Denoising algorithm for inclined tunnel point cloud data based on irregular contour features

In response to the problem where current traditional denoising algorithms cannot effectively remove noise from inclined tunnel point cloud data with irregular contours. This paper proposes a denoising algorithm for inclined tunnel point cloud data based on irregular contour features. The algorithm combines the DBSCAN clustering algorithm with polynomial curve fitting to obtain sequential point cloud slices along the perpendicular direction to the centerline of the inclined tunnel. By identifying and extracting irregular contour feature points from these slices, it achieves the extraction of irregular wall shapes inside the tunnel. Based on these irregular wall shape features, noise points are effectively removed using distance iteration calculations. Experimental results demonstrate that the proposed algorithm can effectively handle the irregular shapes and elevation variations in inclined tunnel point cloud data and achieve good denoising performance for various types of noise within the tunnel. This algorithm lays a solid foundation for subsequent three-dimensional modeling of tunnels with high precision.


Introduction
Mine is the important source of energy resources, and its exploitation and production have important strategic significance for ensuring national energy supply.Tunnels serve as the production pathways in underground mines, and a comprehensive and reliable three-dimensional visualization solution is instrumental in analyzing and optimizing mine conditions (Wang et al 2010), thus ensuring the safety of national energy Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.resources, as well as lives and property.The construction of an underground mine's three-dimensional model allows for a more precise understanding of its structure and status.This is advantageous for managers to promptly identify and prevent potential safety hazards, thereby ensuring the safety of mining operations.Traditional manual modeling and photogrammetric methods suffer from issues such as low accuracy and timeconsuming processes (Yi et al 2019).Three-dimensional laser scanning technology, characterized by high precision, high density, and ease of operation (Qin et al 2016, Yang et al 2017, Shen et al 2021), has become an essential means of collecting spatial data in underground mine shafts and tunnels.The high-precision point cloud data acquired through this technology enables the rapid construction of three-dimensional models for tunnel engineering.Effective extraction of the tunnel wall is the basis for detailed 3D modeling of the entire shaft space.However, due to the complex production conditions underground, in the process of acquiring the tunnel point cloud data, it is inevitable to cause obstructions by the mine cars, pipelines, cables, pedestrians and other facilities.These obstructions constitute noise in the tunnel point cloud data, and the cleanliness of this noise removal directly affects the accuracy of three-dimensional surface modeling in the tunnel.
At present, point cloud denoising methods mainly include filter-based, optimization-based, and deep learning-based methods (Han et al 2017, Zhou et al 2022, Jun and Guangtian 2023).For the research of the filter-based point cloud denoising method, Li and Wu (2021) proposed a denoising method based on ellipse fitting for subway tunnels, which combined the least square method and Lagrange multiplier method to carry out ellipse fitting for tunnel point cloud models, and applied it to circular tunnel point cloud filtering; Hou (2021) proposed a distance denoising method based on iterative filtering model for point cloud data at the same location in different periods.This algorithm obtained tunnel filtering model through manual denoising to achieve noise removal of point cloud data at other periods.However, the filter-based method is limited by the shape and location of the point cloud, so it is only suitable for the point cloud data with regular shape and smooth inner wall.For the research of the optimization-based point cloud denoising method, Zheng et al (2023) used the local optimal neighborhood method to perform vector estimation to complete the tunnel point cloud denoising.However, this method takes the angle difference as the threshold value, and the normal vector of the sampling point needs to be calculated before the calculation, which increases the data processing time.Xu and Foi (2021) proposed a dense aggregation anisotropic denoising algorithm based on MLS estimation defined in the asymmetric direction neighborhood, which has a very good denoising effect in removing noise points on the surface of objects.However, tunnel noise is located in the interior, and part of the noise has no contact with the tunnel surface, so this method is not suitable for mine tunnel denoising.In recent years, the application of deep learning methods to point cloud data has become increasingly mature, and has produced some better research results on point cloud denoising based on deep learning.Hermosilla et al (2019) extended the learning of unsupervised image denoisers to unstructured 3D point clouds, achieving desirable denoising effects without relying on a noise-free training dataset when a sufficient number of training instances are available.Wang et al (2023) combined traditional filtering methods with deep learning to propose the PointFilterNet filtering network, which learns to generate the coefficients needed for filtering methods, thus accomplishing noise removal.Pistilli et al (2021) introduced a deep neural network based on graph convolution layers to construct a complex feature system, enhancing normal quality and being applicable in cases of high noise and structured noise.However, such methods are heavily influenced by the choice of datasets and evaluation metrics (2023), and there is limited research on point cloud denoising in the context of irregular, inclined tunnels.Based on the current research status, studies in the field of denoising for tunnel-like point cloud data primarily involve methods based on geometric feature fitting and optimization.These methods work well in straight tunnels with smooth inner walls but are not suitable for inclined tunnels with irregular contours.
As there is currently no effective research method for noise removal in point cloud data from inclined tunnels with irregular contours, this paper proposes a denoising algorithm specifically designed for inclined tunnel point cloud data based on irregular contour features.Based on high-precision tunnel point cloud data, the algorithm couples density clustering and polynomial curve fitting techniques to obtain sequential point cloud slices along the perpendicular direction to the centerline of the inclined tunnel.These slices are then subjected to plane fitting and projection into two-dimensional slices.Irregular contour features are extracted from these slices, and noise removal is achieved through distance iteration calculations based on a given threshold.Through experimentation, this paper demonstrates the feasibility and stability of the proposed algorithm for denoising inclined tunnels with irregular contours.

