3D Polylines Research Articles

Artificial intelligence-aided semi-automatic joint trace detection from textured three-dimensional models of rock mass

It is of great importance to obtain precise trace data, as traces are frequently the sole visible and measurable parameter in most outcrops. The manual recognition and detection of traces on high-resolution three-dimensional (3D) models are relatively straightforward but time-consuming. One potential solution to enhance this process is to use machine learning algorithms to detect the 3D traces. In this study, a unique pixel-wise texture mapper algorithm generates a dense point cloud representation of an outcrop with the precise resolution of the original textured three-dimensional (3D) model. A virtual digital image rendering was then employed to capture virtual images of selected regions. This technique helps to overcome limitations caused by the surface morphology of the rock mass, such as restricted access, lighting conditions, and shading effects. After AI-powered trace detection on two-dimensional (2D) images, a 3D data structuring technique was applied to the selected trace pixels. In the 3D data structuring, the trace data were structured through 2D thinning, 3D reprojection, clustering, segmentation, and segment linking. Finally, the linked segments were exported as 3D polylines, with each polyline in the output corresponding to a trace. The efficacy of the proposed method was assessed using a 3D model of a real-world case study, which was used to compare the results of artificial intelligence (AI)-aided and human intelligence trace detection. Rosette diagrams, which visualize the distribution of trace orientations, confirmed the high similarity between the automatically and manually generated trace maps. In conclusion, the proposed semi-automatic method was easy to use, fast, and accurate in detecting the dominant jointing system of the rock mass.

Automated noise modelling using a triangulated terrain model

ABSTRACTNoise simulations are an important part of noise studies that investigate the impact of noise sources on the environment. In noise simulation, noise levels at receiver points are calculated based on the noise propagation paths between the receiver and source points. These paths are derived from the height of the terrain. In current calculation approaches implemented in noise simulation software, 3D polylines are used as input to describe the height of the terrain. These 3D polylines are semi-automatically generated to meet the highly demanding computing performance of simulation software. In addition, previous research showed that the reconstruction of appropriate height lines as used in noise simulation is very difficult to automate, if not impossible As a solution, this research investigates how noise propagation paths between receiver and source points can directly be generated from a Triangulate Irregular Network (TIN) without creating the height lines. This would allow us to use the automatically generated TIN as input for noise simulation instead of the height lines. In addition, a TIN enables better control of the quality of the data than height lines do. This study uses the 3D noise modeling guidelines of Common Noise Assessment Methods in Europe (CNOSSOS-EU). Algorithms have been developed and implemented in a prototype to generate and validate the paths between receiver and source points using a TIN that includes the buildings as well as the noise absorption properties of the terrain. The prototype is successfully tested on two scenarios from the Netherlands. Since CNOSSOS-EU guidelines were used, the prototype is applicable to the entire European Union and can be the first step in improving the automation of 3D noise modeling using currently available techniques and data.

Supervised tractogram filtering using Geometric Deep Learning.

A tractogram is a virtual representation of the brain white matter. It is composed of millions of virtual fibers, encoded as 3D polylines, which approximate the white matter axonal pathways. To date, tractograms are the most accurate white matter representation and thus are used for tasks like presurgical planning and investigations of neuroplasticity, brain disorders, or brain networks. However, it is a well-known issue that a large portion of tractogram fibers is not anatomically plausible and can be considered artifacts of the tracking procedure. With Verifyber, we tackle the problem of filtering out such non-plausible fibers using a novel fully-supervised learning approach. Differently from other approaches based on signal reconstruction and/or brain topology regularization, we guide our method with the existing anatomical knowledge of the white matter. Using tractograms annotated according to anatomical principles, we train our model, Verifyber, to classify fibers as either anatomically plausible or non-plausible. The proposed Verifyber model is an original Geometric Deep Learning method that can deal with variable size fibers, while being invariant to fiber orientation. Our model considers each fiber as a graph of points, and by learning features of the edges between consecutive points via the proposed sequence Edge Convolution, it can capture the underlying anatomical properties. The output filtering results highly accurate and robust across an extensive set of experiments, and fast; with a 12GB GPU, filtering a tractogram of 1M fibers requires less than a minute.

Using 3D polylines to improve cone-beam CT-guided percutaneous transthoracic needle biopsy.

