Triangulation Of Points Research Articles

A multi‐degree‐of‐freedom monitoring method for slope displacement based on stereo vision

AbstractThree‐dimensional displacement monitoring over long distances has been a long‐standing concern in the structural health monitoring industry. In this study, a multi‐degree‐of‐freedom slope displacement monitoring method is developed by fusing computer vision and the 3D point triangulation method. Attributed to this method, the problems of outdoor binocular camera calibration, multi‐target mismatching, and outdoor illumination effects were solved. First, a two‐stage camera calibration method is proposed to accurately calibrate intrinsic and extrinsic camera parameters under a large field of view and long working distance conditions. Second, the adaptive spatial‐frequency method is proposed to calculate the coding and pixel coordinates of the monitored target. In this step, to solve the problem of mismatching monitored points in different camera frames, the Augmented Reality University of Cordoba code is introduced to provide a unique identity code for each monitored point. To mitigate the impact of illumination and other factors on pixel coordinate calculation, an adaptive pixel coordinate calculation method that combines information from the spatial and frequency domains is proposed., Third, based on the intrinsic and extrinsic parameters of the stereo camera and the pixel coordinates of the monitored points, the 3D coordinates of the monitored points are obtained through triangulation. Finally, the accuracy experiments and stability experiments are conducted. According to the results of the experiments, the measurement distance is positively correlated with the measurement error. And the baseline length is negatively correlated with the measurement error in the z‐direction. Ultimately, we suggest that the ratio of baseline length to measurement distance should be greater than 40%. When the recommended value is satisfied, the measurement error is less than 1 mm when the measurement distance is less than 40 m. When the measurement distance is equal to 90 m, the measurement error is less than 5 mm. Meanwhile, stability experiments of the algorithm were carried out, and in a period of outdoor validation experiments, the fluctuations were only sub‐millimeter, demonstrating good anti‐interference performance. Moreover, the method proposed in this study successfully monitored a landslide disaster in Guangxi, which demonstrated its outstanding practical application capabilities.

Certifiable Solver for Real-Time N-View Triangulation

Cutting-edge field robotic systems, such as UAV or autonomous cars, demand fast and optimal solutions for any component at the core of their critical navigational tasks. Among them, we focus on the triangulation of image points from multiple views, which is a cornerstone for more complex tasks such as visual localization and SLAM. In this letter we present a fast and certifiable solver for the N-view triangulation problem that doesn't require any specific optimization software package and can be implemented with any linear algebra library. The proposal relies on a series of linear convexifications which, in the limit, recovers the original problem, allowing us to solve problem instances with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N=10$</tex-math></inline-formula> views in 150 microseconds on a standard desktop computer. On real data our solver obtains and certifies the optimal solution in more than 99% of the problem instances.

Multi-view triangulation without correspondences

We introduce a novel method to solve the joint problem of correspondence and triangulation of points from multiple calibrated perspective views and show its application to counting the number of leaves present on plants photographed from multiple angles in phenotyping facilities. Assuming there is a set of n calibrated views of an object, the input to our algorithm is a set of 2D points (e.g., leaf tips, fruits, flowers) detected in each of the n views, and the output is a set of 3D points corresponding to the 2D points when re-projected on views. Our approach is robust to noise and occlusion. In particular, it is not required for all points to be visible from one of the views, as our algorithm can infer that a point is occluded by reasoning on the 3D geometry of the scene. Our algorithm is suitable for many points (approx. thousands) reconstructed from a reduced set of views (up to 15). For example, our implementation finds the correspondence of 20 points captured by six cameras in about one second on consumer hardware. We evaluate the performance on synthetic data as well as real examples. We show that the accuracy of leaf counting from multi-view images is drastically improved by our algorithm.

