Geometric Approximation Research Articles

Threads, Ribbons, and Rings in the Radio Galaxy IC 4296

Abstract The nearby elliptical galaxy IC 4296 has produced a large (510 kpc) low-luminosity radio source with typical FR i core/jet/lobe morphology. The unprecedented combination of brightness sensitivity, dynamic range, and angular resolution of a new 1.28 GHz MeerKAT continuum image reveals striking new morphological features, which we call threads, ribbons, and rings. The threads are faint narrow emission features originating where helical Kelvin–Helmholtz instabilities disrupt the main radio jets. The ribbons are smooth regions between the jets and the lobes, and they appear to be relics of jets powered by earlier activity that have since come into pressure equilibrium. Vortex rings in the outer portions of the lobes and their backflows indicate that the straight outer jets and ribbons are inclined by i = 60 ° ± 5 ° from the line of sight, in agreement with photometric, geometric, and gas-dynamical estimates of inclination angles near the nucleus.

Stochastic 3D modelling of discrete sediment bodies for geotechnical applications

In the course of engineering geological ground characterizations, internal structures of sediments are often simplified to continuous units and structures like lenses are drawn in cross sections based on geologists’ experience. Seeing this as oversimplifications, we propose discrete sediment body (DSB) modelling which is a computational workflow that permits generation of 3D meshes of sediment bodies. DSB modelling can be used to stochastically model highly detailed sedimentary underground structures, based on geometrical assumptions (e.g. size and orientation of lenses) that can be derived from engineering geological investigations. From a geological point of view, the framework is suited to model underground conditions where one would describe the occurrence of chaotic lens-shaped sediments. The modelling process follows a pipeline, where first estimations about the distribution and geometries of the sediment bodies are made. To get non-intersecting meshes as a final product, surrogate point clouds are generated that follow the initial geometrical estimations, which are then clustered, and finally alpha shape based meshes are generated around the clusters. Resulting 3D sediment bodies enable easy generation of consistent 2D geological cross sections and can be used as a basis for further analyses. The paper is finished with a case study where a finite element stability analysis is done for a slope excavation with underground conditions featuring clayey silt lenses in a matrix of gravelly sand. It can be shown that the lenses substantially influence the ground behavior in comparison to a classical approach with continuous units.

Continuous-Curvature Trajectory Planning

Continuous‐curvature paths play an important role in the area of driving robots: as vehicles usually cannot changethe steering angle in zero‐time, real trajectories must not have discontinuities in the curvature profile. Typical continuous‐curvature paths are thus built of straight lines, arcs and clothoids. Due to the geometric nature of clothoids, some questions in the area of trajectory planning are difficult the answer – usually we need approximations here. In this paper we describe a full approach for continuous‐curvature trajectory planning for mobile robots – it covers a maneuver‐based planning with Viterbi optimization and geometric approximations required to construct the respective clothoid trajectories.

Increasing Transparency and Feasibility of Auto Accessibility for Project Prioritization

Accessibility, the number of time-decayed jobs available to each zone within a region, can help prioritize candidate transportation investments. This paper demonstrates how to compute auto accessibility using commonly available resources and identifies strategies needed to render calculations feasible and transparent. (The scope excludes transit and pedestrian impacts.) For the first objective, computational solutions included developing a semi-automated method to import legacy transportation networks, automating turn prohibitions, and using an algorithm to check for inconsistently formed service areas that sometimes occur in a random fashion with geographic information system software. Failure to exercise quality control using these approaches gives erroneous results: not solving the problem of inconsistently formed service areas led to a region within 50 mi of a 1-mi corridor (where improvements are proposed) having an accessibility almost 40 times higher than the correct value. For the second objective, the influence area (i.e., catchment radius) mattered most: for one project, the forecast accessibility improvement dropped by 80% when an area within 45 mi of the project, rather than an area within 15 mi, was the basis of the analysis. Other decisions affected forecast accessibility improvement less: the choice of the number of centroid connectors affected forecasts by an average of 23% (with a 10-mi influence area). Choosing to eliminate negative net accessibility contributions, attributed to geometric approximations in the software, affected forecasts by less than 21% (35-mi influence area or smaller). Ranking five proposed investments in relation to their forecast accessibility benefit demonstrated the importance of documenting users’ computational choices.