Sequence point cloud slice generation
Underground mine tunnels possess complex structural and shape characteristics.In order to ensure the production safety and smooth progress, adjustments in depth and angle are made during excavation to adapt to changes in the underground environment.Therefore, fully removing internal noise from these tunnels is quite challenging.This paper employs a slicing approach, which simplifies the denoising process for tunnels.Instead of denoising the entire complex tunnel at once, it divides the task into denoising individual slices.This approach effectively reduces the complexity of noise removal.However, it requires accurate slice data; otherwise, the quality of denoising may suffer.Considering the elevation variations in inclined tunnels, to ensure that the slicing direction remains perpendicular to the tunnel's orientation, this paper proposes a two-step slicing method.It first uses the data from the first slicing to obtain the centerline of the tunnel point cloud and then performs the second slicing vertically along this centerline.Eventually, the sequence slice data that can accurately reflect the contour features of the tunnel section are obtained.
2.1.1.Centerline fitting.Mine shafts are classified into three types: horizontal tunnels, inclined tunnels, and vertical tunnels, based on the relationship between the long axis and the horizontal plane (Sun et al 2018).The inclined tunnels studied in this paper are oriented at a certain angle to the horizontal plane but are primarily constructed along the horizontal direction.Therefore, the point cloud data was projected onto the XOY plane.As shown in figure 1, the red plane is the projected data.The direction of the tunnel is determined by calculating the maximum distance R between the x-axis coordinates and the y-axis coordinates.If the distance in x-axis coordinates is larger than that in y-axis coordinates, the tunnel is sliced along the x-axis; otherwise, it is sliced along the y-axis.Along this direction, the point cloud data is segmented into a series of segments according to the specified step length coefficient S l and distance interval.To obtain the sliced data of all point cloud, the distance interval is usually set to 0. The step length coefficient is inversely proportional to the thickness of the point cloud slices.The larger the step length coefficient, the smaller the thickness of the point cloud slices, the larger the number of slices N slices , and vice versa R = max {x max − x min , y max − y min } (1) where x min , x max , y min , y max represent the minimum and maximum values of the X and Y coordinates in a set of point cloud data.
If the sliced point cloud data is directly used for calculations to extract the central points, the presence of noise data can affect the accurate positioning of the central points.In this paper, an improved DBSCAN algorithm is applied to the sliced data generated in the aforementioned steps.This process involves clustering the data, extracting the point sets required for subsequent central point calculations, and removing noise points.The initial value setup for the improved algorithm is as follows: (1) Computing the Euclidean distance dis(p i , p j ) between two random points p i and p j .Calculating the maximum and minimum values of dis(p i , p j ) using equations ( 4) and (5), then determining the distance interval using equation ( 6) (3) where (x i , y i , z i ) and (x j , y j , z j ) represent the coordinates of points P i and P j , dis(p i , p j ) denotes the Euclidean distance between P i and P j , d min represents the minimum distance between P i and P j , and d max represents the maximum distance between P i and P j , d s denotes the distance interval between two randomly selected points, Pi and Pj.
(2) Calculating initial radius.Dividing the distance between any two points into m equal segments and calculating the frequency p k at which dis(p i , p j ) appears in each segment.Calculating the initial radius by finding the segment with the highest frequency M and using its midpoint.
The formula for calculating the maximum frequency is: (3) Calculating minimum neighborhood count minpts.After determining the initial radius, the minimum neighborhood count is increased, and the count of points with a neighborhood size greater than the minimum neighborhood count, denoted as P N , is calculated.The formula for calculating the neighborhood size P Ni of any point p is as follows: After automatically calculating the minpts and distance parameters, they are then applied to the DBSCAN algorithm for cluster analysis.The workflow for implementing the DBSCAN algorithm is illustrated in figure 2.
After going through the aforementioned steps, the point cloud data is effectively denoised, while preserving the characteristics of the slices, making it suitable for central point calculation.Here, the center of gravity is chosen to represent the center of each tunnel slice.Calculating the centroid for each slice will yield the central points used to form the centerline.
The calculation formula of the center of gravity is: where N is the number of point clouds in the slice point set, and P i is the coordinate of the ith point in the slice.