Improved stretch factor of Delaunay triangulations of points in convex position

Improved stretch factor of Delaunay triangulations of points in convex position

Power Arcing Fault Detection and Location Algorithm Solution in Two and Three Dimensions Euclidean Planes Using an Analytic Geometry Method Instead of an Iterative or Numerical Method

The relationship between the electric current and the magnetism is well demonstrated by the Faraday's induction and conductivity laws. Under this concept, it follows that, through intensive laboratory experiments, it has been established that the arcing fault current path related sparks are indeed source of ElectroMagnetic Radiated (EMR) signals waves. These EMR can be detected and located at a relatively remote distance, with the aid of directional antennas arrays, at considerable and reasonable accuracy. Under this novel concept of power arcing fault source point triangulation, the arc EMR data play a critical role in providing essential timing information onto which the arc fault detection and location algorithm is based. Thus, from these arc EMR recorded and gathered data, the signals Time Differences Of Arrival (TDOA) information or signatures can be easily extracted from a pair of antennas, with the aid of an appropriate signal processing tool, namely the cross-correlation (Xcorr) function. Since the electric arc phenomenon is unpredictable practically, therefore, the use of the arc signal Time Of Arrival (TOA), is impossible for the fault source point triangulation solution. In contrast, the values of TDOA seem to be efficient for solving the system of hyperbolic equations which has been imposed by this particular field measurement structure and constraints. It is of interest to mention that, the arc fault EMR field measurement structure and constraints are given and determined by the distributed antennas arrays locations or positions only. In other words, with the knowledge of both the antennas arrays locations Cartesian Coordinates (CC), together with the TDOA values, it is possible to pinpoint the unknown target power arcing fault exact source point position or location, not only in two-dimensions (2D), but also in three-dimensions (3D) Euclidean plane. Thus, this kind of arc fault source point position or location solution finding is generally referred to as a source point triangulation method. This source point triangulation method consists of solving a system of hyperbolic equations as aforementioned. In fact, under a geometry analysis process, it follows that, if only if the arcing fault hazard formation time is known in advance, therefore, the solution of a system of hyperbolic equations consists of finding the intersection point of at least two or more circles. Such that, each of these circles, will be centered at each antenna in such a way that each circle will have a radius given by the distance derived from the value of TOA together with the power arcing fault hazard ignition time stamp or signature. In contrast, since the arcing fault hazard formation stage time is unknown in practice, therefore the solution of the system of hyperbolic equations consists of finding the intersection point of at least two or more hyperbolas. Such that each of these hyperbolas will have a focal point determined by the location of each antenna and the distance between pair of foci will be given by the values of TDOA. However, generally, a system of hyperbolic equations can be solved either with the aid of an analytic method or with that of a numerical method (also known as iterative method). Unlike the majority of this research field related relevant published literature into which the iterative methods have been used intensively, this paper presents an accurate analytic geometry method in order to solve the electric arc faults EMR source point exact location or position. As a result, it appears that, this novel proposed analytic geometry method has shown its potential in clarifying the power arcing fault source position or location, at a reasonable and considerable accuracy.

ORB-TEDM: An RGB-D SLAM Approach Fusing ORB Triangulation Estimates and Depth Measurements

3-D position estimates of feature points in traditional RGB-D simultaneous localization and mapping (SLAM) systems are directly obtained by depth measurements. However, the available information provided by the triangulation of feature points has not been involved. In this article, a novel RGB-D SLAM approach is proposed based on the ORB-SLAM2 system, by fusing the triangulation estimates and depth measurements of ORB features, termed ORB-TEDM. Specifically, uncertainties on both the pose estimate of the camera and triangulation of ORB features are rigorously computed in a closed form for the ORB-SLAM2 system using covariance propagation and implicit differentiation. On the other hand, the uncertainty is evaluated for the 3-D position estimate of each map point obtained by its depth measurement from the RGB-D camera. Then, the triangulation results and position estimates from depth measurements are further fused with the covariance intersection (CI) filter to generate a more precise and consistent map. In addition, a more flexible selection policy of map points and keyframes is designed based on the uncertainty evaluation results. As a consequence, a more accurate and robust RGB-D SLAM system can be achieved. It is worthwhile to point out that the obtained closed-form solution to uncertainties on estimates of the camera pose and feature points can facilitate further development of the ORB-SLAM framework, such as active SLAM and multisensor SLAM. The experimental results on public datasets and in real-world environments are presented to show the effectiveness of the proposed approach.

