ENHANCED ROBUST 3D PIPELINE RECONSTRUCTION AND MODELING

© 2025 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. ENHANCED ROBUST 3D PIPELINE RECONSTRUCTION AND MODELING Ioannis Karantaidis, Alexandros Zamioudis, Dimitrios Psarras and Ioannis Pitas School of Informatics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece ABSTRACT Although industrial installation inspection is a well-studied topic, 3D reconstruction of industrial pipeline installations remains underexplored. Pipeline installations can be estimated from sensed data, typically acquired via UAV imaging. Existing 3D pipeline modeling algorithms are error prone, as they either lack outlier removal or utilize trivial methods to this end. In this paper, we propose Enhanced Robust Cylinder Fitting (ERCFit), a novel 3D pipeline reconstruction algorithm, that improves upon existing methods by integrating the Local Outlier Factor algorithm with RobustPCA for more effective outlier removal. We further propose a comprehensive 3D pipeline installation reconstruction framework, which makes use of the ERCFit algorithm to fully model and reconstruct all pipelines present in such a 3D industrial scene. Extensive experiments show that our proposed 3D pipeline modeling algorithm outperforms current state-of-the-art methods, accurately reconstructing straight pipelines in real-world chemical plant environments. Index Terms—3D Reconstruction, Pipeline, RobustPCA, Local Outlier Factor, Minimum Covariance Determinant 1. INTRODUCTION Unmanned Aerial Vehicles (UAVs) have become increasingly vital in industrial inspection tasks, particularly in critical infrastructures such as petrochemical refineries [1, 2]. Their versatility, flexibility, and ability to efficiently capture high-quality data (3D point clouds, RGB images), have led to widespread adoption across numerous industries. Pipelines, often exhibiting cylindrical geometry, are among the most frequently encountered structures in these settings. Their condition is crucial for the smooth operation of industrial processes, making damage detection a primary focus in pipeline inspection [3, 4]. Over time, factors such as sudden pressure increases, corrosion, traffic stress, and ground movement significantly elevate the risk of pipeline damages and leaks [5]. Such damages can cause substantial financial losses and environmental harm. UAVs provide a safe, non-invasive, and cost-effective solution for detecting faults without halting normal operations, in contrast to traditional inspection techniques. While 2D damage detection can be achieved by analyzing images captured by drones using deep learning algorithms [3], human inspectors require precise 3D damage location information to perform effective repairs. Thus, reconstructing the 3D scene and geometrically modeling the pipeline installations are key components of the pipeline inspection process. However, this task is complicated This work has received funding from the European Union Horizon Europe research and innovation programme under grant agreement number 101070604 – SIMAR. This publication reflects only the authors’ views. The European Commission is not responsible for any use that may be made of the information it contains. by the complexity of industrial sites and the challenge of converting 2D drone images into accurate 3D models. Surrounding structures often introduce noise into the data, leading to potential modeling errors. To address this, advanced cylinder fitting methods have been developed to improve accuracy and reliability in noisy environments by integrating outlier detection mechanisms. This paper extends the Robust Cylinder Fitting (RCFit) [6] method to enhance pipeline modeling by removing outliers found in real-world industrial environments. It also establishes a reliable framework for reconstructing entire 3D pipeline installations. To improve the robustness of cylinder parameter estimation, the Local Outlier Factor (LOF) algorithm is integrated into the RCFit method, yielding a new approach termed Enhanced Robust Cylinder Fitting (ERCFit). The RCFit algorithm serves as the baseline for evaluating the performance of ERCFit, which is assessed using synthetic data representing cylinders of various predefined lengths, orientations, radii, and positions. The performance of ERCFit is compared against both the baseline RCFit method and a neural network approach. Furthermore, multiple-cylinder modeling of the pipeline installation is conducted using a 3D point cloud derived from SfM applied to RGB images of the entire installation. The connected-component labeling algorithm [7] is utilized to isolate individual pipes from the global 3D point cloud, allowing ERCFit to be applied for accurate modeling of each pipe installation. This sequential process ensures precise identification and modeling of the pipeline components. 