional weighted growth graph theory method to form the final trace result.

[0054] Since trace segments are obtained through the calculation of pairwise intersections of structural surfaces, they exhibit a discontinuous distribution. To achieve a more coherent trace effect, it is necessary to connect the trace segments. In existing research, most scholars use point clouds as the basic connection unit, employing methods such as minimum cost path, MS-LBP, and linear growth with weighted feature parameters. However, the implementation object is generally a point cloud. For trace segments, some scholars have used multiple parameters such as angle and distance to preferentially connect long linear traces to make them connected. Because traces are relatively discrete, the above methods may produce incorrect connections. This invention uses structural surface intersection pairs as the discriminant relationship, taking all trace segments obtained after calculating the intersection pairs involved in the same surface as the objects to be connected, and connecting them through the proposed bidirectional weighted growth graph theory connection method, such as... Figure 6 As shown, the steps are as follows: Step 1: Construct a temporary global index based on the trace segments involved in the current structural plane, and build a neighboring KD tree for each point on the trace segment; Step 2: Using the longest current trace segment as the initial seed segment and the two endpoints as initial seed points, start searching for points within a given radius from any one of these points (the other endpoint is also searched in the same way). Find the trace segments to which these points belong. If there are points belonging to the same trace segment, take the nearest point. If there are no points within the radius, it is determined to be the end of the trace segment and the search stops. At the same time, the trace segments that have been processed are recorded to prevent repeated searches. Step 3: Determine the positional relationship of the searched point within its corresponding trace segment. If it is an endpoint of the trace segment, use it as a new seed point and repeat Step 2. If it is an intermediate point, extend the connection to both endpoints and use them as new seed points, repeating Step 2 as well. Step 4: During the growth search process, construct an undirected graph using the coordinates of each point as nodes and the connections between points as edges. If the search connects to an endpoint, the edge is recorded normally; if it connects to an intermediate point, the node path is split. Step 5: After completing the search of the paths starting from both ends of the initial seed segment, connect the nodes of the two parts through this segment, and merge the undirected graphs at the same time; Step 6: Assign different weights to each path based on its length, number of nodes, and angle variation, as shown in Equation 12, and finally select the weighted score. The highest path is taken as the trace corresponding to the actual structural surface (Dijkstra's algorithm is used in this weighted undirected graph search).

[0055] (12) In the formula This indicates the path length. Indicates the length of all nodes. This indicates the number of nodes in the path. Indicates the total number of nodes. This indicates the maximum node angle deflection along the path. These are the weight coefficients for the three features, with values ​​of 0.8, 0.4, and 0.4 respectively.

[0056] Results Verification and Comparison Case A, as a commonly used open-source dataset in the field of rock mass structural plane research, possesses both well-developed and fractured structural planes and traces, an advantage that has led to its widespread use. Therefore, this invention also selects this dataset as a case for algorithm verification and compares it with several existing research results. The effects of each method are shown in the figure. Figure 7 a represents the trace extraction result of the method proposed in this invention; Figure 7 b represents the trace extraction result of the existing method. This method uses "Normal Tensor Voting Theory" to detect feature points of traces from 3D point cloud data, groups adjacent feature points according to geometric similarity, determines the main direction of the traces through PCA, connects feature points into continuous trace segments based on the growth algorithm, and finally connects segments that belong to the same trace but are segmented, and uses a threshold to remove redundant segments that deviate significantly from the main direction. Figure 7 c represents the trace extraction result of the existing method. This method is based on 1D truncated Fourier series and sets a curvature threshold to screen potential trace feature points. It then uses curvature-weighted Laplacian-like smoothing to refine the potential feature points. Finally, it connects the refined trace points through a feature-parameter-weighted line growing algorithm to form a complete trace. Figure 7 d represents the trace extraction result of the existing method. The first two steps of this method are similar to those of the previous method. The improvement lies in connecting feature points belonging to the same trace into continuous line segments according to geometric rules, dividing nonlinear connection segments to generate linearized sub-segments, and finally merging discrete linear segments belonging to the same trace into a complete trace by using axial and radial distances and curvature thresholds.

[0057] Overall, all four methods shown in the figure can identify the main traces. By comparison, the advantage of this method lies in extracting traces through the intersection of defined structural surfaces, clearly defining the relationship between the trace and the structural surface. Furthermore, by connecting the traces through designated structural surfaces, good trace connectivity can be maintained. In contrast, other methods produce discontinuous trace segments, resulting in a more discrete overall appearance. Secondly, other methods extract trace points based on the principal curvature of triangular meshes or point clouds. While this allows for rapid feature point extraction, it cannot achieve fine-grained trace extraction in complex structural surface regions. This is because the structural surfaces in these areas are fragmented, and during the initial extraction of potential feature points, some planar points on the structural surfaces are easily mistaken for trace points, resulting in the omission of many short traces. In the area enclosed by the white rectangle in Figure a, the structural surfaces are fragmented and complexly distributed. This method identifies small structural surfaces through single-surface segmentation, and further refines the capture of fine traces through intersection lines.