Secondary slicing of tunnel based on centerline.
In the previous steps, the point cloud data was sliced roughly according to the direction of the tunnel point cloud dataset.However, due to directional issues, there may be shape deviations in the data distribution at the ends of the tunnel.To address this, the paper employs the RANSAC algorithm to eliminate problematic scattered data points and optimize the fitting of the centerline in irregular tunnels (Wang et al 2023).The curve fitted using the RANSAC algorithm more accurately represents the direction of the tunnel.Following this direction, slices are made perpendicular to the centerline, resulting in precise slice data.
(1) Direction Determination and Tunnel Splitting Projecting point data from three-dimensional space onto curve data is a complex task.In addition, the direction of inclined tunnel segments can change angles.By splitting the tunnel at these angle-changing locations, you can obtain segments of the tunnel that approximate a linear direction.Leveraging the preliminary centerline of the tunnel generated in the earlier steps, which is projected onto the XOY plane.Then, as shown in figure 3, calculating the angle α between adjacent points and the x-axis, assess the angle difference between two straight lines.If the angle difference exceeds a specified threshold, the point is considered a boundary point.The normal vector of the fitting curve at this boundary point is calculated, and a slicing plane is determined based on the normal vector and the point, allowing the point set to be divided (figure 4).Conversely, if the angle difference is below the threshold, the   process continues to calculate the angle difference between subsequent adjacent lines, identifying turning points, and splitting the tunnel into segments with different directions.After splitting, it is easier to treat each segment as a tunnel with approximately linear direction during subsequent denoising.
(2) Line Projection and Point Cloud Slicing After segmenting the tunnel into parts, each segment does not exhibit significant angle changes, allowing for the projection of point cloud data onto straight line for slicing.In this paper, the RANSAC algorithm is used to fit the central points and remove outliers (figure 5).
In three-dimensional space, the line can typically be represented in three ways: general form, point-direction form, and parametric form (Guo et al 2011).The fitted line is represented using the point-direction form, as shown in equation ( 11), which is characterized by a direction vector and the center point of the line where the direction vector is represented as L = (m, n, p), and the known coordinates of the center point are (x 0 , y 0 , z 0 ).According to this expression, the formula for projecting an external three-dimensional point data (x 1 , y 1 , z 1 ) onto the line is as follows: x p , y p , z p are the coordinates after projection, where: The point cloud data, after being projected onto the line, aligns with the direction of the tunnel.Using the new coordinates, the point cloud data is subjected to vertical slicing once again to obtain its index values.Based on these index values, the original point cloud data can be sliced to obtain slice data aligned with the new direction of the tunnel.

