Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling

Terrestrial laser scanners (TLS) capture a large number of 3D points rapidly, with high precision and spatial resolution. These scanners are used for applications as diverse as modeling architectural or engineering structures, but also high-resolution mapping of terrain. The noise of the observations cannot be assumed to be strictly corresponding to white noise: besides being heteroscedastic, correlations between observations are likely to appear due to the high scanning rate. Unfortunately, if the variance can sometimes be modeled based on physical or empirical considerations, the latter are more often neglected. Trustworthy knowledge is, however, mandatory to avoid the overestimation of the precision of the point cloud and, potentially, the non-detection of deformation between scans recorded at different epochs using statistical testing strategies. The TLS point clouds can be approximated with parametric surfaces, such as planes, using the Gauss–Helmert model, or the newly introduced T-splines surfaces. In both cases, the goal is to minimize the squared distance between the observations and the approximated surfaces in order to estimate parameters, such as normal vector or control points. In this contribution, we will show how the residuals of the surface approximation can be used to derive the correlation structure of the noise of the observations. We will estimate the correlation parameters using the Whittle maximum likelihood and use comparable simulations and real data to validate our methodology. Using the least-squares adjustment as a “filter of the geometry” paves the way for the determination of a correlation model for many sensors recording 3D point clouds.

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Fitting Terrestrial Laser Scanner Point Clouds with T-Splines: Local Refinement Strategy for Rigid Body Motion

Remote Sensing ◽

10.3390/rs13132494 ◽

2021 ◽

Vol 13 (13) ◽

pp. 2494

Author(s):

Gaël Kermarrec ◽

Niklas Schild ◽

Jan Hartmann

Keyword(s):

Point Cloud ◽

Goodness Of Fit ◽

Laser Scanner ◽

Point Clouds ◽

Statistical Testing ◽

Computational Time ◽

Terrestrial Laser Scanner ◽

Reference Surface ◽

Local Refinement ◽

Surface Approximation

T-splines have recently been introduced to represent objects of arbitrary shapes using a smaller number of control points than the conventional non-uniform rational B-splines (NURBS) or B-spline representatizons in computer-aided design, computer graphics and reverse engineering. They are flexible in representing complex surface shapes and economic in terms of parameters as they enable local refinement. This property is a great advantage when dense, scattered and noisy point clouds are approximated using least squares fitting, such as those from a terrestrial laser scanner (TLS). Unfortunately, when it comes to assessing the goodness of fit of the surface approximation with a real dataset, only a noisy point cloud can be approximated: (i) a low root mean squared error (RMSE) can be linked with an overfitting, i.e., a fitting of the noise, and should be correspondingly avoided, and (ii) a high RMSE is synonymous with a lack of details. To address the challenge of judging the approximation, the reference surface should be entirely known: this can be solved by printing a mathematically defined T-splines reference surface in three dimensions (3D) and modeling the artefacts induced by the 3D printing. Once scanned under different configurations, it is possible to assess the goodness of fit of the approximation for a noisy and potentially gappy point cloud and compare it with the traditional but less flexible NURBS. The advantages of T-splines local refinement open the door for further applications within a geodetic context such as rigorous statistical testing of deformation. Two different scans from a slightly deformed object were approximated; we found that more than 40% of the computational time could be saved without affecting the goodness of fit of the surface approximation by using the same mesh for the two epochs.

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Comparison of Depth Camera and Terrestrial Laser Scanner in Monitoring Structural Deflections

Sensors ◽

10.3390/s21010201 ◽

2020 ◽

Vol 21 (1) ◽

pp. 201

Author(s):

Michael Bekele Maru ◽

Donghwan Lee ◽

Kassahun Demissie Tola ◽

Seunghee Park

Keyword(s):