Wearable biosensors have the potential to monitor physiological changes associated with opioid overdose among people who use drugs: A proof-of-concept study in a real-world setting

IntroductionWearable biosensors have the potential to monitor physiological change associated with opioid overdose among people who use drugs. MethodsWe enrolled 16 individuals who reported ≥ 4 daily opioid use events within the previous 30 day. Each was assigned a wearable biosensor that measured respiratory rate (RR) and actigraphy every 15 s for 5 days and also completed a daily interview assessing drug use. We describe the volume of RR data collected, how it varied by participant characteristics and drug use over time using repeated measures one-way ANOVA, episodes of acute respiratory depression (≤5 breaths/minute), and self-reported overdose experiences. ResultsWe captured 1626.4 h of RR data, an average of 21.7 daily hours/participant over follow-up. Individuals with longer injection careers and those engaging in polydrug use captured significantly fewer total hours of respiratory data over follow-up compared to those with shorter injections careers (94.7 vs. 119.9 h, p = 0.04) and injecting fentanyl exclusively (98.7 vs. 119.5 h, p = 0.008), respectively. There were 385 drug use events reported over follow-up. There were no episodes of acute respiratory depression which corresponded with participant reports of overdose experiences. DiscussionOur preliminary findings suggest that using a wearable biosensor to monitor physiological changes associated with opioid use was feasible. However, more sensitive biosensors that facilitate triangulation of multiple physiological data points and larger studies of longer duration are needed.

Voronoi Diagram and Delaunay Triangulation with Independent and Dependent Geometric Uncertainties

We address the problems of constructing the Voronoi diagram (VD) and Delaunay triangulation (DT) of points in the plane with mutually dependent location uncertainties, testing their stability, and computing their components. Point coordinate uncertainties are modeled with the Linear Parametric Geometric Uncertainty Model (LPGUM), a deterministic, expressive and computationally efficient first order linear approximation of geometric uncertainty that supports parametric dependencies between point locations. We define an uncertain three-point circle and its properties and present in-circle-test algorithms for the dependent and the independent cases whose respective time complexity is [Formula: see text] and [Formula: see text], where [Formula: see text] is the number of parameters that describe the points location uncertainty and [Formula: see text] is the complexity of quartic [Formula: see text]-variable optimization. We define the uncertain VD and DT of [Formula: see text] LPGUM points and show that an unstable VD may have an exponential number of topologically different instances. We describe algorithms for testing VD and DT stability whose time complexity is [Formula: see text] and [Formula: see text] for the dependent and independent cases when the nominal (exact) VD is given. We present algorithms to compute the vertices, edges, and faces of uncertain VD and DT for the independent case whose complexity is [Formula: see text] time and [Formula: see text] space. Finally, we describe algorithms for answering exact and uncertain point location queries in a stable uncertain VD and for dynamically updating it in [Formula: see text] and [Formula: see text] average case time complexity for the independent and dependent cases.

Survey and Evaluation of RGB-D SLAM

The traditional visual SLAM systems take the monocular or stereo camera as input sensor, with complex map initialization and map point triangulation steps needed for 3D map reconstruction, which are easy to fail, computationally complex and can cause noisy measurements. The emergence of RGB-D camera which provides RGB image together with depth information breaks this situation. While a number of RGB-D SLAM systems have been proposed in recent years, the current classification research on RGB-D SLAM is very lacking, and their advantages and shortcomings remain unclear regarding different applications and perturbations, such as illumination transformation, noise and rolling shutter effect of sensors. In this paper, we mainly introduced the basic concept and structure of the RGB-D SLAM system, and then introduced the differences between the various RGB-D SLAM systems in the three aspects of tracking, mapping, and loop detection, and we make a classification study on different RGB-D SLAM algorithms according to the three aspect. Furthermore, we discuss some advanced topics and open problems of RGB-D SLAM, hoping that it will help for future exploring. In the end, we conducted a large number of evaluation experiments on multiple RGB-D SLAM systems, and analyzed their advantages and disadvantages, as well as performance differences in different application scenarios, and provided references for researchers and developers.