To investigate the diagnostic accuracy of using 3D polylines (3DPs) to improve cone-beam CT (CBCT) virtual navigation (VN)-guided percutaneous transthoracic needle biopsies (PTNB) of pulmonary lesions. From May 2021 to November 2021, patients (81 males and 41 females; age, 65 ± 12 years) who underwent CBCT VN with 3DPs for PTNB of pulmonary lesions were retrospectively reviewed. Fluoroscopic visibility of target lesions was evaluated using captured images from a Bull's eye view. Diagnostic accuracy was calculated, and complications were assessed. The mean size of biopsied lesions was 23 ± 13 mm (range: 6-75 mm). Overall, 13.9% (17/122) were small pulmonary nodules (diameter ≤1 cm), and 68.0% (83/122) of biopsied lesions were fluoroscopic visible. The overall diagnostic accuracy was 94.3%. The diagnostic accuracy for visible and invisible lesions was 94.0 and 94.9%, respectively (p = 0.843), and 100% for small pulmonary nodules. Major complications occurred in 8.2% (10/122; eight pneumothorax with chest tube insertion, one hemoptysis with transfusion, and one air embolism) of patients. CBCT VN with 3DP guidance provide a real-time outline of pulmonary lesions, thus enabling a reliable and accurate PTNB. 3DP guidance could be useful technique for CBCT-guided PTNB, especially in small pulmonary nodules.

Fiblets for Real‐Time Rendering of Massive Brain Tractograms

AbstractWe present a method to render massive brain tractograms in real time. Tractograms model the white matter architecture of the human brain using millions of 3D polylines (fibers), summing up to billions of segments. They are used by neurosurgeons before surgery as well as by researchers to better understand the brain. A typical raw dataset for a single brain represents dozens of gigabytes of data, preventing their interactive rendering. We address this challenge with a new GPU mesh shader pipeline based on a decomposition of the fiber set into compressed local representations that we call fiblets. Their spatial coherence is used at runtime to efficiently cull hidden geometry at the task shader stage while synthesizing the visible ones as polyline meshlets in a warp‐scale parallel fashion at the mesh shader stage. As a result, our pipeline can feed a standard deferred shading engine to visualize the mesostructures of the brain with various classical rendering techniques, as well as simple interaction primitives. We demonstrate that our algorithm provides real‐time framerates on very large tractograms that were out of reach for previous methods while offering a fiber‐level granularity in both rendering and interaction.

Directional-Layered Space-Time Densities: A New Spatiotemporal Trajectory Aggregation and Geographic Visualization Approach

One approach used in GIScience to investigate movement data is adopting time-geography theory and its important principles/methods: space-time paths and space-time cube. Thus, the movement of a moving object can be represented as a 3D polyline in a space-time cube. However, with the advent of larger movement datasets, this type of display can easily become cluttered and incomprehensible. In this article, we propose a new space-time aggregation algorithm, i.e., directional-layered space-time densities (DLSTDs), to solve the problem of trajectory clutter in a space-time cube. The approach is an extension of the pixel (2D raster cell) density around a point in two-dimensional space to the voxel density around a trajectory line segment in three-dimensional space-time $(x-y+t)$ . In the algorithm, the horizontal or vertical voxel layers are first calculated around the trajectory based on the direction of each trajectory line segment. Subsequently, the voxel density is calculated by substituting the distance of the voxel from the trajectory segment into a Gaussian-based attenuation function. Finally, the resulting layered densities are presented using volume rendering techniques. We demonstrate the DLSTDs on 30-day movement data of transport trucks in a mine in China and compare the algorithm with two other algorithms. At the end of the article, we summarize the research and consider further developments of the proposed approach.

4D Time Density of Trajectories: Discovering Spatiotemporal Patterns in Movement Data

Modern positioning and sensor technology enable the acquisition of movement positions and attributes on an unprecedented scale. Therefore, a large amount of trajectory data can be used to analyze various movement phenomena. In cartography, a common way to visualize and explore trajectory data is to use the 3D cube (e.g., space-time cube), where trajectories are presented as a tilted 3D polyline. As larger movement datasets become available, this type of display can easily become confusing and illegible. In addition, movement datasets are often unprecedentedly massive, high-dimensional, and complex (e.g., implicit spatial and temporal relations and interactions), making it challenging to explore and analyze the spatiotemporal movement patterns in space. In this paper, we propose 4D time density as a visualization method for identifying and analyzing spatiotemporal movement patterns in large trajectory datasets. The movement range of the objects is regarded as a 3D geographical space, into which the fourth dimension, 4D time density, is incorporated. The 4D time density is derived by modeling the movement path and velocity separately. We present a time density algorithm, and demonstrate it on the simulated trajectory and a real dataset representing the movement data of aircrafts in the Hong Kong International and the Macau International Airports. Finally, we consider wider applications and further developments of time density.