Optical Sensors ◽

Point Cloud ◽

Three Dimensional ◽

Laser Scanner ◽

Point Clouds ◽

Depth Camera ◽

Terrestrial Laser Scanner ◽

Cloud Data ◽

3D Point Clouds ◽

3D Information

Modeling a structure in the virtual world using three-dimensional (3D) information enhances our understanding, while also aiding in the visualization, of how a structure reacts to any disturbance. Generally, 3D point clouds are used for determining structural behavioral changes. Light detection and ranging (LiDAR) is one of the crucial ways by which a 3D point cloud dataset can be generated. Additionally, 3D cameras are commonly used to develop a point cloud containing many points on the external surface of an object around it. The main objective of this study was to compare the performance of optical sensors, namely a depth camera (DC) and terrestrial laser scanner (TLS) in estimating structural deflection. We also utilized bilateral filtering techniques, which are commonly used in image processing, on the point cloud data for enhancing their accuracy and increasing the application prospects of these sensors in structure health monitoring. The results from these sensors were validated by comparing them with the outputs from a linear variable differential transformer sensor, which was mounted on the beam during an indoor experiment. The results showed that the datasets obtained from both the sensors were acceptable for nominal deflections of 3 mm and above because the error range was less than ±10%. However, the result obtained from the TLS were better than those obtained from the DC.

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Estimating tree stem diameters and volume from smartphone photogrammetric point clouds

Forestry An International Journal of Forest Research ◽

10.1093/forestry/cpz067 ◽

2019 ◽

Vol 93 (3) ◽

pp. 411-429 ◽

Cited By ~ 3

Author(s):

Maria Immacolata Marzulli ◽

Pasi Raumonen ◽

Roberto Greco ◽

Manuela Persia ◽

Patrizia Tartarino

Keyword(s):

Low Cost ◽

Three Dimensional ◽

Laser Scanner ◽

Point Clouds ◽

Stem Volume ◽

Forest Plot ◽

3D Point Clouds ◽

Dense Point ◽

Minimum Number ◽

Scale Point

Abstract Methods for the three-dimensional (3D) reconstruction of forest trees have been suggested for data from active and passive sensors. Laser scanner technologies have become popular in the last few years, despite their high costs. Since the improvements in photogrammetric algorithms (e.g. structure from motion—SfM), photographs have become a new low-cost source of 3D point clouds. In this study, we use images captured by a smartphone camera to calculate dense point clouds of a forest plot using SfM. Eighteen point clouds were produced by changing the densification parameters (Image scale, Point density, Minimum number of matches) in order to investigate their influence on the quality of the point clouds produced. In order to estimate diameter at breast height (d.b.h.) and stem volumes, we developed an automatic method that extracts the stems from the point cloud and then models them with cylinders. The results show that Image scale is the most influential parameter in terms of identifying and extracting trees from the point clouds. The best performance with cylinder modelling from point clouds compared to field data had an RMSE of 1.9 cm and 0.094 m3, for d.b.h. and volume, respectively. Thus, for forest management and planning purposes, it is possible to use our photogrammetric and modelling methods to measure d.b.h., stem volume and possibly other forest inventory metrics, rapidly and without felling trees. The proposed methodology significantly reduces working time in the field, using ‘non-professional’ instruments and automating estimates of dendrometric parameters.

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Extracting Geometric Edges from 3D Point Clouds Based on Normal Vector Change

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.571-572.729 ◽

2014 ◽

Vol 571-572 ◽

pp. 729-734

Author(s):

Jia Li ◽

Huan Lin ◽

Duo Qiang Zhang ◽

Xiao Lu Xue

Keyword(s):

Point Clouds ◽

Detection Algorithm ◽

Growth Strategy ◽

Normal Vector ◽

Geometric Morphometric ◽

3D Point Clouds ◽

Real Scene ◽

Edge Points ◽

Normal Vectors ◽

Change Intensity

Normal vector of 3D surface is important differential geometric property over localized neighborhood, and its abrupt change along the surface directly reflects the variation of geometric morphometric. Based on this observation, this paper presents a novel edge detection algorithm in 3D point clouds, which utilizes the change intensity and change direction of adjacent normal vectors and is composed of three steps. First, a two-dimensional grid is constructed according to the inherent data acquisition sequence so as to build up the topology of points. Second, by this topological structure preliminary edge points are retrieved, and the potential directions of edges passing through them are estimated according to the change of normal vectors between adjacent points. Finally, an edge growth strategy is designed to regain the missing edge points and connect them into complete edge lines. The results of experiment in a real scene demonstrate that the proposed algorithm can extract geometric edges from 3D point clouds robustly, and is able to reduce edge quality’s dependence on user defined parameters.

