Geometric Mapping Research Articles

Neural Networks as Geometric Chaotic Maps.

The use of artificial neural networks (NNs) as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how NNs learn chaos is lacking. Here, we employ a geometric perspective to show that NNs can efficiently model chaotic dynamics by becoming structurally chaotic themselves. We first confirm NN's efficiency in emulating chaos by showing that a parsimonious NN trained only on few data points can reconstruct strange attractors, extrapolate outside training data boundaries, and accurately predict local divergence rates. We then posit that the trained network's map comprises sequential geometric stretching, rotation, and compression operations. These geometric operations indicate topological mixing and chaos, explaining why NNs are naturally suitable to emulate chaotic dynamics.

Optical and SAR Image Dense Registration Using a Robust Deep Optical Flow Framework

The coregistration of optical and synthetic aperture radar (SAR) imageries is the bottleneck in exploring the complementary information from the two multimodal datasets. The difficulties lie in not only the complex radiometric relationship between them, but also the distinct geometrical models of the optical and SAR imaging systems, which cause it nontrivial to explicitly depict the spatial relationship between the corresponding image regions when elevation fluctuations exist. This article aims to investigate the optical flow technique for the pixelwise dense registration of the high-resolution optical and SAR images, so as to get rid of the outlier removal and geometric mapping procedures, which have to be conducted in the classical image registration approaches that are based on sparse feature point matching. Herein, a deep optical flow framework is designed. First, a dilated feature concatenation method is proposed to enhance the discriminability of the pixelwise features for similarity measurement. An effective network training strategy is used, based on a smoothed flow loss, and also a training dataset that contains simulated elevation fluctuations. Second, we propose a self-supervised optical flow fine-tuning strategy. It incorporates the strength of the blockwise matching approach, which produces better matching precision, into the proposed pixelwise matching procedure. In this way, the accuracy of the optical-SAR dense registration is substantially improved. Extensive experiments conducted on the 1-m resolution optical-SAR image pairs of different land-cover types and distinct topographic conditions indicate that the proposed optical-SAR optical flow network -Ft framework is quite robust, and has the potential to perform the optical-SAR image dense registration in practical applications. The Python code of the proposed deep optical flow network will be made available.

Long-Term Localization Using Semantic Cues in Floor Plan Maps

Lifelong localization in a given map is an essential capability for autonomous service robots. In this letter, we consider the task of long-term localization in a changing indoor environment given sparse CAD floor plans. The commonly used pre-built maps from the robot sensors may increase the cost and time of deployment. Furthermore, their detailed nature requires that they are updated when significant changes occur. We address the difficulty of localization when the correspondence between the map and the observations is low due to the sparsity of the CAD map and the changing environment. To overcome both challenges, we propose to exploit semantic cues that are commonly present in human-oriented spaces. These semantic cues can be detected using RGB cameras by utilizing object detection, and are matched against an easy-to-update, abstract semantic map. The semantic information is integrated into a Monte Carlo localization framework using a particle filter that operates on 2D LiDAR scans and camera data. We provide a long-term localization solution and a semantic map format, for environments that undergo changes to their interior structure and detailed geometric maps are not available. We evaluate our localization framework on multiple challenging indoor scenarios in an office environment, taken weeks apart. The experiments suggest that our approach is robust to structural changes and can run on an onboard computer. We released the open source implementation of our approach written in C++ together with a ROS wrapper.

A stochastic finite element scheme for solving partial differential equations defined on random domains

This paper proposes a novel stochastic finite element scheme to solve partial differential equations defined on random domains. A geometric mapping algorithm first transforms the random domain into a reference domain. By combining the mesh topology (i.e. the node numbering and the element numbering) of the reference domain and random nodal coordinates of the random domain, random meshes of the original problem are obtained by only one mesh of the reference domain. In this way, the original problem is still discretized and solved on the random domain instead of the reference domain. A random isoparametric mapping of random meshes is then proposed to generate the stochastic finite element equation of the original problem. We adopt a weak-intrusive method to solve the obtained stochastic finite element equation. In this method, the unknown stochastic solution is decoupled into a sum of the products of random variables and deterministic vectors. Deterministic vectors are computed by solving deterministic finite element equations, and corresponding random variables are solved by a proposed sampling method. The computational effort of the proposed method does not increase dramatically as the stochastic dimension increases and it can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality successfully. Four numerical examples are given to demonstrate the good performance of the proposed method.

Learning robotic navigation from experience: principles, methods and recent results.