Distance iteration denoising algorithm based on contour feature points
The shape of the tunnel is challenging to determine in threedimensional space.Therefore, it is projected onto a twodimensional plane for processing.Slice data is obtained based on the direction of the centerline, and this slice data is then projected onto a plane perpendicular to the direction of the centerline.The equation for the plane in three-dimensional space is typically represented in general form as: A, B, C can be expressed as: where (o x , o y , o z ) represents the direction vector of this section of the tunnel.By using the center point extraction algorithm, the center point (x, y, z) of this section of the slice data can be determined, and thus, the plane equation can be obtained.Let any point in this section of the point cloud be denoted as p with coordinates (x p , y p , z p ).The equation of the straight line passing through this point P and perpendicular to the plane is as follows: Rearranging the straight line equation, we obtain: Substituting this into the plane equation, we can calculate: After projection, the coordinates of point p ′ become (A•t + x p , B•t + y p , C•t + z p ).Following the projection formula, the coordinates of all points are successively projected onto the specified plane.Even after projecting the point cloud onto the plane, the coordinates are still in three dimensions.However, since the projected points all lie on the same plane, the relationships in three-dimensional space can be transformed into two-dimensional relationships for easier processing.Converting the three-dimensional coordinates to twodimensional coordinates reduces computational complexity.Based on the projected data, convex hull calculation is performed to obtain contour feature points of the slice, and then a distance iteration denoising is conducted.The algorithm proceeds as follows: (1) For each segment of original data, an initial slicing is performed along the direction of the point cloud to obtain the center points of the tunnel.
(2) The centerline of the tunnel is fitted, and the original point cloud is projected onto the centerline.A secondary slicing is performed in the direction tangent to the centerline, resulting in precise tunnel slice data.
(3) For each slice data, a plane perpendicular to the centerline is fitted.The slice data is projected onto the slicing plane, generating two-dimensional plane data.(4) Calculating the convex hull of the slicing plane to obtain the convex hull points, which represent the contour feature points of the tunnel slice{p 1 , p 2 , p 3 , … p n }. (5) Taking any point p i from the slice data and calculating the distance from p i to the line connecting the contour points{(p 1 , p 2 ), (p 2 , p 3 ), … (p n−1 , p n ), (p n , p 1 )}.Obtaining the minimum distance min and set a distance threshold t based on the thickness of the tunnel wall point cloud.If min > t, then p i is considered a noise point and is removed.(6) Repeating steps 3 through 5 for all slices until processing is complete.

Experimental data
The data used in this paper is the underground mine tunnel point cloud data collected by the mine management department for mine monitoring, and the proposed algorithm is validated by selecting a, b, and c tunnel types with different noise point types, shapes, and densities among them.As shown in figure 6 and table 1, category 'a' tunnel: Length of 44.8 meters, with 51 399 point clouds.The primary noise is in the form of human shadows.The point cloud distribution is uniform and has low density, the tunnel wall is relatively smooth.Category 'b' tunnel: Length of 37.1 meters, with 3161 182 point clouds.The primary noise is pipelinerelated noise, closely attached to the tunnel wall.Due to pipeline obstructions, there are data gaps in the tunnel wall, and the point cloud density is relatively high.Category 'c' tunnel: Length of 10.5 meters, with 1088 819 point clouds.The primary noise points are mine cars, which occupy a significant volume.The tunnel wall has undulations, and data gaps due to vehicle obstructions are more severe.