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Mapping Forest Structure Using UAS inside Flight Capabilities

Sensors ◽

10.3390/s18072245 ◽

2018 ◽

Vol 18 (7) ◽

pp. 2245 ◽

Cited By ~ 6

Author(s):

Karel Kuželka ◽

Peter Surový

Keyword(s):

Least Squares ◽

Forest Structure ◽

European Beech ◽

Point Clouds ◽

Unmanned Aerial Systems ◽

Structure Mapping ◽

Close Range Photogrammetry ◽

3D Point Clouds ◽

Ellipse Method ◽

Close Range

We evaluated two unmanned aerial systems (UASs), namely the DJI Phantom 4 Pro and DJI Mavic Pro, for 3D forest structure mapping of the forest stand interior with the use of close-range photogrammetry techniques. Assisted flights were performed within two research plots established in mature pure Norway spruce (Picea abies (L.) H. Karst.) and European beech (Fagus sylvatica L.) forest stands. Geotagged images were used to produce georeferenced 3D point clouds representing tree stem surfaces. With a flight height of 8 m above the ground, the stems were precisely modeled up to a height of 10 m, which represents a considerably larger portion of the stem when compared with terrestrial close-range photogrammetry. Accuracy of the point clouds was evaluated by comparing field-measured tree diameters at breast height (DBH) with diameter estimates derived from the point cloud using four different fitting methods, including the bounding circle, convex hull, least squares circle, and least squares ellipse methods. The accuracy of DBH estimation varied with the UAS model and the diameter fitting method utilized. With the Phantom 4 Pro and the least squares ellipse method to estimate diameter, the mean error of diameter estimates was −1.17 cm (−3.14%) and 0.27 cm (0.69%) for spruce and beech stands, respectively.

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Bézier Curve and Surface Fitting of 3D Point Clouds Through Genetic Algorithms, Functional Networks and Least-Squares Approximation

Lecture Notes in Computer Science - Computational Science and Its Applications – ICCSA 2007 ◽

10.1007/978-3-540-74477-1_62 ◽

2007 ◽

pp. 680-693 ◽

Cited By ~ 40

Author(s):

Akemi Gálvez ◽

Andrés Iglesias ◽

Angel Cobo ◽

Jaime Puig-Pey ◽

Jesús Espinola

Keyword(s):

Genetic Algorithms ◽

Least Squares ◽

Point Clouds ◽

Surface Fitting ◽

Bézier Curve ◽

Bezier Curve ◽

Functional Networks ◽

Least Squares Approximation ◽

3D Point Clouds ◽

Curve And Surface Fitting

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A novel method for extracting skeleton of fruit tree from 3D point clouds

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962320500518 ◽

2020 ◽

pp. 2050051

Author(s):

Shenglian lu ◽

Guo Li ◽

Jian Wang

Keyword(s):

Laser Scanning ◽

Laser Scanner ◽

Point Clouds ◽

Fruit Trees ◽

Fruit Tree ◽

Tree Canopy ◽

3D Point Clouds ◽

Novel Method ◽

Manual Interaction ◽

Traditional Approaches

Tree skeleton could be useful to agronomy researchers because the skeleton describes the shape and topological structure of a tree. The phenomenon of organs’ mutual occlusion in fruit tree canopy is usually very serious, this should result in a large amount of data missing in directed laser scanning 3D point clouds from a fruit tree. However, traditional approaches can be ineffective and problematic in extracting the tree skeleton correctly when the tree point clouds contain occlusions and missing points. To overcome this limitation, we present a method for accurate and fast extracting the skeleton of fruit tree from laser scanner measured 3D point clouds. The proposed method selects the start point and endpoint of a branch from the point clouds by user’s manual interaction, then a backward searching is used to find a path from the 3D point cloud with a radius parameter as a restriction. The experimental results in several kinds of fruit trees demonstrate that our method can extract the skeleton of a leafy fruit tree with highly accuracy.

