Plane Fitting Algorithm Research Articles

An unsupervised method for rock discontinuities rapid characterization from 3D point clouds under noise

The presence of rock discontinuities significantly affects the strength, permeability, and stability of rock masses, so it is crucial to characterize them accurately and efficiently. However, existing discontinuity characterization methods mainly focus on improving automation level and computational efficiency and pay little attention to the effect of noise, which may lead to unsatisfactory results. To address this, we present an unsupervised method to characterize rock discontinuities. The method contains five denoising operations which greatly mitigate the effects of noise while mapping discontinuities rapidly. The proposed approach comprises four steps: (1) remote sensing technology used to collect point cloud data; (2) a Modified Mean Shift algorithm (MMS) including five denoising operations developed to identify group discontinuity; (3) a density-based cluster algorithm employed to detect individual discontinuity; and (4) plane fitting algorithm applied to calculate the orientation of each discontinuity. The working procedure was displayed using a regular cube, and the proposed approach was validated on two real road-cut slopes. The average error degrees in dip angle and dip direction are within 3° for both cases, indicating the excellent accuracy of the presented method. Then, a sensitivity analysis of the parameters in the MMS was conducted, and some recommendations for the selection of these parameters were given (ηmax was suggested to be 0.02–0.2, while R was recommended to be 0.2–0.3). Finally, the computational efficiency of the presented method was compared with the other two algorithms, and the results show that the computational efficiency was improved by 13 and 30 times respectively, which proves that it is computationally efficient. This approach gives geological and geotechnical engineers a new solution to rapidly map rock structures under noise, which is significant for improving the accuracy of rock characterization.

Development of an Uneven Terrain Decision-Aid Landing System for Fixed-Wing Aircraft Based on Computer Vision

This paper presents a computer vision-based standalone decision-aid landing system for light fixed-wing aircraft, aiming to enhance safety during emergency landings. Current landing assistance systems in airports, such as Instrument Landing Systems (ILSs) and Precision Approach Path Indicators (PAPIs), often rely on costly and location-specific ground equipment, limiting their utility for low-payload light aircraft. Especially in emergency conditions, the pilot may be forced to land on an arbitrary runway where the road flatness and glide angle cannot be ensured. To address these issues, a stereo vision-based auxiliary landing system is proposed, which is capable of estimating an appropriate glide slope based on the terrain, to assist pilots in safe landing decision-making. Moreover, in real-world scenarios, challenges with visual-based methods arise when attempting emergency landings on complex terrains with diverse objects, such as roads and buildings. This study solves this problem by employing the Gaussian Mixture Model (GMM) to segment the color image and extract ground points, while the iterative weighted plane fitting (IWPF) algorithm is introduced to mitigate the interference of outlier feature points, reaching a highly robust plane normal estimation. With the aid of the proposed system, the pilot is able to evaluate the landing glide angle/speed with respect to the uneven terrain. Simulation results demonstrate that the proposed system can successfully achieve landing guidance in unknown environments by providing glide angle estimations with an average error of less than 1 degree.

Precise underwater fish measurement: A geometric approach leveraging medium regression

Accurate estimation of fish length is crucial aquaculture processes. Precise and real-time estimation of fish length aids fish farmers in formulating effective farming strategies. Existing methods for estimating the length of underwater fish have made significant advancements in overcoming the interferences present in complex underwater environments. Nevertheless, the measurement results of some methods continue to be limited by variations in the refractive index of multiple media and deviations in imaging angles, resulting in measurement errors and diminished practicality. Consequently, we propose a measurement method that aims to address the aforementioned challenges in fisheries aquaculture by providing more accurate and cost-effective solutions. This method initially introduces the concept of regressing multiple media into a single medium to correct underwater depth estimation and enhance underwater imaging quality. Subsequently, an accurate plane fitting algorithm is applied to precisely fit the fish body plane and extract its corresponding normal vector information. Finally, taking into account the light propagation path and accounting for the limitations of precise values, we utilize the geometric relationship between the length of the bounding box and the actual length of the fish to calculate a more accurate estimation of fish body length. Experimental validation showcases the applicability of our measurement method to diverse fish species and substantiates its exceptional performance in both experimental and real-world scenarios. The maximum average relative errors for each group are within 8%, and the average relative error is 3.28% under the exact value constraints presented in the experiments. This method makes a significant contribution to fish length estimation and offers valuable insights for applications in fisheries and aquaculture.