Alignment of Tractograms As Graph Matching

The white matter pathways of the brain can be reconstructed as 3D polylines, called streamlines, through the analysis of diffusion magnetic resonance imaging (dMRI) data. The whole set of streamlines is called tractogram and represents the structural connectome of the brain. In multiple applications, like group-analysis, segmentation, or atlasing, tractograms of different subjects need to be aligned. Typically, this is done with registration methods, that transform the tractograms in order to increase their similarity. In contrast with transformation-based registration methods, in this work we propose the concept of tractogram correspondence, whose aim is to find which streamline of one tractogram corresponds to which streamline in another tractogram, i.e., a map from one tractogram to another. As a further contribution, we propose to use the relational information of each streamline, i.e., its distances from the other streamlines in its own tractogram, as the building block to define the optimal correspondence. We provide an operational procedure to find the optimal correspondence through a combinatorial optimization problem and we discuss its similarity to the graph matching problem. In this work, we propose to represent tractograms as graphs and we adopt a recent inexact sub-graph matching algorithm to approximate the solution of the tractogram correspondence problem. On tractograms generated from the Human Connectome Project dataset, we report experimental evidence that tractogram correspondence, implemented as graph matching, provides much better alignment than affine registration and comparable if not better results than non-linear registration of volumes.

From oblique photogrammetry to a 3D model – Structural modeling of Kilen, eastern North Greenland

We present a workflow for building 3D geological models from oblique photogrammetry of outcrops. The workflow is used to build a 3D model of Kilen, a structurally complex and remotely located pseudo-nunatak in eastern North Greenland. The area was visited during two brief field seasons during which 1300 oblique photographs were taken by a hand held digital camera from a helicopter. The photos were triangulated and georeferenced and visible geological features as bedding and faults were mapped as 3D polylines. The polylines were used to calculate strike and dip of bedding and faults, generating a large number of structural information. These were imported into a 3D modeling software along with the 3D polylines, an unpublished digitized field map, a Digital Elevation Model, an orthophoto and georeferenced field observations. The 3D modeling software allows us to produce 2D cross-sections and 3D surfaces so that structural hypotheses could be tested through restoration and extrapolation of the data. This workflow proved effective in improving the structural knowledge of a remote area in the Arctic, showing that it is possible to produce quality 3D data from oblique photogrammetry and that those data can be used for 3D modeling.

Tractome: a visual data mining tool for brain connectivity analysis

Diffusion magnetic resonance imaging data allows reconstructing the neural pathways of the white matter of the brain as a set of 3D polylines. This kind of data sets provides a means of study of the anatomical structures within the white matter, in order to detect neurologic diseases and understand the anatomical connectivity of the brain. To the best of our knowledge, there is still not an effective or satisfactory method for automatic processing of these data. Therefore, a manually guided visual exploration of experts is crucial for the purpose. However, because of the large size of these data sets, visual exploration and analysis has also become intractable. In order to make use of the advantages of both manual and automatic analysis, we have developed a new visual data mining tool for the analysis of human brain anatomical connectivity. With such tool, humans and automatic algorithms capabilities are integrated in an interactive data exploration and analysis process. A very important aspect to take into account when designing this tool, was to provide the user with comfortable interaction. For this purpose, we tackle the scalability issue in the different stages of the system, including the automatic algorithm and the visualization and interaction techniques that are used.

Realistic road path reconstruction from GIS data

We introduce a new approach to construct smooth piecewise curves representing realistic road paths. Given a GIS database of road networks in which sampled points are organized in 3D polylines, our method creates horizontal, then vertical curves, and finally combines them to produce 3D road paths. We first estimate the possibility of each point of being a junction between two separate primitive curve segments. Next, we design a tree-traversal algorithm to expand sequences of local best fit primitives which are then merged together with respect to the G1 continuity constraint and civil engineering rules. We apply the Levenberg-Marquardt method to minimize the error between the resulting curve and the sampled points while preserving the G1 continuity.

Accuracy of automatically extracted geomorphological breaklines from airborne lidar curvature images

Rutzinger, M., Höfle, B. and Kringer, K., 2012. Accuracy of automatically extracted geomorphological breaklines from airborne LiDAR curvature images. Geografiska Annaler: Series A, Physical Geography, 94, 33–42. doi:10.1111/j.1468‐0459.2012.00453.xABSTRACTGeomorphological breaklines are 3D polylines extracted from high‐resolution digital terrain models (DTMs), which have manifold applications in geomorphology and related fields. Breaklines are used to maintain and refine the characteristic information on discontinuities in the process of DTM filtering and interpolation. Knowledge about the quality of the derived breaklines is important in order to provide adequate input data for DTM generation, geomorphological feature mapping, and change detection analysis. The spatial accuracy and the classification accuracy of derived breaklines depend on data acquisition settings and processing steps. The critical criteria are the precision and density of the LiDAR point cloud, the resolution and quality of the filtered and interpolated DTM and the target scale breaklines are derived for. In this paper a quantitative method for assessing the quality of derived breaklines, which are extracted from regions with high curvature, is presented. Selected components of the breakline detection workflow are analysed. In addition, the reliability of manually digitized reference lines is investigated. Selected geometric properties such as line length, slope and sinuosity are computed and compared to reference data. The properties are discussed regarding their explanatory power with respect to accuracy and precision. Automatic extraction results strongly differ from manually digitized breaklines. Breaklines from manual digitalization are found to vary in coverage and spatial accuracy and thus reflect always the operator's ability, perception and intention. The advantage of automated extracted breaklines is their reproducibility and adaptability to scale.