Spatiotemporal Bundle Adjustment for Dynamic 3D Human Reconstruction in the Wild.

Bundle adjustment jointly optimizes camera intrinsics and extrinsics and 3D point triangulation to reconstruct a static scene. The triangulation constraint, however, is invalid for moving points captured in multiple unsynchronized videos and bundle adjustment is not designed to estimate the temporal alignment between cameras. We present a spatiotemporal bundle adjustment framework that jointly optimizes four coupled sub-problems: estimating camera intrinsics and extrinsics, triangulating static 3D points, as well as sub-frame temporal alignment between cameras and computing 3D trajectories of dynamic points. Key to our joint optimization is the careful integration of physics-based motion priors within the reconstruction pipeline, validated on a large motion capture corpus of human subjects. We devise an incremental reconstruction and alignment algorithm to strictly enforce the motion prior during the spatiotemporal bundle adjustment. This algorithm is further made more efficient by a divide and conquer scheme while still maintaining high accuracy. We apply this algorithm to reconstruct 3D motion trajectories of human bodies in dynamic events captured by multiple uncalibrated and unsynchronized video cameras in the wild. To make the reconstruction visually more interpretable, we fit a statistical 3D human body model to the asynchronous video streams. Compared to the baseline, the fitting significantly benefits from the proposed spatiotemporal bundle adjustment procedure. Because the videos are aligned with sub-frame precision, we reconstruct 3D motion at much higher temporal resolution than the input videos. Website: http://www.cs.cmu.edu/~ILIM/projects/IM/STBA.

Non-Invertible cancellable fingerprint template for fingerprint biometric

Fingerprint biometric has emerged as a highly successful biometric recognition system and find its application in the diverse domain. The fingerprint template database needs to be protected from unauthorized access. If an adversary has acquired the unprotected fingerprint template, then he/she may reconstruct original fingerprint which can be used for unauthorized access of all the systems where the same fingerprint has been used. Hence, securing the fingerprint template is required. In this paper, a non-invertible cancellable fingerprint template based on information extracted from the Delaunay triangulation of minutiae points is proposed. For making the template cancellable a user-specific key of a random binary string is used. The proposed template is revocable, diverse, secure and also gives a good recognition accuracy. The proposed template is tested with a standard FVC2002 database and gives good results as compared with the latest methods.

Automated architectural reconstruction using reference planes under convex optimization

In this paper, a method for the automated reconstruction of architectures from two views of a monocular camera is proposed. While this research topic has been studied over the last few decades, we contend that a satisfactory approach has not yet been devised. Here, a new method to solve the same problem with several points of novelty is proposed. First, reference planes are automatically detected using color, straight lines, and edge/vanishing points. This approach is quite robust and fast even when different views and complicated conditions are presented. Second, the camera pose and 3D points are accurately estimated by a two-view geometry constraint in the convex optimization approach. It has been demonstrated that camera rotations are appropriately estimated, while translations induce a significant error in short baseline images. To overcome this problem, we rely only on reference planes to estimate image homography instead of using the conventional camera pose estimation method. Thus, the problem associated with short baseline images is adequately addressed. The 3D points and translation are then simultaneously triangulated. Furthermore, both the homography and 3D point triangulation are computed via the convex optimization approach. The error of back-projection and measured points is minimized in L ∞-norm so as to overcome the local minima problem of the canonical L 2-norm method. Consequently, extremely accurate homography and point clouds can be achieved with this scheme. In addition, a robust plane fitting method is introduced to describe a scene. The corners are considered as properties of the plane in order to limit the boundary. Thus, it is necessary to find the exact corresponding corner positions by searching along the epipolar line in the second view. Finally, the texture of faces is mapped from 2D images to a 3D plane. The simulation results demonstrate the effectiveness of the proposed method for scenic images in an outdoor environment.