A human-machine interaction method for rock discontinuities mapping by three-dimensional point clouds with noises

Rock discontinuities control rock mechanical behaviors and significantly influence the stability of rock masses. However, existing discontinuity mapping algorithms are susceptible to noise, and the calculation results cannot be fed back to users timely. To address this issue, we proposed a human-machine interaction (HMI) method for discontinuity mapping. Users can help the algorithm identify the noise and make real-time result judgments and parameter adjustments. For this, a regular cube was selected to illustrate the workflows: (1) point cloud was acquired using remote sensing; (2) the HMI method was employed to select reference points and angle thresholds to detect group discontinuity; (3) individual discontinuities were extracted from the group discontinuity using a density-based cluster algorithm; and (4) the orientation of each discontinuity was measured based on a plane fitting algorithm. The method was applied to a well-studied highway road cut and a complex natural slope. The consistency of the computational results with field measurements demonstrates its good accuracy, and the average error in the dip direction and dip angle for both cases was less than 3°. Finally, the computational time of the proposed method was compared with two other popular algorithms, and the reduction in computational time by tens of times proves its high computational efficiency. This method provides geologists and geological engineers with a new idea to map rapidly and accurately rock structures under large amounts of noises or unclear features.

A Mine Intersection Recognition Method Based on Geometric Invariant Point Detection Using 3D Point Cloud

In large-scale underground mines and mine-like deep urban canyons, intersections are crucial geometry structures. Accurate recognition of intersections is of great importance to improve localization precision for Unmanned Aerial Vehicles(UAVs) and Unmanned Ground Vehicles(UGVs). Currently, traditional Lidar-based localization methods are limited in the mine environment. While 3D Lidar data is accurate but sparse and disordered, making it difficult to extract valid semantic information to correct the accumulated error. The similar geometry structure leads to the challenge of forming a uniform description for recognizing the same intersection with different scanning poses. To overcome these issues, this paper presents a novel real-time intersection recognition method in mine scenarios, encoding the 3D point cloud into a compact vector. RANSAC plane fitting algorithm is employed to extract stable ground plane feature. By compressing representative wall points segmented from raw point cloud into a 2D grid image and detecting the geometry invariant point in the ground plane, the proposed method completes a generic intersection description robust to spatial x-y-z translation and roll-pitch rotation variation. In addition, yaw rotation invariance is achieved through maximum cosine similarity searching in matching two point clouds. Experimental results on simulation mine and public deep urban canyon datasets demonstrate its superiority in the recognition of intersections in mine scenarios.

Real and Pseudo Pedestrian Detection Method with CA-YOLOv5s Based on Stereo Image Fusion.

With the development of convolutional neural networks, the effect of pedestrian detection has been greatly improved by deep learning models. However, the presence of pseudo pedestrians will lead to accuracy reduction in pedestrian detection. To solve the problem that the existing pedestrian detection algorithms cannot distinguish pseudo pedestrians from real pedestrians, a real and pseudo pedestrian detection method with CA-YOLOv5s based on stereo image fusion is proposed in this paper. Firstly, the two-view images of the pedestrian are captured by a binocular stereo camera. Then, a proposed CA-YOLOv5s pedestrian detection algorithm is used for the left-view and right-view images, respectively, to detect the respective pedestrian regions. Afterwards, the detected left-view and right-view pedestrian regions are matched to obtain the feature point set, and the 3D spatial coordinates of the feature point set are calculated with Zhengyou Zhang’s calibration method. Finally, the RANSAC plane-fitting algorithm is adopted to extract the 3D features of the feature point set, and the real and pseudo pedestrian detection is achieved by the trained SVM. The proposed real and pseudo pedestrian detection method with CA-YOLOv5s based on stereo image fusion effectively solves the pseudo pedestrian detection problem and efficiently improves the accuracy. Experimental results also show that for the dataset with real and pseudo pedestrians, the proposed method significantly outperforms other existing pedestrian detection algorithms in terms of accuracy and precision.