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Robust external calibration of terrestrial laser scanner and digital camera for structural monitoring

Journal of Applied Geodesy ◽

10.1515/jag-2018-0038 ◽

2019 ◽

Vol 13 (2) ◽

pp. 105-134 ◽

Cited By ~ 2

Author(s):

Mohammad Omidalizarandi ◽

Boris Kargoll ◽

Jens-André Paffenholz ◽

Ingo Neumann

Keyword(s):

Em Algorithm ◽

Laser Scanner ◽

Digital Camera ◽

Point Clouds ◽

Deformation Monitoring ◽

Deformation Analysis ◽

Terrestrial Laser Scanner ◽

External Calibration ◽

3D Point Clouds ◽

Calibration Parameters

Abstract In the last two decades, the integration of a terrestrial laser scanner (TLS) and digital photogrammetry, besides other sensors integration, has received considerable attention for deformation monitoring of natural or man-made structures. Typically, a TLS is used for an area-based deformation analysis. A high-resolution digital camera may be attached on top of the TLS to increase the accuracy and completeness of deformation analysis by optimally combining points or line features extracted both from three-dimensional (3D) point clouds and captured images at different epochs of time. For this purpose, the external calibration parameters between the TLS and digital camera needs to be determined precisely. The camera calibration and internal TLS calibration are commonly carried out in advance in the laboratory environments. The focus of this research is to highly accurately and robustly estimate the external calibration parameters between the fused sensors using signalised target points. The observables are the image measurements, the 3D point clouds, and the horizontal angle reading of a TLS. In addition, laser tracker observations are used for the purpose of validation. The functional models are determined based on the space resection in photogrammetry using the collinearity condition equations, the 3D Helmert transformation and the constraint equation, which are solved in a rigorous bundle adjustment procedure. Three different adjustment procedures are developed and implemented: (1) an expectation maximization (EM) algorithm to solve a Gauss-Helmert model (GHM) with grouped t-distributed random deviations, (2) a novel EM algorithm to solve a corresponding quasi-Gauss-Markov model (qGMM) with t-distributed pseudo-misclosures, and (3) a classical least-squares procedure to solve the GHM with variance components and outlier removal. The comparison of the results demonstrates the precise, reliable, accurate and robust estimation of the parameters in particular by the second and third procedures in comparison to the first one. In addition, the results show that the second procedure is computationally more efficient than the other two.

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INDOOR NAVIGATION FROM POINT CLOUDS: 3D MODELLING AND OBSTACLE DETECTION

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprsarchives-xli-b4-275-2016 ◽

2016 ◽

Vol XLI-B4 ◽

pp. 275-281 ◽

Cited By ~ 8

Author(s):

L. Díaz-Vilariño ◽

P. Boguslawski ◽

K. Khoshelham ◽

H. Lorenzo ◽

L. Mahdjoubi

Keyword(s):

Laser Scanner ◽

Route Planning ◽

Point Clouds ◽

3D Modelling ◽

Obstacle Detection ◽

Indoor Navigation ◽

3D Point Clouds ◽

Emergency Assistance ◽

Planning Methodology ◽

Real State

In the recent years, indoor modelling and navigation has become a research of interest because many stakeholders require navigation assistance in various application scenarios. The navigational assistance for blind or wheelchair people, building crisis management such as fire protection, augmented reality for gaming, tourism or training emergency assistance units are just some of the direct applications of indoor modelling and navigation. <br><br> Navigational information is traditionally extracted from 2D drawings or layouts. Real state of indoors, including opening position and geometry for both windows and doors, and the presence of obstacles is commonly ignored. <br><br> In this work, a real indoor-path planning methodology based on 3D point clouds is developed. The value and originality of the approach consist on considering point clouds not only for reconstructing semantically-rich 3D indoor models, but also for detecting potential obstacles in the route planning and using these for readapting the routes according to the real state of the indoor depictured by the laser scanner.

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