Guaranteed-quality higher-order triangular meshing of 2D domains

We present a guaranteed quality mesh generation algorithm for the curvilinear triangulation of planar domains with piecewise polynomial boundary. The resulting mesh consists of higher-order triangular elements which are not only regular (i.e., with injective geometric map) but respect strict bounds on quality measures like scaled Jacobian and MIPS distortion. This also implies that the curved triangles' inner angles are bounded from above and below. These are key quality criteria, for instance, in the field of finite element analysis. The domain boundary is reproduced exactly, without geometric approximation error. The central idea is to transform the curvilinear meshing problem into a linear meshing problem via a carefully constructed transformation of bounded distortion, enabling us to leverage key results on guaranteed-quality straight-edge triangulation. The transformation is based on a simple yet general construction and observations about convergence properties of curves under subdivision. Our algorithm can handle arbitrary polynomial order, arbitrarily sharp corners, feature and interface curves, and can be executed using rational arithmetic for strict reliability.

3D lidar point-cloud projection operator and transfer machine learning for effective road surface features detection and segmentation

The classification and extraction of road markings and lanes are of critical importance to infrastructure assessment, planning and road safety. We present a pipeline for the accurate segmentation and extraction of rural road surface objects in 3D lidar point-cloud, as well as a method to extract geometric parameters belonging to tar seal. To decrease the computational resources needed, the point-clouds were aggregated into a 2D image space before being transformed using affine transformations. The Mask R-CNN algorithm is then applied to the transformed image space to localize, segment and classify the road objects. The segmentation results for road surfaces and markings can then be used for geometric parameter estimation such as road widths estimation, while the segmentation results show that the efficacy of the existing Mask R-CNN to segment needle-type objects is improved by our proposed transformations.

Clinical Pharmacology of CTL019 in Patients with Relapsed/Refractory (r/r) Diffuse Large B-Cell Lymphoma (DLBCL)

Clinical Pharmacology of CTL019 in Patients with Relapsed/Refractory (r/r) Diffuse Large B-Cell Lymphoma (DLBCL)

A seasonally invariant deep transform for visual terrain-relative navigation.

Visual terrain-relative navigation (VTRN) is a localization method based on registering a source image taken from a robotic vehicle against a georeferenced target image. With high-resolution imagery databases of Earth and other planets now available, VTRN offers accurate, drift-free navigation for air and space robots even in the absence of external positioning signals. Despite its potential for high accuracy, however, VTRN remains extremely fragile to common and predictable seasonal effects, such as lighting, vegetation changes, and snow cover. Engineered registration algorithms are mature and have provable geometric advantages but cannot accommodate the content changes caused by seasonal effects and have poor matching skill. Approaches based on deep learning can accommodate image content changes but produce opaque position estimates that either lack an interpretable uncertainty or require tedious human annotation. In this work, we address these issues with targeted use of deep learning within an image transform architecture, which converts seasonal imagery to a stable, invariant domain that can be used by conventional algorithms without modification. Our transform preserves the geometric structure and uncertainty estimates of legacy approaches and demonstrates superior performance under extreme seasonal changes while also being easy to train and highly generalizable. We show that classical registration methods perform exceptionally well for robotic visual navigation when stabilized with the proposed architecture and are able to consistently anticipate reliable imagery. Gross mismatches were nearly eliminated in challenging and realistic visual navigation tasks that also included topographic and perspective effects.