2. RELATED WORK 3D cylinder modeling for fitting refers to the process of estimating the parameters of a cylinder from a given point cloud, such as position, radius, length and orientation. A plethora of different approaches have been proposed on this front, though not without their drawbacks. Methods like multi-view imaging [8] have demonstrated their potential but are error prone. Pre-processing of raw 3D point clouds [6] is insufficient when dealing with large point clouds. RANSAC (Random Sample Consensus) [9], who has long been a foundational method for model fitting in computer vision and 3D reconstruction tasks, is computationally expensive and its accuracy is heavily dependent on the choice of initial parameters. More refined methods like Jet Fitting [10] are sensitive to noisy data. With the recent advances in deep learning many such methods have been proposed, like DeepPipes [11], DeepFit [12], Scan2CAD [13] and DiffusionNet [14]. Although each one is more than adequate in its specific task they are wholly depended on the amount and quality of data given in order to accurately model 3D pipelines. 3. BACKGROUND 3.1. Robust PCA Principal Component Analysis (PCA) identifies directions that maximize data variability by calculating the covariance matrix Σand applying eigen analysis to determine the Principal Components (PCs), in the form of eigenvalues and eigenvectors. However, PCA is highly sensitive to outliers, which can significantly affect its accuracy. ROBPCA algorithm [15], has been developed to improve PCA robustness by effectively removing outliers, before identifying the Robust Principal Components (RPCs). ROBPCA combines the Minimum Covariance Determinant (MCD) algorithm with the detection of multivariate outliers. In this study, we exclusively utilize the MCD method, as the low dimensionality of the point cloud data enables its effective application without significant challenges. Consequently, we refer to this approach as Robust PCA. When Robust PCA is applied to cylinder modeling from a 3D point cloud of its surface, the first eigenvector i.e. Principal Component PCA1 is selected to represent the cylinder axis, as it captures maximum data variability. The 3D point cloud is then projected onto PCA1 for determining the cylinder length by calculating the difference between the maximum and minimum projection values along the cylinder axis. Accurate cylinder axis estimation relies on the assumption that the cylinder’s length exceeds its radius, thereby ensuring the proper orientation of the principal directions. By projecting the data onto the second and third principal components (PC2 and PC3), the cylinder cross-section (circle) is identified. The Hyper algorithm [16] is then employed to accurately compute the circle radius and center. It offers several advantages, including efficient circle fitting to arcs, precise data point sampling along circle circumference, superior performance for modeling circles with small radius, and fast computation compared to traditional geometric fitting methods [6]. Additionally, Hyper algorithm results are invariant under 3D data point rotation and translation. Moreover, results can be improved by applying Least-trimmed Squares (LTS) regression [6], which employs only a 3D data point subset of nobservations for circle fitting to reduce the influence of outliers. The subset cardinality nis chosen to have the minimum sum of sorted square residuals. It is empirically set to n=⌊0.5N⌋, where Nis the number of the whole 3D data point. 3.2. DNN cylinder parameter regression Recently, Deep Neural Networks (DNNs) have been employed to regress parameters for various primitive surfaces, including planes, spheres, cylinders, cones, and tori [17]. In the DNN context, each 3D surface is considered to be one 3D shape class, whose parameters should be regressed. This approach typically involves two main steps: shape classification and parameter regression [17]. The PointNet architecture [18] serves as the foundational network, initially extracting features from the input 3D point cloud. Subsequently, a classification network performs 3D surface classification to the primitive shape class. A specific regression DNN is assigned to each 3D shape class. These regression networks are tailored with unique final layers comprising MLP (Multi-Layer Perceptron) heads to produce the output vector (3D shape parameters). The cylinder regression network is used to estimate the cylinder parameters, including orientation, center, and radius. 