Tunnel point cloud slicing
Based on the method described in section 2.1 of this paper, the three datasets mentioned above underwent an initial slicing process to extract the centerline.As shown in figure 7, because the direction of the mine tunnel does not align with   the coordinate axes, the initial slicing introduces angular deviations, resulting in sliced data that is not aligned with the tunnel direction and has relatively large errors.
The centerline extracted from the first slicing was used as the direction for the point cloud.Following the method described in section 2.1, a second slicing of the point cloud data was performed, as shown in figures 8 and 9.The slicing data obtained using the algorithm proposed in this paper can maintain perpendicularity to the inclined tunnel direction, laying a crucial foundation for noise point removal.

Noise reduction result analysis and comparison
To demonstrate the feasibility and accuracy of the denoising algorithm proposed in this paper, noise reduction was applied to the selected three datasets.First, the original data underwent Gaussian filtering to remove obvious outliers, avoiding interference with contour points and affecting denoising accuracy.Then, the sliced data was subjected to plane fitting to project the original data onto a two-dimensional plane for extracting contour feature points (figure 10).
In order to effectively eliminate noise data while maximizing the retention of tunnel wall data, this study, through multiple comparative experiments, analyzed and selected parameter for tunnel slicing and distance iteration calculation.When performing slicing, the parameter to be set is the step length coefficient.A larger step length coefficient results in more slices and consequently more calculations.To ensure the algorithm's efficiency and denoising accuracy, preliminary experiments selected a step length coefficient between 3 and 7. Simultaneously, considering the characteristics of point cloud thickness and the unevenness of tunnel walls, the distance threshold was roughly determined to be around 0.2.
We conducted experiments using three distance threshold values: 0.19, 0.2, and 0.21, as shown in figure 11.In the figure, the rows represent the influence of changes in the step length coefficient on the denoising results, while the columns represent the influence of changes in the distance threshold on the denoising results.By observing the changes in the red noise points on the walls of the tunnel in each row of images, it can be found that as the step length coefficient increases, the denoising effect gradually improves.The denoising effects of 5 and 6 are quite similar upon manual observation, and the denoising times are also relatively close as shown in table 2. However, when the step coefficient increases to 7, as shown in the figure with a step length coefficient of 7 and a distance threshold of 0.21, there is an issue of overly dense slicing leading to incomplete edge slicing and failure in denoising.Therefore, a step coefficient of 5-6 is recommended as more appropriate.According to table 3, further comparison of the number of noise points incorrectly removed by coefficients 5 and 6 revealed that the total number of noise points incorrectly removed is less with a coefficient of 6.Thus, the step length coefficient is set to 6, and five distance thresholds between 0.19 and 0.23 are selected for comparison.As shown in figure 12, observing the red noise points on the tunnel walls reveals that a larger distance threshold results in more complete preservation of the tunnel walls and fewer incorrectly removed points.Thus, when the threshold is 0.19 and 0.20, holes appear in the tunnel walls, while no significant difference is observed manually between distance thresholds of 0.21-0.23,recommending a threshold range of 0.21-0.23.For better denoising results, the experiment, by comparing wrongly preserved tunnel wall points (U) incorrectly removed noise points (V), as shown in table 4, sets the distance threshold at 0.21, achieving relatively better denoising effects.
According to the selected parameters, all experimental data were denoised, and the results are shown in figures 13-15.The blue points represent the denoised data, and the red points represent the noise points.In the a-class tunnel, the point cloud data is relatively regular, and noise points were successfully removed, with the tunnel wall being well preserved.In the bclass tunnel, where pipeline noise closely adheres to the tunnel wall, denoising results in gaps in the tunnel wall, primarily due to data loss in the original data.In the c-class tunnel, affected by vehicle obstructions and data loss during data collection, the generated slices exhibit data gaps.Despite incomplete slices, this algorithm can still process them and maintain adaptability.Furthermore, it effectively suppresses noise points while avoiding erroneous removal of tunnel wall data.As a result, this algorithm demonstrates excellent denoising effects on tunnel data with different types of noise points, shapes, and densities.
To evaluate the advantage of this algorithm in denoising mine tunnel point cloud data compared to other methods, we applied the region-growing denoising algorithm and an ellipsoid fitting denoising method to the three tunnel types and  compared the denoising results with the method proposed in this paper.
For the region-growing algorithm, after several experiments and comparisons, the neighborhood search point count was set to 100, the smoothing threshold was set to 8.0, and the curvature threshold was set to 0.1 for optimal denoising results.As shown in figure 16, the region-growing algorithm performs well in removing noise located in the middle of the tunnel, such as shadows, mine cars, and pipelines in the middle.However, compared to this algorithm, the region-growing algorithm leaves some scattered points in the a-class tunnel and requires additional removal of these outliers.In the b-class tunnel, the region-growing algorithm better preserves the tunnel walls compared to this algorithm.However, its effectiveness in removing noise closely adhering to the tunnel wall is not ideal, as a significant amount of pipeline noise remains on the sides and bottom of the tunnel.In the c-class tunnel, the region-growing algorithm successfully removes the transport vehicles but also removes a portion of tunnel wall data, creating some substantial gaps.Thus, this algorithm outperforms the region-growing algorithm in terms of noise removal near the tunnel wall and for handling large-volume noise.
The ellipsoid fitting denoising method was applied to the data processing results, as shown in figure 17.Due to the flat bottom of the tunnel and surface unevenness, applying this method results in inevitable gaps at the tunnel bottom.This method demonstrates some denoising effectiveness for sparse noise points located in the middle, but its effectiveness in removing noise on the tunnel wall is poor.Additionally, when the volume of objects within the tunnel is large, it significantly affects ellipsoid fitting accuracy, making this method unsuitable for such cases.