Design and Research of Low‐Cost and Self‐Adaptive Terrestrial Laser Scanning for Indoor Measurement Based on Adaptive Indoor Measurement Scanning Strategy and Structural Characteristics Point Cloud Segmentation

Nowadays, TLS (terrestrial laser scanning) has been a relatively mature measuring equipment categorized to indoor measuring robots, but it is not widely adopted in indoor construction measurement at present. What accounts for its limited application are as follows: (1) the high cost of high‐accuracy laser LIDAR and (2) existing TLS equipment does not possess self‐adaptation scanning planning and takes no account of efficiency of point cloud processing and consumption of computing power. This paper proposes a novel TLS equipment and a high‐efficiency point cloud processing method customized for the novel equipment, with purpose to achieve self‐adaption measurement on the basis of indoor characteristics of construction during civil engineering at low cost. This paper mainly presents two parts of innovations: (1) for planning of scanning, the novel TLS features planning sampling density of scanning according to room size and converting scanning data from poses to point clouds, and (2) for processing of point clouds, this paper proposes two novel segmentation algorithms, namely, “on‐boundary segmentation algorithm” and “on‐angular‐distance segmentation algorithm,” based on indoor spatial structure features and characteristics of TLS. Besides, this paper presents modified RANSAC‐TLS (random sample consensus‐total least squares) plane fitting algorithm, on basis of TLS point cloud distribution characteristics and spatial transformation. Through actual measurement test, it is concluded that the “on‐boundary segmentation algorithm” and “on‐angular‐distance segmentation algorithm” are suitable for point cloud segmentation in different types of scenes. The modified RANSAC‐TLS have made a great improvement on accuracy of fitting versus LS (least squares), TLS (total least squares), and RANSAC‐LS. Finally, this paper conducts an experiment by executing an actual measurement and then preliminarily testifies the potential and future application of the proposed novel TLS (terrestrial laser scanning) equipment, with measurement parameters from it being changed in the experiment, by comparing with one existing TLS equipment—FARO. The test thus proves the relatively high feasibility and potential of the novel TLS presented in the paper (terrestrial laser scanning) in actual indoor measurement.

Fast Positioning Method of Truck Compartment Based on Plane Segmentation

To improve the loading efficiency and shorten the loading time, a method based on LIDAR point cloud segmentation for fast positioning of trucks is proposed for the scenario of level-push automatic loading, in which the truck position and attitude are random. The point cloud data are collected by LIDAR and pre-processed by traditional methods in the order of straight pass filtering, voxel filtering, and plane segmentation. Four planar regions are segmented using the region growth algorithm, and then planar fitting is performed for each of these four regions, which requires a large number of iterations and complex calculations by the traditional planar segmentation method. Focusing on these drawbacks this paper first uses the region growing algorithm to cluster and group the matching points, then combines the least squares and RANSAC algorithms for plane fitting optimization to calculate the intercept of each plane, and finally uses these intercept values to perform spatial geometry calculations to obtain the exact position and locus of the carriage. Experiments show that the method reduces the number of iterations and improves the computational efficiency compared with the traditional RANSAC algorithm, thus improving the efficiency and accuracy of the plane fitting algorithm.

Real-time indirect illumination by virtual planar area lights

This paper presents a method called Virtual Planar Area Lights (VPALs) to generate single-bounce diffuse-to-diffuse indirect illumination for dynamic scenes and light sources. Different from the VPLs (Virtual Point Lights) based methods, which extract point lights from RSM (Reflective Shadow Map), our method fits RSM by many planar regions which will be directly used as virtual light sources to generate the indirect illumination. In order to reduce the illumination errors introduced by plane fitting, we propose several strategies, including an illumination-guided plane fitting algorithm, a normal correction factor and a virtual light sources reuse strategy. Our experimental results indicate that our method can achieve a good balance between the rendering performance and quality. Compared with traditional light culling and clustering methods, the rendering consumption of our algorithm is reduced by at least 67% with the similar RMSE (Root Mean Squared Error).