4. ENHANCED ROBUST CYLINDER FITTING (ERCFIT) The proposed Enhanced Robust Cylinder Fitting (ERCFit) algorithm integrates the Local Outlier Factor (LOF) algorithm [19] to improve RCFit robustness, by effectively removing outliers from the 3D point cloud of a chemical plant pipework, resulting in more accurate cylinder fitting to the straight pipelines. The proposed ERCFit workflow can be seen Figure 1. Minimum Covariance Determinant PCA Local Outlier Factor Hyper circle fit + Least Trimmed Squares Orientation Length Center + Radius RobustPCA Point Cloud Point Cloud PC1 PC2/PC3 : Parameter : Algorithm(s) : Principal Component PC1 : Added phase Fig. 1. ERCFit algorithm workflow In the original RCFit algorithm [6], the 3D point cloud is projected onto the first principal component (PC1) to compute the cylinder length. However, some outliers persist, even after applying Minimum Covariance Determinant (MCD), because MCD needs prior knowledge of the outlier percentage, which is critical for maximizing outlier exclusion. Despite effectively removing most outliers, the presence of even a single outlier can significantly impact the accuracy of the computed cylinder length. To mitigate this issue, the LOF [19] algorithm is applied to the 3D points projected onto PC1 and PC2, rather than only on PC1, thereby revealing the density of the data points more clearly. Only after LOF has successfully removed the outliers, the 2D points (projected onto PCA1 and PCA2) are then projected onto PC1 for the estimation of cylinder length. LOF evaluates the outlierness of each data point based on its deviation from the density of its nearest neighbors within a predefined threshold k. This approach ensures that points not adequately filtered by MCD are excluded as outliers based on their local neighborhood density. Mathematically, the LOF of a point xiis defined as: L(xi) = Pxj∈Nk(xi)r(xi, xj) |Nk(xi)|(1) where: •Nk(xi)represents the cardinality of the knearest neighbor set of xiwithin a predefined threshold, •r(xi, xj)denotes the reachability distance between xiand xj, defined as the maximum of the distance between xiand xj. L(xi)range is [0, 1]. Values greater than 1 indicates that the point xiis an outlier, as it deviates significantly from its neighbors in terms of density. Conversely, a L(xi)value close to 1 suggests that xiis similar to its neighbors in terms of density and is less likely to be an outlier. By integrating LOF into the robust cylinder fitting process, outliers that escape detection by MCD due to uncertain outlier percentages are effectively identified and removed. This enhancement improves the robustness of computing cylinder parameters, such as length and center of a cylinder, by ensuring that outliers with anomalous relationships to their local neighborhoods do not influence the calculations. Thus, the combination of MCD and LOF in the proposed novel ERCFit algorithm, provides a more comprehensive and reliable approach to outlier detection in the context of 3D point cloud analysis. This is particularly useful 3D in environments prone to noise and clutter as is the case of industrial pipeline installations. 5. 3D PIPE SCENE RECONSTRUCTION SYSTEM RGB images 2D masks Structure from motion Modelled pipes3D point cloud Labeling Components Enhanced Robust Cylinder Fitting (ERCFit) Segmented pipes Fig. 2. 3D Reconstruction system workflow 3D pipeline installations can be imaged using LiDAR and/or RGB cameras. Both sensors can be airborne using UAV imaging or ground-based. LiDAR provides a global 3D point cloud of the pipeline installation surfaces. RGB cameras provide multi-view RGB images that can feed a Structure from Motion (SfM) algorithm [20] to obtain the 3D surface point cloud. The RGB images of pipelines can be segmented using DNNbased methods [4]. Segmentation masks corresponding to the class pipeline contain image pixels that are projections of the 3D pipelines. In the 3D pipeline reconstruction process, only image pixels of pipelines can feed the SfM algorithm. This approach greatly reduces 3D point cloud and clutter during the process of generating a 3D point cloud of the scene. However, due to the use of DNN-based segmentation algorithm errors, some background noise may remain in the 3D point cloud. The 3D pipe scene reconstruction system consists of two main components: a) the Connected-component labeling algorithm [7] and b) the ERCFit algorithm. Alternatively, a DNN cylinder modeling alogrithm can replace the ERCFit algorithm. The global 3D point cloud contains numerous cylindrical elements, such as pipes and storage tanks. For further analysis, the point cloud is segmented into individual pipe segments using a Connectedcomponent labeling algorithm, which identifies and isolates different connected components within the point cloud. The labeling process assigns a unique label to each 3D connected component by analyzing the spatial 3D point connectivity. 