Navigation is one of the most heavily studied problems in robotics and is conventionally approached as a geometric mapping and planning problem. However, real-world navigation presents a complex set of physical challenges that defies simple geometric abstractions. Machine learning offers a promising way to go beyond geometry and conventional planning, allowing for navigational systems that make decisions based on actual prior experience. Such systems can reason about traversability in ways that go beyond geometry, accounting for the physical outcomes of their actions and exploiting patterns in real-world environments. They can also improve as more data is collected, potentially providing a powerful network effect. In this article, we present a general toolkit for experiential learning of robotic navigation skills that unifies several recent approaches, describe the underlying design principles, summarize experimental results from several of our recent papers, and discuss open problems and directions for future work. This article is part of the theme issue 'New approaches to 3D vision'.

Prediction of Residual Strains Due to In-Plane Fibre Waviness in Defective Carbon-Fibre Reinforced Polymers Using Ultrasound Data

Residual strains affect the properties and performance of composite components, therefore measuring and predicting them are important. The prediction of residual strains from a model can be achieved by two steps: the generation of a geometric ply map and the modelling based on that to predict 3D residual strains. A novel method for identifying the most effective algorithm for characterising fibre orientation for the geometric ply map using ultrasound C-scan data has been developed. Finite element models were generated based on the fibre-orientation data from three different algorithms: the Radon transform, 2D fast Fourier transform, and Sobel filter. The models were used to predict residual strains due to three different severities of in-plane fibre waviness induced in a set of 18 specimens. Stratified leave-one-out cross validation was applied to obtain optimum parameters for the three characterisation algorithms and to update the values of the coefficient of thermal expansion for the material. Residual strains on the surface of the specimens were obtained from calculations based on the out-of-plane displacements measured using a digital image correlation system. The predicted and measured residual strain maps were decomposed into feature vectors using orthogonal polynomials to reduce data dimensionality and make quantitative comparisons. The measured residual strains and the predictions based on models using optimised parameters showed good agreement. The differences in performance were quantified based on the accuracy of the predicted residual strains, which showed that the Radon transform performed best.

Change in humeral anchor position significantly affects isometry in ulnar collateral ligament repair: a 3-dimensional computer modeling study.

Medial ulnar collateral ligament (UCL) repair utilization is increasing in recent years, bolstered by shorter rehabilitation and satisfactory clinical outcomes. Although previous literature has illustrated the importance of tunnel position on restoring graft isometry in reconstruction, there remains a paucity of literature guiding anchor placement in UCL repair. The purpose of this study is to design a 3-dimensional (3D) elbow model to understand the effect of anchor location on UCL repair isometry. A 3D computer model of an elbow joint was created using computed tomographic and magnetic resonance imaging MRI scans from a single patient. The humeral and ulnar attachments of the UCL were plotted using 3 methodologies: (1) geometric cloud mapping and (2) quantitative measurements from the anatomic studies by Camp etal and (3) Frangiamore etal. A 3.5-mm-diameter clockface was placed on each attachment site, which allowed for simulation of 12 distinct 1.75-mm deviations in anchor position. The 3 models were ranged through 0°-120° at 10° increments, and the 3D distances were measured between the ligament centroids. The humeral and ulnar anchors were sequentially repositioned around the clockfaces, and construct lengths were again measured to evaluate changes in isometry. A paired Student t test was performed to determine if there was a significant difference in isometry between the humeral and ulnar anchor deviations. Using method 1, the UCL repair length at 90° of elbow flexion was 26.8 mm. This construct underwent 13.6 mm of total excursion for a 46.4% change in length throughout its arc of motion. Method 2 produced a 19.3-mm construct that underwent 0.8 mm of excursion for a 3.9% length change throughout the arc. Method 3 produced a 24.5-mm construct that underwent 2.3 mm of excursion for a 9.4% length change. Identifying ligament footprints using the quantitative anatomic measurements from Camp etal and Frangiamore etal improved construct isometry through 120° of flexion (length changes of 3.9% and 9.4%, respectively) when compared to using the geometric cloud technique alone (46.4% length change). Humeral anchor deviations produced a significant increase in repair construct excursion compared with ulnar anchor deviations (P<.001). When performing UCL repair, small deviations in humeral anchor position may significantly influence ligament repair isometry. Using quantitative anatomic data may help identify anchor positions with improved repair isometry. Particularly when addressing detachments of the humeral footprint, surgeons should be critical of the humeral anchor position in order to restore native anatomy and optimal biomechanics.