Plane-Edge-SLAM: Seamless Fusion of Planes and Edges for SLAM in Indoor Environments

Planes and edges are attractive features for simultaneous localization and mapping (SLAM) in indoor environments because they can be reliably extracted and are robust to illumination changes. However, it remains a challenging problem to seamlessly fuse two different kinds of features to avoid degeneracy and accurately estimate the camera motion. In this article, a plane-edge-SLAM system using an RGB-D sensor is developed to address the seamless fusion of planes and edges. Constraint analysis is first performed to obtain a quantitative measure of how the planes constrain the camera motion estimation. Then, using the results of the constraint analysis, an adaptive weighting algorithm is elaborately designed to achieve seamless fusion. Through the fusion of planes and edges, the solution to motion estimation is fully constrained, and the problem remains well-posed in all circumstances. In addition, a probabilistic plane fitting algorithm is proposed to fit a plane model to the noisy 3-D points. By exploiting the error model of the depth sensor, the proposed plane fitting is adaptive to various measurement noises corresponding to different depth measurements. As a result, the estimated plane parameters are more accurate and robust to the points with large uncertainties. Compared with the existing plane fitting methods, the proposed method definitely benefits the performance of motion estimation. The results of extensive experiments on public data sets and in real-world indoor scenes demonstrate that the plane-edge-SLAM system can achieve high accuracy and robustness. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the robust localization and mapping for mobile robots. We suggest a novel simultaneous localization and mapping (SLAM) approach fusing the plane and edge features in indoor scenes (plane-edge-SLAM). This newly proposed approach works well in the textureless or dark scenes and is robust to the sensor noise. The experiments are carried out in various indoor scenes for mobile robots, and the results demonstrate the robustness and effectiveness of the proposed framework. In future work, we will address the fusion of other high-level features (for example, 3-D lines) and the active exploration of the environments.

An Improved Building Reconstruction Algorithm Based on Manhattan World Assumption and Line-Restricted Hypothetical Plane Fitting

An improved patch-based multiview stereo (PMVS) algorithm based on Manhattan world assumption and the line-restricted hypothetical plane fitting method according to buildings’ spatial characteristics is proposed. Different from the original PMVS algorithm, our approach generates seed points purely from 3D line segments instead of using those feature points. First, 3D line segments are extracted using the existing Line3D++ algorithm, and the 3D line segment clustering criterion of buildings is established based on Manhattan world assumption. Next, by using the normal direction obtained using the result of 3D line segment clustering, we propose a multihypothetical plane fitting algorithm based on the mean shift method. Then, through subdividing on the triangle mesh constructed based on the building hypothetical plane model, semidense point cloud can be quickly obtained, and it is used as seed points of the PMVS pipeline instead of the sparse and noisy seed points generated by PMVS itself. After that, dense point cloud can be obtained through the existing PMVS expansion pipeline. Finally, unit and integration experiments are designed; the test results show that the proposed algorithm is 15%∼23% faster than the original PMWS in running time, and at the same time, the reconstruction quality of buildings is improved as well by successfully removing many noise points in the buildings.

Outlier detection and robust plane fitting for building roof extraction from LiDAR data

ABSTRACT Individual roof plane extraction from Light Detection and Ranging (LiDAR) point-cloud data is a complex and difficult task because of unknown semantic characteristics and inharmonious behaviour of input data. Most of the existing state-of-the-art methods fail to detect small true roof planes with exact boundaries due to outliers, occlusions, complex building structures, and other inconsistent nature of LiDAR data. In this paper, we have presented an improved building detection and roof plane extraction method, which is less sensitive to the outliers and unlikely to generate spurious planes. For this, a robust outlier detection algorithm has been proposed in this paper along with a robust plane-fitting algorithm based on M-estimator SAmple Consensus (MSAC) for detecting individual roof planes. Using two benchmark datasets (Australian and International Society for Photogrammetry and Remote Sensing benchmark) with different numbers of buildings and sizes, trees and point densities, we have evaluated the proposed method. Experimental results show that the method removes outliers and vegetation almost accurately and offers a high success rate in terms of completeness and correctness (between 80% and 100% per-object) for both roof plane extraction and building detection. In most of the cases, the proposed method shows above 90% correctness.