A Novel Improved Genetic Algorithm Based on the Fixed Point Theorem and Triangulation Method

Genetic algorithms are widely used for solving a multitude of complex problems. Methods for increasing the genetic algorithms accuracy are of great importance. One such method consist of using the fixed point theory combined with an improved genetic algorithm. This paper aims to provide such an algorithm with an increased convergence accuracy. In order to increase the algorithm operates on a simplicial triangulation over the searching space. We use the crossover, mutation and increase dimension genetic operators to obtain a convergent population that contains only fully labelled simplexes. In order to obtain better results, we use a custom increase dimension operator that significantly boosts the overall fitness. The increase dimension operator converts non-labelled individuals into nearly labelled/fully labelled ones. The solution, the global optimum point, is obtained after applying the Hessian matrix onto the final population. Our obtained results clearly show an improvement over existing work due to implementation particularities of the algorithm.

Self-calibration and visual SLAM with a multi-camera system on a micro aerial vehicle

The use of a multi-camera system enables a robot to obtain a surround view, and thus, maximize its perceptual awareness of its environment. If vision-based simultaneous localization and mapping (vSLAM) is expected to provide reliable pose estimates for a micro aerial vehicle (MAV) with a multi-camera system, an accurate calibration of the multi-camera system is a necessary prerequisite. We propose a novel vSLAM-based self-calibration method for a multi-camera system that includes at least one calibrated stereo camera, and an arbitrary number of monocular cameras. We assume overlapping fields of view to only exist within stereo cameras. Our self-calibration estimates the inter-camera transforms with metric scale; metric scale is inferred from calibrated stereo. On our MAV, we set up each camera pair in a stereo configuration which facilitates the estimation of the MAV’s pose with metric scale. Once the MAV is calibrated, the MAV is able to estimate its global pose via a multi-camera vSLAM implementation based on the generalized camera model. We propose a novel minimal and linear 3-point algorithm that uses relative rotation angle measurements from a 3-axis gyroscope to recover the relative motion of the MAV with metric scale and from 2D-2D feature correspondences. This relative motion estimation does not involve scene point triangulation. Our constant-time vSLAM implementation with loop closures runs on-board the MAV in real-time. To the best of our knowledge, no published work has demonstrated real-time on-board vSLAM with loop closures. We show experimental results from simulation experiments, and real-world experiments in both indoor and outdoor environments.

A graph-based method for fitting planar B-spline curves with intersections

Abstract The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing outliers. A skeleton representation is utilized to represent the topological structure which is further used to create a weighted graph for deciding the merging of curve segments. Different to existing approaches which utilize local shape information near intersections, our method considers shape characteristics of curve segments in a larger scope and is thus capable of giving more satisfactory results. By fitting each group of data points with a B-spline curve, we solve the problems of curve structure reconstruction from point clouds, as well as the vectorization of simple line drawing images by drawing lines reconstruction.

Highly Parallel Algorithm for Large Data In–Core and Out–Core Triangulation in E 2 and E 3

Abstract A triangulation of points in E 2 , or a tetrahedronization of points in E 3 , is used in many applications. It is not necessary to fulfill the Delaunay criteria in all cases. For large data (more then 5 · 10 7 points),parallel methods are used for the purpose of decreasingrun–time. A new approach for fast, effective and highly parallel CPU and GPU triangulation, or tetrahedronization, of large data sets in E 2 or E 3 suitable for in–core and out–core memory processing, is proposed. Experimental results proved that the resulting triangulation/tetrahedralization is close to the Delaunay triangulation/tetrahedralization. It also demonstrates the applicability of the methodproposed in applications.