Evaluation of results
The performance of the ellipsoid fitting method for denoising irregular tunnels was found to be unsatisfactory.Therefore, we conducted a specific comparison between the region-growing algorithm and the algorithm proposed in this paper.Due to the large dataset size and length, it was not convenient to perform a direct comparison.We selected the same segment from the three types of experimental data and evaluated the results.For a-class data, a segment with a length of 2.5 m was selected, consisting of 3140 point clouds.For b-class data, a segment with a length of 1.4 m was chosen, comprising 136 876 point clouds.For c-class data, a segment with a length of 2.46 m was selected, including 206 541 point clouds.The denoising results are displayed in figures 18-20, red points are the noise points removed, and blue points are the tunnel wall data retained.For the a-class data, as the number of point clouds decreases, the denoising quality of the region growing algorithm deteriorates.In the green box of figure 18(a), it can be seen that the human shadow is not completely removed, and other attachments inside the tunnel wall are not removed either.Regarding the b-class data, both methods have good  denoising effect for the attached pipes on both sides of the tunnel wall.However, in the red circle of figure 19(a), the region growing algorithm displays poor recognition capability for the track at the bottom of the tunnel, failing to remove track point clouds, and also missing the middle scattered noise points.Conversely, the algorithm in this paper effectively eliminates noise from pipes, tracks, and scattered points.For the c-class data, both methods adequately remove vehicle point clouds in the middle.However, for such uneven density data, the region growing algorithm mistakenly removes some sparse points on the tunnel wall as noise, creating numerous holes as seen in figure 20(a) within the red circle.In contrast, the algorithm in this paper preserves the tunnel wall more comprehensively.
For evaluating denoising results, this paper selected the first type of error (false positive rate) and the second type of error (false negative rate) in point cloud filtering as evaluation metrics (Ci et al 2023), as per equation ( 19) where u represents the tunnel wall data retained after manual denoising (figure 21), v represents the manually removed noise data, m indicates the number of times the algorithm mistakenly identified tunnel wall points as noise during denoising, and T 2 (%) q represents the number of times the algorithm mistakenly identified noise points as tunnel wall points during denoising, T 1 represents the percentage of the number of tunnel wall points misclassified as noise points; T 2 represents the percentage of the number of noise points misclassified as tunnel wall points.
The results of point cloud count and accuracy evaluation are presented in tables 5 and 6.For smaller datasets, the regiongrowing algorithm tends to be more conservative in denoising, as it does not misclassify tunnel wall points as noise.However, it does not completely remove the noise.For larger point cloud counts, the algorithm's results are more error-prone, leading to unstable performance.In contrast, the algorithm proposed in this paper achieves ideal denoising results for these three types of data, and it exhibits stability.In summary, the algorithm presented in this paper outperforms the region-growing algorithm in preserving tunnel walls and ensuring complete noise removal.It effectively removes noise points from point cloud data in irregular sloping mine tunnels, providing a solid foundation for real-time 3D modeling of underground mines.