[0058] Case B also serves as a validation object for the method of automatic extraction of structural surfaces and traces. In its application to this dataset, it proposes converting RGB point clouds to grayscale values ​​to extract color abrupt boundary points as potential trace points, proposing a multi-scale spatial local binary mode (MS-LBP) algorithm to eliminate the influence of illumination and shadows, generating feature values ​​by analyzing the grayscale contrast of eight-quadrant voxels to filter redundant shadow points, and finally performing shadow processing using a bidirectional local vector buffer concatenation algorithm. Since it has already been compared with three different methods in the previous section, this section chooses to compare it with the MS-LBP method, and the results are shown in the figure. Figure 8 a is a single-sided segmentation effect using ARCG. Figure 8 b represents the trace recognition effect of the method of the present invention. Figure 8 c. The existing MS-LBP method uses a yellow rectangle to delineate a representative comparison region; therefore, this invention is based on comparison within this region. In contrast, in Figure 8 Within the two rectangles to the left of c, this method not only identified the corresponding traces, but also showed slightly stronger overall trace connectivity. However, the trace enclosed by the rightmost rectangle did not exhibit obvious 3D features, making it difficult to determine its existence without extraction based on structural surface intersections. Therefore, it is necessary to combine the RGB values ​​of the point cloud for further judgment. Furthermore, existing methods propose an open-source software platform for point cloud processing, supporting users in point cloud sampling and denoising, geometric fitting, and feature extraction. Therefore, the extraction results obtained on CloudCompare and related trace metrics are compared to further quantify the extraction performance. Detailed parameter comparison results are shown in the table. It can be seen that this method improves efficiency by 96.6% compared to CloudCompare. The area density calculation is defined by Equation 13: (13) In the formula Represents the total length of the two-dimensional projection trace. Represents the two-dimensional projected area.

[0059] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0060] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0061] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0062] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0063] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for extracting traces based on the intersection lines of three-dimensional spatial constraints on discontinuous surface boundaries, characterized in that, Includes the following steps: S1. Perform single-face segmentation and contour extraction on the three-dimensional point cloud data to obtain the contour point cloud of each structural surface. S2. Based on the spatial geometric relationship of the point cloud of the structural surface contour, determine the intersection relationship between structural surfaces and identify the intersection pairs; S3. Extract the intersection lines between structural surfaces based on the intersection pairs, and perform fitting and vectorization processing on the intersection lines; S4. Connect the intersection segments of the same structural surface using the bidirectional weighted growth graph theory method to form the final trace result.

2. The trace extraction method based on the intersection line of three-dimensional spatial constraints of discontinuous surface boundaries according to claim 1, characterized in that, The specific method for single-face segmentation and contour extraction of the structural surface in S1 is as follows: S11. Calculate the normal vector and curvature of each point in the point cloud. The normal vector is calculated by random Hough transform, and the curvature is quantized by the neighborhood difference of the normal vector. S12. An adaptive region contour growth algorithm is adopted, which uses the point with the minimum curvature as the initial seed point, dynamically adjusts the normal vector and curvature threshold, and simultaneously completes single-sided segmentation of the structural surface and extraction of contour points.

3. The trace extraction method based on the intersection line of three-dimensional spatial constraints of discontinuous surface boundaries according to claim 2, characterized in that, The adaptive normal vector threshold and curvature threshold in S12 are calculated as follows: In the formula, For adaptive normal vector thresholding, , These represent the maximum and minimum values ​​within a given threshold range, respectively. There are already points in the current area. A scaling factor to control the growth rate; In the formula, For adaptive curvature threshold, It is the set of curvature values ​​within the current region. , This represents the absolute deviation of the median curvature of the region. Given a lower limit for the curvature threshold, It is the curvature growth sensitivity coefficient.

4. The trace extraction method based on the intersection line of three-dimensional spatial constraints of discontinuous surface boundaries according to claim 1, characterized in that, The specific method for determining the intersection relationship of structural surfaces in S2 is as follows: S21. Select a parallelogram as the structural surface fitting model and calculate the minimum circumscribed parallelogram for each structural surface. S22. Filter potentially intersecting structural faces based on spatial distance; S23. Calculate the line of intersection of the planes containing the two parallelograms, and determine whether the line of intersection intersects both parallelograms at two points. If so, it is considered a true intersection.

5. The trace extraction method based on the intersection line of three-dimensional spatial constraints of discontinuous surface boundaries according to claim 4, characterized in that, The area ratio AR of the parallelogram model in S21 is defined as follows: In the formula, This represents the area of ​​the fitted model. This represents the actual area of ​​the minimum convex hull of the structural surface.

6. The trace extraction method based on the intersection line of three-dimensional spatial constraints of discontinuous surface boundaries according to claim 1, characterized in that, The specific method for extracting and vectorizing the intersection line in S3 is as follows: S31. Using the contour points of one intersecting structural surface as the search set, search the contour points of the other structural surface through the KD tree neighborhood to obtain two sets of nearly linear points. S32. After denoising the point set, calculate the centroid and principal direction, and fit it as a straight line in three-dimensional space. S33. Divide the straight line into segments and take the centroid of each segment, then connect them to form a broken line segment as the trace segment.

7. The trace extraction method based on the intersection line of three-dimensional spatial constraints of discontinuous surface boundaries according to claim 1, characterized in that, The specific method for connecting the trace segments in S4 is as follows: S41. Construct an undirected graph using trace segments involved in the same structural plane, and use the longest trace segment as the seed segment to search for neighboring points in both directions. S42. Expand the path based on the positional relationship of the trace segments to which the point belongs, and construct a weighted undirected graph; S43. Calculate the weight score based on path length, number of nodes and angle deflection, and select the optimal path as the final trace.

8. The trace extraction method based on the intersection line of three-dimensional spatial constraints of discontinuous surface boundaries according to claim 7, characterized in that, The weighted score in S43 is calculated as follows: In the formula, To select the final weighted score, This indicates the path length. Indicates the length of all nodes. This indicates the number of nodes in the path. Indicates the total number of nodes. This indicates the maximum angle deflection of the node on the path. These are the weight coefficients for the three features.

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