Space–time density of trajectories: exploring spatio-temporal patterns in movement data

Modern positioning and identification technologies enable tracking of almost any type of moving object. A remarkable amount of new trajectory data is thus available for the analysis of various phenomena. In cartography, a typical way to visualise and explore such data is to use a space–time cube, where trajectories are shown as 3D polylines through space and time. With increasingly large movement datasets becoming available, this type of display quickly becomes cluttered and unclear. In this article, we introduce the concept of 3D space–time density of trajectories to solve the problem of cluttering in the space–time cube. The space–time density is a generalisation of standard 2D kernel density around 2D point data into 3D density around 3D polyline data (i.e. trajectories). We present the algorithm for space–time density, test it on simulated data, show some basic visualisations of the resulting density volume and observe particular types of spatio-temporal patterns in the density that are specific to trajectory data. We also present an application to real-time movement data, that is, vessel movement trajectories acquired using the Automatic Identification System (AIS) equipment on ships in the Gulf of Finland. Finally, we consider the wider ramifications to spatial analysis of using this novel type of spatio-temporal visualisation.

Innovative sensing for real-time health monitoring of geostructural systems

Recent advances in miniaturizing sensors and electronics and the development of a pervasive wireless infrastructure have enabled a paradigm shift in the health monitoring of soilstructure systems. Created by researchers at Rensselaer Polytechnic Institute (RPI)1 and Measurand Inc.,2 the wireless ShapeAccelArray (SAA) sensing system is capable of measurements that represent a significant advance in implementing this shift. Over the last 50 years engineers have used traditional, manual slope inclinometers to monitor the health of landslides and construction activities. However, the frequency and accuracy of this labor-intensive monitoring rely on a trained engineer manually collecting and managing the data. The low sensor density provided by this method results in very limited data. State departments of transportation and federal agencies continue to spend significant resources monitoring possible slope failures using manual inclinometers or in-place inclinometer arrays. The expense and inflexibility of the slope inclinometer arrays, and the need for torsional alignment, make installation of multiple setups at a single site relatively rare, severely limiting the ability to conduct pervasive real-time monitoring. The wireless SAA system can remotely collect both 3D deformation and acceleration readings anywhere there is cell-phone coverage. The SAA system enables gravity-based shape calculation along a sensorized substrate through an extension of technologies that use fiber-optic orientation sensing to calculate 3D polylines representing the shape of a sensor array.3 The SAA uses microelectromechanical systems (MEMS) accelerometers in a precalibrated, geometrically constrained arrangement4 to provide long-term stability previously unattainable with fiber-optic Figure 1. Advancing polyvinyl chloride casing segments along the wireless ShapeAccelArray (SAA).

Stacks, Queues and Tracks: Layouts of Graph Subdivisions

A \emphk-stack layout (respectively, \emphk-queuelayout) of a graph consists of a total order of the vertices, and a partition of the edges into k sets of non-crossing (non-nested) edges with respect to the vertex ordering. A \emphk-track layout of a graph consists of a vertex k-colouring, and a total order of each vertex colour class, such that between each pair of colour classes no two edges cross. The \emphstack-number (respectively, \emphqueue-number, \emphtrack-number) of a graph G, denoted by sn(G) (qn(G), tn(G)), is the minimum k such that G has a k-stack (k-queue, k-track) layout.\par This paper studies stack, queue, and track layouts of graph subdivisions. It is known that every graph has a 3-stack subdivision. The best known upper bound on the number of division vertices per edge in a 3-stack subdivision of an n-vertex graph G is improved from O(log n) to O(log min\sn(G),qn(G)\). This result reduces the question of whether queue-number is bounded by stack-number to whether 3-stack graphs have bounded queue number.\par It is proved that every graph has a 2-queue subdivision, a 4-track subdivision, and a mixed 1-stack 1-queue subdivision. All these values are optimal for every non-planar graph. In addition, we characterise those graphs with k-stack, k-queue, and k-track subdivisions, for all values of k. The number of division vertices per edge in the case of 2-queue and 4-track subdivisions, namely O(log qn(G)), is optimal to within a constant factor, for every graph G. \par Applications to 3D polyline grid drawings are presented. For example, it is proved that every graph G has a 3D polyline grid drawing with the vertices on a rectangular prism, and with O(log qn(G)) bends per edge. Finally, we establish a tight relationship between queue layouts and so-called 2-track thickness of bipartite graphs. \par