Discussion
The effective extraction of the tunnel is the basis for the mine real scene 3D modeling.3D laser scanning technology can quickly scan the entire space of mine shafts and obtain high-density three-dimensional point cloud data.However, the internal environment of the tunnel is complex and there are many equipments, which will inevitably obscure the tunnel wall and form interference noise during the data acquisition process.Therefore, an effective denoising method is needed to remove objects other than the tunnel wall.Currently, researching in this area mostly focuses on shield tunnels, which are approximately standard circles, and commonly using ellipsoid fitting methods for noise removal (Xu et al 2018, Cui et al 2019, Yi et al 2020, Zhang et al 2024).Researching on denoising in mine tunnel mostly involves the removal of drifting points, isolated points, and mixed points (Jing et al 2018, Wang et al 2021).There are fewer studies on denoising for inclined tunnels with irregular contours.Thus, an effective denoising method is needed to be able to remove interference objects inside them and achieve mine tunnel extraction.Therefore, we addressed the denoising issue of irregular inclined mine tunnels by adopting a divide-and-conquer approach.By densely slicing the tunnel, fitting the outer contours of the slices, capturing the irregular contour features of the tunnel, and utilizing distance iterative calculations to achieve effective noise removal.Experimental results show that the algorithm proposed in this paper can effectively remove attachments and interferences such as pipelines, pedestrians, and mining carts inside the tunnel, demonstrating high feasibility and stability.

Selection of denoising parameters
For denoising parameter selection, the paper initially screens the results of denoising using step length coefficients from 3 to 7 and distance thresholds from 0.19 to 0.21.It was found that for step coefficients of 5 and 6, it was not possible to select a more suitable value through visual observation alone.Therefore, an analysis of the noise removed by step length coefficients of 5 and 6 was conducted, focusing on the number of points mistakenly identified as noise.As show in figure 22, it was observed that the overall noise points incorrectly removed were fewer when the step length coefficient was 6.Hence, the experiment chose a step length coefficient of 6.
When choosing the distance threshold, visual observation could not determine the best parameters.Therefore, the denoising results for parameters between 0.19 to 0.23 were compared, focusing on wrongly preserved tunnel wall points (U) and incorrectly removed noise points (V).As show in figure 23, it was found that a step coefficient of 6 with a distance threshold of 0.21 yielded the most optimal denoising results.

Failure case analysis
Although the proposed algorithm realizes interference noise rejection for irregularly inclined tunnel, it has some limitations.When the concavity and convexity of the tunnel wall is large, it may lead to removing the tunnel wall data incorrectly.As shown in figure 24, the blue color is the original data and the green color is the denoised data, the top shape of the data in this section is more complicated and the surface concavity  is very large.Therefore, the surface shape of the data segment cannot be well fitted during noise removal, so holes are inevitably generated.