3D connected components having few possible sparse 3D points are discarded as noise. Finally, the ERCFit algorithm is applied iteratively to fit each segmented cylinder in order to produce the final 3D pipeline scene. This whole workflow can be seen in Figure 2 6. EXPERIMENTAL RESULTS The main goal of the experiments is to test the robustness of the proposed methodology and its competitors, compare the performance of classical and DNN-based 3D cylinder modeling approaches, and validate the 3D pipe installation reconstruction system of a chemical plant data set. To test the robustness of the proposed method, a dataset containing 3D surface point clouds of pipes was created containing 100 cylinders, each having 1000 3D surface points; when needed, an arbitrary amount outliers were added following the Gaussian distribution with σ= 5m. The ERCFit algorithm was compared with the RCFit and the PointNet-based DNN. A key concept of the minimum covariance determinant algorithm, is the determination of the 3D data point percentage (”support of the estimate”) to be included in the core subset for estimating the point cloud mean and covariance [21]. This parameter ensures that the algorithm can effectively manage the trade-off between excluding noise and capturing the true underlying distribution of the data. Experiments were conducted to determine the optimal percentage (10%, 30%, 50%, 70%) while injecting Gaussian noise at data point percentages ranging from 10% to 80%. The effectiveness of each setting was assessed using the Area Under Curve (AUC) metric for every experiment and parameter combination. This approach facilitated the identification of the most suitable hyperparameter value for future following experiments. 100 200 300 400 500 600 700 # of outliers 0 200 400 600 800 1000 rmse Radius mcd:0.1, auc:141750.50 mcd:0.3, auc:5603.20 mcd:0.5, auc:11.90 mcd:0.7, auc:7160.50 mcd:0.9, auc:4094.30 100 200 300 400 500 600 700 # of outliers 0 200 400 600 800 1000 rmse Center Bias mcd:0.1, auc:141020.00 mcd:0.3, auc:5484.70 mcd:0.5, auc:163.40 mcd:0.7, auc:7165.90 mcd:0.9, auc:3902.10 100 200 300 400 500 600 700 # of outliers 5 10 15 20 25 rmse Height mcd:0.1, auc:12768.80 mcd:0.3, auc:5996.00 mcd:0.5, auc:4565.00 mcd:0.7, auc:3301.90 mcd:0.9, auc:2550.90 100 200 300 400 500 600 700 # of outliers 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 rmse Theta mcd:0.1, auc:501.70 mcd:0.3, auc:336.80 mcd:0.5, auc:341.20 mcd:0.7, auc:331.80 mcd:0.9, auc:475.60 RMSE Values for Different Parameters Fig. 3. RMSE values for different parameters (Radius, Center Bias, Length, Orientation) across varying numbers of outliers and support MCD values. Figure 3 displays the Root Mean Square Error (RMSE) values for four cylinder parameters (radius, center, length, orientation) across varying numbers of outliers and different Support of Estimate (SoE) values. Each subplot illustrates how RMSE changes with increasing outliers, with multiple lines representing different SoE values. To determine the optimal SoE value (λ∗), the mean RMSE across all parameters iis computed and evaluated for each SoE value λ: λ∗= arg min λ 1 4 4 X i=1 RMSEiλ (2) Here, RMSEiλ denotes the RMSE value for parameter iat SoE value λ. Across all evaluations, λ∗= 0.5consistently yielded the lowest mean RMSE for all parameters. This finding indicates that using SoE with a value of 0.5optimally reduces overall RMSE values in estimating cylinder parameters. After establishing the optimal hyperparameter value for the MCD algorithm, the proposed ERCFit was compared to the baseline (RCFit) one. To evaluate the robustness of the two approaches, 20% of the cylinder points were added as outliers following the Gaussian distribution with σ= 5m. The experimental results are presented in Table 1. It was observed that incorporating theLOF algorithm significantly lowered the RMSE for the center and length parameters. Specifically, the RMSE for the center parameter decreased from 0.254 to 0.21, and the RMSE for the length parameter was drastically reduced from 2.313 to 0.141. The Radius and Orientation parameters maintained consistent RMSE values of 0.007 and 0.646, respectively, across both methods. These findings indicate that integrating LOF into the methodology effectively reduces the RMSE for critical parameters, notably the length, thereby enhancing the overall accuracy of the cylinder fitting process. Table 