Point cloud-based elastic reverse time migration for ultrasonic imaging of components with vertical surfaces

This work presents a new ultrasonic imaging framework for non-destructive evaluation of components with vertical or steeply dipping surfaces and demonstrates its ability of accurately characterizing multiple defects hidden in the interior of the component based on a limited coverage of ultrasonic linear phased array. Central to the framework is a point cloud-based elastic reverse time migration (PC-based ERTM) method. First, a surface reconstruction is derived from the point cloud provided through photos of an object from multiple views by bundle adjustment. Second, by taking the surface reconstruction as a geometric background estimate for elastic reverse time migration, the algorithm considers information of multiple scattering and mode conversions as well as multiple wave reflections from the component’s bottom and aims at detecting internal defects. The effectiveness and accuracy of the PC-based ERTM approach is examined by experiments with multiple defects in extruded aluminum specimens with vertical surfaces. Experimental results show that notches and side-drilled holes in components can be reconstructed accurately.

ROBUST ESTIMATION IN ROBOT VISION AND PHOTOGRAMMETRY: A NEW MODEL AND ITS APPLICATIONS

Abstract. Robust estimation (RE) is a fundamental issue in robot vision and photogrammetry, which is the theoretical basis of geometric model estimation with outliers. However, M-estimations solved by iteratively reweighted least squares (IRLS) are only suitable for cases with low outlier rates (< 50%); random sample consensus (RANSAC) can only obtain approximate solutions. In this paper, we propose an accurate and general RE model that unifies various robust costs into a common objective function by introducing a “robustness-control” parameter. It is a superset of typical least-squares, l1-l2, Cauchy, and Geman-McClure estimates. We introduce a parameter-decreasing strategy into the IRLS to optimize our model, called adaptive IRLS. The adaptive IRLS begins with a least-squares estimate for initialization. Then, the “robustness-control” parameter is decreased along with iterations so that the proposed model acts as different robust loss functions and has different degrees of robustness. We also apply the proposed model in several important tasks of robot vision and photogrammetry, such as line fitting, feature matching, image orientation, and point cloud registration (scan matching). Extensive simulated and real experiments show that the proposed model is robust to more than 80% outliers and preserves the advantages of M-estimations (fast and optimal). Our source code will be made publicly available in https://ljy-rs.github.io/web.

Research on Estimation Method of Geometric Features of Structured Negative Obstacle Based on Single-Frame 3D Laser Point Cloud

A single VLP-16 LiDAR estimation method based on a single-frame 3D laser point cloud is proposed to address the problem of estimating negative obstacles’ geometrical features in structured environments. Firstly, a distance measurement method is developed to determine the estimation range of the negative obstacle, which can be used to verify the accuracy of distance estimation. Secondly, the 3D point cloud of a negative obstacle is transformed into a 2D elevation raster image, making the detection and estimation of negative obstacles more intuitive and accurate. Thirdly, we compare the effects of a StatisticalOutlierRemoval filter, RadiusOutlier removal, and Conditional removal on 3D point clouds, and the effects of a Gauss filter, Median filter, and Aver filter on 2D image denoising, and design a flowchart for point cloud and image noise reduction and denoising. Finally, a geometrical feature estimation method is proposed based on the elevation raster image. The negative obstacle image in the raster is used as an auxiliary line, and the number of pixels is derived from the OpenCV-based Progressive Probabilistic Hough Transform to estimate the geometrical features of the negative obstacle based on the raster size. The experimental results show that the algorithm has high accuracy in estimating the geometric characteristics of negative obstacles on structured roads and has a practical application value for LiDAR environment perception research.

Interpreting the radiative properties of advanced high strength steel using the geometric optics ray-tracing approximation

This study investigates the relationship between surface topography and radiative properties of advanced high strength steel (AHSS) alloys using the geometric optics approximation (GOA) with ray tracing. Five AHSS coupons with different alloy compositions and surface topographies are investigated. The directional-hemispherical and specular reflectance of samples are measured using a UV-Vis-NIR spectrophotometer (0.25–2.5 μm) and two FTIR spectrometers (2.5-20 μm), while surface profiles used in the ray tracing model are obtained using an optical profilometer. Predictions of directional-hemispherical reflectance are consistent with the experimental data when the surface parameters and incident wavelengths are within the valid GOA domain. Reflectance predictions in the specular direction are also in line with the measurements when the roughness parameters are in the specular approximation domain.