Thermal Power Plant Turbine Rotor Digital Twin Automation Construction and Monitoring System

Based on the digital twin technology, this article investigates the physical rules fusion model of the turbine rotor operation in thermal power plants, establishes the geometric behavior mapping method of the turbine rotor in the virtual scenario of thermal power plants, and develops a real-time data-driven virtual monitoring system of the rotor operation, which realizes the virtual control of the rotor operation process from the physical and geometric levels, respectively. The 3D model created by Creo was imported into ADAMS in x_t format, constraints were added, and model data input and output interfaces were established in ADAMS software to build its dynamics model. The foundation of the joint simulation with the AMESim model is laid. The information fusion technology based on D-S evidence theory, fusing multisensor data and information from other channels, can more accurately and comprehensively understand and describe the diagnostic object, to make correct judgment and decisions on complex fault diagnosis. We propose an integrated modeling method for multiview control scenarios of manufacturing units based on digital twins and finalize the construction of digital twin models of manufacturing units based on the definition of the multiview model collaboration mechanism, which provides model support for the research of digital twin-driven manufacturing unit control technology. For the twin data perception and interaction problem, a unified architecture-standardized communication protocol is established based on OPC UA technology to solve the problem of difficult data perception and interaction caused by the nonuniform communication interface protocol of different devices on the automated production line. The model change is intended to help improve the visualization level of digital production line monitoring and improve the operating efficiency of the turbine rotor. The experimental results show that the application of digital twin to thermal turbine rotor operation monitoring provides a new method for turbine rotor vibration fault diagnosis; D-S evidence theory can fuse information from multiple aspects of the fault, thus improving the probability of fault diagnosis and reducing uncertainty.

Mapping of thoracic aorta growth rate on serial self-navigated 3D whole-heart magnetic resonance angiographies by image registration

Abstract Introduction Accurate and reproducible assessment of aortic diameters and their growth rate is of key importance for the management of patients with thoracic aortic aneurysms [1,2]. It has been recently shown that image registration permits the assessment of progressive aortic dilation on ECG-gated contrast-enhanced CT angiography, outperforming manual quantification and allowing for 3D aortic size and growth mapping [3]. However, exposure to radiation makes it convenient to limit the use of CT for serial follow-up, especially in young patients. Self-navigated 3D whole-heart CMR acquisitions provides excellent image quality overcoming these limitations [4]. Purpose To evaluate the accuracy and reproducibility of registration-based assessment of aortic dilation using self-navigated 3D whole-heart CMR acquisitions. Methods Fifteen patients with two self-navigated 3D whole-heart CMR images obtained at least 1 year apart were included. Aortic root and thoracic aorta diameters were measured by 2 independent observers both manually (multiplanar reconstruction) and with the registration-based technique. To perform registration-based assessment, the aorta was semi-automatically segmented and typical anatomical landmarks were placed by each observer at baseline [3]. Geometrical mapping between baseline and follow-up acquisitions was obtained using deformable image registration, and applied to the baseline aortic surface points to obtain their location at follow-up. Finally, aortic diameters and their growth rate were automatically measured and used to calculated 3D aortic dilation maps. Agreement between techniques and their inter-observer reproducibility were calculated. Results Patients age was 27.2±14.5 years and 40% were male. Mean follow-up duration was 2.7±1.6 years. Compared to manual assessment, the registration-based technique presented low bias and excellent agreement for aortic diameters (Table 1), and low bias and moderate agreement for growth rates both in the aortic root and the thoracic aorta (Table, Fig. 1A). The techniques presented similar inter-observer reproducibility in the assessment of aortic diameters (Table 1), while the registration-based method demonstrated much higher inter-observer reproducibility in the assessment of growth rates in the aortic root and the thoracic aorta (Table 1, Fig. 1A and B). Three-dimensional mapping of thoracic aortic diameters and growth was highly reproducible (mean regional ICC=0.90 for diameters; 0.82 for growth rate). Conclusion The assessment of the dilation rate of the thoracic aorta via registration of serial self-navigated 3D whole-heart CMR acquisitions is accurate and reproducible in the aortic root and the thoracic aorta. Thus, it allows to assess local aortic growth without the drawbacks of CT. Funding Acknowledgement Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Instituto de Salud Carlos III and Ministerio de Ciencia e Innovaciόn (Spain)

Precise High‐order Meshing of 2D Domains with Rational Bézier Curves

AbstractWe propose a novel method to generate a high‐order triangular mesh for an input 2D domain with two key characteristics: (1) the mesh precisely conforms to a set of input piecewise rational domain curves, and (2) the geometric map on each curved triangle is injective. Central to the algorithm is a new sufficient condition for placing control points of a rational Bézier triangle to guarantee that the conformance and injectivity constraints are theoretically satisfied. Taking advantage of this condition, we provide an explicit construct that robustly creates higher‐order 2D meshes satisfying the two characteristics. We demonstrate the robustness and effectiveness of our algorithm over a data set containing 2200 examples.