Short-Range Sensor for Underwater Robot Navigation using Line-lasers and Vision

This paper investigates a minimalistic laser-based range sensor, used for underwater inspection by Autonomous Underwater Vehicles (AUV). This range detection system system comprise two lasers projecting vertical lines, parallel to a camera's viewing axis, into the environment. Using both lasers for distance estimation, the sensor offers three dimensional interpretation of the environment. This is obtained by triangulation of points extracted from the image using the Hough Transform. We evaluate the system in simulation and by physical proof-of-concept experiments on an OpenROV platform.

Tight stretch factors for [formula omitted]- and [formula omitted]-Delaunay triangulations

In this paper we determine the exact stretch factor of L∞-Delaunay triangulations of points in the plane. We do this not only when the distance between the points is defined by the usual L2-metric but also when it is defined by the Lp-metric, for any p∈[1,∞]. We then apply this result to compute the exact stretch factor of L1-Delaunay triangulations when the distance between the points is defined by the L1-, L∞-, or L2-metric.In the important case of the L2-metric, we obtain that the stretch factor of L1-Delaunay and L∞-Delaunay triangulations is exactly 4+22≈2.61. This is the first time that the stretch factor of an Lp-Delaunay triangulation, for any p∈[1,∞], is determined exactly. We show, in particular, how to construct between any two points a and b of an L1-Delaunay or L∞-Delaunay triangulation a path whose length is no more than 4+22 times the Euclidean distance between a and b. This improves the bound of 10 by Chew (SoCG '86) [5]. We also describe families of point sets whose L1-Delaunay or L∞-Delaunay triangulation has a stretch factor that can be made arbitrarily close to 4+22.

Greedy Geometric Algorithms for Collection of Balls, with Applications to Geometric Approximation and Molecular Coarse‐Graining

AbstractChoosing balls that best approximate a 3D object is a non‐trivial problem. To answer it, we first address the inner approximation problem, which consists of approximating an object defined by a union of n balls with balls defining a region . This solution is further used to construct an outer approximation enclosing the initial shape, and an interpolated approximation sandwiched between the inner and outer approximations. The inner approximation problem is reduced to a geometric generalization of weighted max k‐cover, solved with the greedy strategy which achieves the classical lower bound. The outer approximation is reduced to exploiting the partition of the boundary of by the Apollonius Voronoi diagram of the balls defining the inner approximation. Implementation‐wise, we present robust software incorporating the calculation of the exact Delaunay triangulation of points with degree two algebraic coordinates, of the exact medial axis of a union of balls, and of a certified estimate of the volume of a union of balls. Application‐wise, we exhibit accurate coarse‐grain molecular models using a number of balls 20 times smaller than the number of atoms, a key requirement to simulate crowded cellular environments.

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

ABSTRACTIn recent years, techniques for monitoring displacements and surface strains in laboratorial tests have been introduced. Some of those methods are based on photogrammetry and image post‐processing, allowing both displacement and strain fields to be monitored at a significant number of target points at any stage.This manuscript aims at contributing by proposing a simple and comprehensive approach for monitoring experimental tests using photogrammetry. An innovative strategy is introduced to efficiently recover the strain fields at the surface of a loaded specimen. This technique is based on a meshless approach and does not require any triangulation of data points. In this approach, shape functions are constructed from radial basis function interpolation in local subdomains, for which different numbers of data points may be included. To allow accounting for the presence of generic geometries, which may include concavities or convexities, the selection of interpolating points is performed considering a line‐of‐sight algorithm, avoiding inappropriate selection of neighbouring points.A number of practical examples are here presented for different concrete specimens tested in the laboratory. The presented results indicate that the proposed method can provide smooth strain fields, which allow an easy identification of microcracking development at early stages of loading.