Model-free pose estimation using point cloud data

A model-free pose (relative attitude and position) estimation process using point cloud data is developed to support envisioned autonomous satellite servicing missions. Unlike model-based pose estimation that typically requires a three-dimensional geometric model of a satellite to be serviced, the model-free pose estimation presented in this paper employs object features detected in situ using point cloud data. Its overall process is similar to existing model-free pose estimation algorithms in that it requires edge detection, object boundary identification, edge vector determination to form an orthogonal triad for attitude estimation, and object area and centroid calculation for position estimation with respect to the sensor. However, significant improvements have been made toward fully autonomous, model-free pose estimation by employing the Hough transform that allows robust line fitting of jagged edges resulting from object rotations and the discrete nature of point cloud data. In addition, a plane fitting algorithm using the homogeneous transformation was developed to compute plane normal vectors to help improve attitude estimation accuracy. Using both measured and simulated point cloud data of test objects, the performance of the developed model-free pose estimation process was examined. It was able to produce accurate position and attitude of the objects. Future effort will be needed to include more general geometric features such as circles, ellipses, and arcs to provide capabilities needed toward fully autonomous model-free pose estimation process.

An Innovative Detection Method of High-Speed Railway Track Slab Supporting Block Plane Based on Point Cloud Data from 3D Scanning Technology

The dimension detection of high-speed railway track slabs is one of the most important tasks before the track slabs delivery. Based on the characteristics of a 3D scanner which can acquire a large amount of measurement data continuously and rapidly in a short time, this paper uses the integration of 3D scanner and the intelligent robot to detect the CRTSIII (China Railway Track System) track slab supporting block plane, then the dense and accurate supporting block plane point cloud data is obtained, and the point cloud data is registered with the established model. An improved Random Sample Consensus (RANSAC) plane fitting algorithm is also proposed to extract the data of supporting block plane point cloud in this paper. The detection method is verified and the quality analysis of the detection results is assessed by a lot of real point cloud data obtained on site. The results show that the method can meet the quality control of CRTSIII finished track slab and the detection standard. Compared with the traditional detection methods, the detection method proposed in this paper can complete the detection of a track slab in 7 min, which greatly improves the detection efficiency, and has better reliability. The method has wide application prospects in the field of railway component detection.

Obstacle Tracking for Unmanned Surface Vessels Using 3-D Point Cloud

In this paper, we present a method for detecting and tracking waterborne obstacles from an unmanned surface vehicle (USV) for the purpose of short-term obstacle avoidance. A stereo camera system provides a point cloud of the scene in front of the vehicle. The water surface is estimated by fitting a plane to the point cloud and outlying points are further processed to find potential obstacles. We propose a new plane fitting algorithm for water surface detection that applies a fast approximate semantic segmentation to filter the point cloud and utilizes an external IMU reading to constrain the plane orientation. A novel histogram-like depth appearance model is proposed to keep track of the identity of the detected obstacles through time and to filter out false detections that negatively impact the vehicle's automatic guidance system. The improved plane fitting algorithm and the temporal verification using depth fingerprints result in notable improvement on the challenging MODD2 data set by significantly reducing the amount of false positive detections. The proposed method is able to run in real time on board of a small-sized USV, which was used to acquire the MODD2 data set as well.