Future research direction
According to the problems generated during denoising and the shortcomings of the algorithm, relevant research will continue in the following aspects in the future: (1) Automatic threshold fitting.Researching the method for dynamically setting distance thresholds based on tunnel characteristics.Adaptive adjustment of distance thresholds can improve algorithm efficiency and enhance denoising effectiveness.(2) Research on point cloud completion algorithm.Aiming at the holes caused by missing original point cloud data and the holes caused by denoising, the completion algorithm of point cloud data is studied to obtain complete tunnel wall data and better serve 3D modeling.

Conclusions
This paper addressed the challenges of denoising point cloud data in inclined underground mine tunnels with varying elevations and irregular contours.It introduced a denoising algorithm based on contour feature points and distance iteration to eliminate noise points that obscure tunnel walls.In the denoising process, the paper adopted a divide-and-conquer approach to slice the tunnel.To ensure the correctness of the slicing direction, a secondary slicing method based on the DBSCAN clustering algorithm and polynomial curve fitting was proposed to correct the directional errors that occurred when slicing with the ground as a reference.To address the irregularity of tunnel contours, contour feature extraction was employed to adapt to changes in tunnel shape.Distance iteration was conducted based on a given threshold to effectively remove internal noise points within the tunnel.
The results show that the denoising algorithm proposed in this paper is more precise in denoising inclined tunnels compared to the widely used ellipsoid fitting-based denoising algorithm and the region-growing algorithm.In experiments with three different types of tunnels, it effectively removed noise points, such as shadows, pipelines, equipment, and mine cars that obscured the tunnel wall.When partial data was selected for experiments, the denoising results remained accurate, indicating good stability.Currently, the denoising algorithm in this paper still has room for improvement in removing attachments closely adhered to the uneven surfaces of the tunnel wall.Additionally, the distance threshold needs manual setting.In the next step, we will further study automatic fitting of the distance threshold and select suitable thresholds for different tunnels.

Figure 5 .
Figure 5.Comparison of central point fitting before and after.(a) Extract the initial center point.(b) Central point fitting with RANSAC.

Figure 10 .
Figure 10.Two-dimensional plane fitting and contour feature extraction.

Figure 11 .
Figure 11.Comparison of experimental results of parameter combinations.

Figure 12 .
Figure 12.Denoising results comparison for the step length coefficient 6 and distance threshold values ranging from 0.19 to 0.23.(a) Distance threshold value of 0.19.(b) Distance threshold value of 0.20.(c) Distance threshold value of 0.21.(d) Distance threshold value of 0.22.(e) Distance threshold value of 0.23.

Figure 16 .
Figure 16.Denoising results using region growing algorithm.(a) Noise reduction effect of Class a tunnel.(b) Noise reduction effect of Class b tunnel.(c) Noise reduction effect of Class c tunnel.

Figure 17 .
Figure 17.Denoising results using the ellipsoid fitting method.(a) Noise reduction effect of Class a tunnel.(b) Noise reduction effect of Class b tunnel.(c) Noise reduction effect of Class c tunnel.

Figure 18 .
Figure 18.Comparison of denoising results for a-class data.(a) Denoising effect of region growing algorithm.(b) Denoising effect of this paper's method.

Figure 19 .
Figure 19.Comparison of denoising results for b-class data.(a) Denoising effect of region growing algorithm.(b) Denoising effect of this paper's method.

Figure 20 .
Figure 20.Comparison of denoising results for c-class data.(a) Denoising effect of region growing algorithm.(b) Denoising effect of this paper's method.

Figure 22 .
Figure 22.Analysis of denoising results for step size coefficients 5 and 6.

Figure 23 .
Figure 23.Analysis of denoising results with a distance threshold of 0.19-0.23 (the step length coefficient is 6).

Table 1 .
Experimental data information.

Table 3 .
The step length coefficient comparison.

Table 4 .
The distance threshold comparison.

Table 5 .
Partial point cloud denoising results.

Table 6 .
Accuracy evaluation of partial point cloud denoising results.