Nonlocal continuum damage modeling for functionally graded plates of third-order shear deformation theory

This article presents an effective computational approach that incorporates a quasi-brittle damage model into the isogeometric analysis of plates made of functionally graded materials. The plate kinematics is represented by a third-order shear deformation theory for higher accuracy. A coupling nonlocal equivalent strain field is introduced on the plate neutral surface to control the softening behavior. The utilization of the neutral surface in functionally graded plates enables the use of a single damage parameter over each plate cross-section. As a consequence, plate stiffness matrices can be calculated analytically, which simplifies the proposed damage model and its computer implementation. The discretization of the problem domain is based on basis functions generated from the non-uniform rational B-splines (NURBS) which are used for both geometric representation and field variable approximations, i.e., displacement and nonlocal equivalent strain. Owing to the high-order continuity of the NURBS basis functions, local features such as fracture damage zones can be resolved accurately. The performance of the proposed approach is demonstrated through several numerical examples under different loading configurations and compared with results from other approaches.

Learning Multiple‐Scattering Solutions for Sphere‐Tracing of Volumetric Subsurface Effects

AbstractAccurate subsurface scattering solutions require the integration of optical material properties along many complicated light paths. We present a method that learns a simple geometric approximation of random paths in a homogeneous volume with translucent material. The generated representation allows determining the absorption along the path as well as a direct lighting contribution, which is representative of all scatter events along the path. A sequence of conditional variational auto‐encoders (CVAEs) is trained to model the statistical distribution of the photon paths inside a spherical region in the presence of multiple scattering events. A first CVAE learns how to sample the number of scatter events, occurring on a ray path inside the sphere, which effectively determines the probability of this ray to be absorbed. Conditioned on this, a second model predicts the exit position and direction of the light particle. Finally, a third model generates a representative sample of photon position and direction along the path, which is used to approximate the contribution of direct illumination due to in‐scattering. To accelerate the tracing of the light path through the volumetric medium toward the solid boundary, we employ a sphere‐tracing strategy that considers the light absorption and can perform a statistically accurate next‐event estimation. We demonstrate efficient learning using shallow networks of only three layers and no more than 16 nodes. In combination with a GPU shader that evaluates the CVAEs’ predictions, performance gains can be demonstrated for a variety of different scenarios. We analyze the approximation error that is introduced by the data‐driven scattering simulation and shed light on the major sources of error.

The alternative Kirchhoff approximation in elastodynamics with applications in ultrasonic nondestructive testing

The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing. doi:10.1017/S1446181120000036

Impact of fine divertor geometrical features on the modelling of JET corner configurations

The modelling of JET corner configurations, in which the strike points are positioned deep in the corners of the divertor, is extremely challenging for edge plasma fluid modelling tools. To circumvent this technical limitation, a geometrical approximation has been proposed, consisting in considering an artificial minor modification of the geometry of the divertor targets plates. In this paper, we investigate how significantly this approximation impacts the output of transport simulations. Using the SOLEDGE2D-EIRENE transport code which has the unique capability to be able to cope with both the full and the approximated geometry, we have performed a density scan in H-mode for pulses in which the outer strike-point lies in the corner of the divertor. We report here how simulations in the artificial geometry differ from the ones in unaltered geometry. At the exception of low density cases, mid-plane profiles in the closed field lines region and the near scrape-off layer are little impacted. Further out however, in flux-surfaces that are concerned by the geometrical modification, we find that modifying the geometry leads to a strong overestimate of the plasma density. The density perturbation is not local and concerns the whole flux surfaces. Although the divertor geometry is modified only on the outer side, the largest impact is found at the inner divertor where densities are systematically overestimated by a factor that can exceed 10 in low density cases in the far Scrape-Off Layer (SOL) and temperature underestimated by 10 to 20 eV in most of the studied density range. The near SOL and strike point peak values are also impacted in the same direction with density changes by a factor of 2. As a consequence, the threshold to detachment of the inner divertor is found lower in the approximate geometry than in the unaltered one. Due to the large flux expansion between the outer and the inner target, the difference in plasma is especially sensitive at the top of the inner divertor baffle, which could have consequence on the evaluation of physical sputtering at that critical location. • Minor modification of the divertor geometry impacts the edge plasma equilibrium. • The impact is not local and can be larger on the opposite side of the divertor. • Care must be taken when modelling divertor geometry with approximate description. • Mean-field codes with up to the wall capability should be used in such cases.