AUTOMATIC 3D RECONSTRUCTION OF BUILDINGS ROOF TOPS IN DENSELY URBANIZED AREAS

Abstract. 3D reconstruction of the urban environment constitutes a well-studied problem in the field of photogrammetry and computer vision, attracting the growing interest of the scientific community, for many years. Although the current state of the art present very impressive results, there is still room for improvements. The production of reliable and accurate 3D reconstructions is useful for a wide range of applications, such as urban planning, GIS, tax assessment, cadastre, insurance, 3D city modelling, etc. In this paper, a methodology for the automatic 3D reconstruction of buildings roof tops in densely urbanized areas, utilizing dense point clouds data, is proposed. It consists of three (3) main phases, each of which comprises a set of processing steps. In the first phase, the point cloud is simplified and smoothed. Outliers and non-roof elements are detected and removed utilizing shape, position and area criteria. In the second phase, the geometry buildings roof tops is optimized, by detecting and normalizing the edges. In the last phase, the reconstruction of the buildings roof tops is conducted. A progressive process, utilizing a plane fitting algorithm in combination with Screened Poisson Surface Reconstruction is performed. Buildings roof tops surfaces are produced and optimized. A software tool is developed and utilized for the implementation of the proposed methodology. The produced results are assessed and a comparison with another open-source software is conducted. The proposed methodology seems to be effective providing satisfactory results, as it can manage properly the really noisy point clouds of densely urbanized environments.

H-RANSAC: A HYBRID POINT CLOUD SEGMENTATION COMBINING 2D AND 3D DATA

Abstract. In this paper, we present a novel 3D segmentation approach operating on point clouds generated from overlapping images. The aim of the proposed hybrid approach is to effectively segment co-planar objects, by leveraging the structural information originating from the 3D point cloud and the visual information from the 2D images, without resorting to learning based procedures. More specifically, the proposed hybrid approach, H-RANSAC, is an extension of the well-known RANSAC plane-fitting algorithm, incorporating an additional consistency criterion based on the results of 2D segmentation. Our expectation that the integration of 2D data into 3D segmentation will achieve more accurate results, is validated experimentally in the domain of 3D city models. Results show that HRANSAC can successfully delineate building components like main facades and windows, and provide more accurate segmentation results compared to the typical RANSAC plane-fitting algorithm.

LANDSLIDE MONITORING AND ASSESSMENT FOR HIGHWAY RETAININGWALL: THE CASE STUDY OF TAŞKENT(TURKEY) LANDSLIDE

Abstract. Landslide monitoring and assessment of the highways retaining walls are a crucial task. Because there exist a risk and danger with regard to the movement of the wall to the highway by landslide force that may spread further. To evaluate the changing, movements have to be monitored. For this reason, we practised mobile LiDAR surveys on the landslide effected wall on the highway. The usage of the mobile LiDAR systems have significantly increased in recent years, especially for road management. Currently, mobile LiDAR technology is capable of measuring the earth surface with high precision and density as a 3D point clouds. As stated in this study, the point cloud data processing have been analysed further and the wall surface points fitted to a plane object for monitoring of the landslide effects. This study focuses on different plane fitting algorithms which represents the retaining wall, a performance assessment and evaluation of the deformation between two plane models. The analysis indicates that the uncertainty of the measurements between the two epochs on stable areas survey was within ±2 cm. According to the experimental results, the proposed methods performed promising results that can be used for monitoring of retaining walls for fast processing and assessment.

Disparity refinement process based on RANSAC plane fitting for machine vision applications

This paper presents a new disparity map refinement process for stereo matching algorithm and the refinement stage that will be implemented by partitioning the place or mask image and re-projected to the preliminary disparity images. This process is to refine the noise and sparse of initial disparity map from weakly textured. The plane fitting algorithm is using Random Sample Consensus. Two well-known stereo matching algorithms have been tested on this framework with different filtering techniques applied at disparity refinement stage. The framework is evaluated on three Middlebury datasets. The experimental results show that the proposed framework produces better-quality and more accurate than normal flow state-of-the-art stereo matching algorithms. The performance evaluations are based on standard image quality metrics i.e. structural similarity index measure, peak signal-to-noise ratio and mean square error.

Preprocessing Algorithms for Filtering Airborne LiDAR Data

Filter of airborne LiDAR data is a primary step of data processing.This paper reviews the literatures of filter algorithms from aspects of theory and performance. The moving plane fitting algorithm is introduced and improved especially. In addition, the Experiments show the method is effective and lays a foundation for the subsequent regularization of complex building boundaries.