1. Comparison of ERCFit and RCFit cylinder parameter estimation accuracy Parameter Robust Cylinder Fit (RMSE) [6] ERCFit (RMSE) Improvement (%) Radius (m) 0.007 0.007 0% Center (m) 0.254 0.21 17.32% Length (m) 2.313 0.141 93.90% Orientation (deg) 0.646 0.646 0% Additionally, to compare the PointNet-based DNN method with ERCFit, 10,000 cylinders with varying radii, positions, lengths, and orientations were generated and provided with known parameters. These cylinders were used to train the neural network from scratch, with a subset of 100 cylinders serving as the test set. However, PointNet-based DNN does not predict the length parameter, so the comparison focused solely on the radii, positions, and orientations. Moreover, the comparison was conducted without introducing any outliers into the data, since the PointNet-based DNN does not include a mechanism for outlier removal. Table 2. Comparison of ERCFit and PointNet cylinder parameter estimation accuracy. Parameter PointNet based DNN (RMSE)[17] ERCFit (RMSE) Improvement (%) Radius (m) 0.394 0.004 98.98% Center (m) 0.281 0.228 18.86% Length (m) - 0.087 - Orientation (deg) 1.731 0.511 70.49% The RMSE values for the radius, center, and orientation parameters of both algorithms are presented in Table 2. The ERCFit method is much better than the PointNet-based DNN approach across multiple parameters. Specifically, the ERCFit method achieves a remarkably low RMSE of 0.004 for Radius, compared to 0.394 for the PointNet-based DNN. For the Center parameter, ERCFit records an RMSE of 0.228, which is lower than the PointNet-based DNN RMSE of 0.281. Additionally, ERCFit demonstrates superior performance in estimating Orientation, with an RMSE of 0.511, substantially better than the PointNet-based DNN RMSE of 1.731. The length parameter is only computed by ERCFit, with a very low RMSE of 0.087, substantiating its robustness. 6.1. Chemical plant 3D pipeline installation reconstruction The performance of the proposed 3D pipe scene reconstruction system is validated by applying the system to a real world scenario of an chemical plant pipeline installation. Initially, the Structure From Motion (SFM) algorithm was employed to generate the comprehensive 3D global point cloud of the pipeline installation using 169 UAV images, processed using Agisoft Metashape software [22]. Next, the 3D point cloud was segmented into individual components using the Connected-component labeling algorithm using the CloudCompare software [23]. Each labeled 3D point component was modeled using the ERCFit method, to estimate its radius, center, length, and orientation. ERCFit ensures that the calculated parameters are not significantly affected by noise and outliers present in the point cloud data. Fig. 4. 3D point cloud along with straight modeled pipes. To visually validate the computed parameters, only the straight pipes were geometrically modeled and plotted onto the point cloud, as presented in Fig. 4. Since ERCFit is not designed to process nonpipe elements or pipes with elbows, these components were manually excluded from the model. All of the accurately reconstructed 3D point clouds corresponding to individual pipes were successfully geometrically modeled, resulting in a total of 38 pipes. This modeling process confirmed the effectiveness of the proposed method and provided a clear representation of the spatial arrangement of the pipes within the plant. The robust cylinder fit enabled an accurate reconstruction of the 3D model of the straight pipelines. The integration of the baseline method with the LOF algorithm proved to be particularly effective in reducing RMSE values, especially for the length parameter, as demonstrated in the comparative analysis. The resulting 3D model showcases the potential of the proposed approach to deliver precise and reliable pipe modeling in complex industrial environments. 7. CONCLUSION This paper introduces ERCFit, a novel comprehensive methodology for modeling pipes in industrial settings. By integrating RobustPCA with the LOF algorithm, ERCFit significantly mitigates the impact of outliers in cylinder modeling, outperforming RCFit and PointNet in the accuracy of cylinder parameter estimation. The application of our method to a real-world 3D point cloud from an chemical plant highlighted its practical utility. Accurate reconstruction of the pipe network within the point cloud underscores ERCFit robustness and precision, making it a valuable tool for industrial facility inspection, digital twin modeling and maintenance. 8. REFERENCES [1] Thumeera R. Wanasinghe, Raymond G. Gosine, Oscar De Silva, George K. I. 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