Development of analytical models for calculating the characteristics of intense acoustic waves propagating in a stratified atmosphere

The time profiles and characteristics of sonic boom waves during propagation in a density-stratified atmosphere are calculated. It is shown that this stratification leads to a significant change in wave parameters: the wave amplitude, the characteristic distances at which the wave transformation is manifested, the width of the shock front. It is shown that the effective role of viscosity decreases when the shock wave propagates down to the earth's surface. So the width of the shock front decreases. Two methods are being developed for analytical calculation. The first one, the nonlinear geometric acoustics approximation, allows obtaining the Burgers equation with a variable viscosity to describe the wave field along the ray. Some exact solutions and asymptotic solution for low viscosity are obtained. This method is not applicable in focusing regions. The second method is based on the application of a modular nonlinearity model. Replacing the quadratic nonlinearity with a modular one allows obtaining a system of linear equations, the solution of which is possible. The difficulty lies in the correct construction of the discontinuity in the profile and subsequent stitching of solutions for different polarities. [This study was supported by the Russian Foundation for Basic Research (Project No. 20-02-00493-a).]

REDE: End-to-End Object 6D Pose Robust Estimation Using Differentiable Outliers Elimination

Object 6D pose estimation is a fundamental task in many applications. Conventional methods solve the task by detecting and matching the keypoints, then estimating the pose. Recent efforts bringing deep learning into the problem mainly overcome the vulnerability of conventional methods to environmental variation due to the hand-crafted feature design. However, these methods cannot achieve end-to-end learning and good interpretability at the same time. In this paper, we propose REDE, a novel end-to-end object pose estimator using RGB-D data, which utilizes network for keypoint regression, and a differentiable geometric pose estimator for pose error back-propagation. Besides, to achieve better robustness when outlier keypoint prediction occurs, we further propose a differentiable outliers elimination method that regresses the candidate result and the confidence simultaneously. Via confidence weighted aggregation of multiple candidates, we can reduce the effect from the outliers in the final estimation. Finally, following the conventional method, we apply a learnable refinement process to further improve the estimation. The experimental results on three benchmark datasets show that REDE slightly outperforms the state-of-the-art approaches and is more robust to object occlusion.

Tolerance estimation and metrology for reverse engineering based remanufacturing systems

ABSTRACT Tolerances are critical to the product’s design, manufacturing, and quality. However, tolerances are often overlooked in a reverse engineering (RE) process for industrial applications, especially in legacy parts or spare parts remanufacturing. Ignoring tolerances could either unnecessarily call for high precision remanufacturing processes or make the reproduced parts unqualified. Additive manufacturing (AM) techniques are used in remanufacturing applications because of their ability to manufacturing intricated parts. Due to its layer-by-layer fabrication nature, the metrology for AM-created parts is drastically different when compared to traditional feature-generation processes. In this study, we first propose a novel way to classify manufacturing processes based on whether they directly identify or generate features, which could profoundly affect their metrology tools. Next, a systematic geometric inspection and tolerance estimation methodology for the RE system is proposed. A set of tools is developed to extract various geometric dimensional values from the point clouds based on their tolerancing types. Moreover, based on the domain knowledge in production process design and planning, methods are developed to estimate empirical tolerances from a small batch of legacy parts. Comparisons of empirical tolerances of real machined parts to their designed tolerances are presented to evaluate the performance of the proposed framework.

Model order reduction of flow based on a modular geometrical approximation of blood vessels

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g., straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by Proper Orthogonal Decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier–Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton–Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.