Hierarchical map representation using vector maps and geometrical maps for self-localization

Map-based self-localization estimates the pose of the self-driving vehicle in an environment, becoming an essential part of autonomous driving tasks. Generally, maps used in self-localization have detailed geometric information on an environment in formats such as point cloud maps and Gaussian mixture model (GMM) maps. As other maps are widely developed for autonomous driving, vector maps store more object-focused information, such as buildings and road facilities, for navigation and scene understanding in autonomous driving tasks. However, it is not compatible with self-localization due to the lack of detailed geometric information. The two different map formats of vector maps and maps for self-localization complicate the management, preventing the development of the area where a self-driving vehicle can drive stably. This paper proposes a unified map format with a hierarchical structure that enables both vector maps and self-localization maps (i.e., GMM maps) to be managed more easily. Because proposed maps can be treated as vector maps at the high-level layer, various tasks related to navigation and scene understanding in autonomous driving can utilize. A GMM map is stored at the low-level layer associated with a vector map component, enabling accurate self-localization in an environment. The proposed map format is compatible with vector maps widely developed by mapping companies on the surface and facilitates future map management. The experimental results of self-localization in urban areas showed that the proposed map gives the competitive self-localization accuracy compared with the GMM map even with fewer cells that link to vector components. The proposed maps enable self-localization with sufficient accuracy for safe autonomous driving operations.

Geometric Mapping Evaluation for Real-Time Local Sensor Simulation.

Medical augmented reality and simulated test environments struggle in accurately simulating local sensor measurements across large spatial domains while maintaining the proper resolution of information required and real time capability. Here, a simple method for real-time simulation of intraoperative sensors is presented to aid with medical sensor development and professional training. During a surgical intervention, the interaction between medical sensor systems and tissue leads to mechanical deformation of the tissue. Through the inclusion of detailed finite element simulations in a real-time augmented reality system the method presented will allow for more accurate simulation of intraoperative sensor measurements that are independent of the mechanical state of the tissue. This concept uses a coarse, macro-level deformation mesh to maintain both computational speed and the illusion of reality and a simple geometric point mapping method to include detailed fine mesh information. The resulting system allows for flexible simulation of different types of localized sensor measurement techniques. Preliminary simulation results are provided using a real-time capable simulation environment and prove the feasibility of the method.

Paper 36: Change in Humeral Anchor Position Significantly Affects Isometry in UCL Repair: A 3-Dimensional Computer Modeling Study

Objectives:Medial ulnar collateral ligament (UCL) repair utilization is increasing in recent years, bolstered by shorter rehabilitation and satisfactory clinical outcomes. While previous literature has illustrated the importance of tunnel position on restoring graft isometry in UCL reconstruction, there remains a paucity of literature guiding anchor placement in UCL repair. Herein, we describe a 3-dimensional (3D) elbow model to measure and optimize anchor location during UCL repair.Methods:A 3D computer model of a human elbow joint was created using CT and MRI images from a single patient. The humeral and ulnar attachments of the UCL were plotted using three distinct methodologies: 1) geometric cloud mapping; 2) quantitative measurements as described by the anatomical studies by Camp et al1; and 3) Frangiamore et al2. A 3.5mm-diameter clockface was placed on each attachment site which allowed for simulation of 12 distinct, 1.75mm deviations in anchor position. The three elbow models were then ranged through 0-120 degrees of flexion at 10-degree increments, and the 3D distances were measured between the two ligament centroids. The humeral and ulnar anchors were sequentially repositioned around the clockfaces, and ligament lengths were again measured to evaluate changes in isometry. An independent t-test was performed to determine if there was a significant difference in isometry between the humeral or ulnar anchor deviations.Results:Using method 1, the UCL length at 90 degrees of elbow flexion was 26.8mm. This ligament underwent 13.6mm of total excursion for a 46.4% change in length throughout arc of motion. Method 2 produced a 19.3mm ligament that underwent 0.8mm of excursion for a 3.9% length change throughout the arc. Method 3 produced a 24.5mm ligament that underwent 2.3mm of excursion for a 9.4% length change throughout arc. Identifying ligament footprints using the quantitative anatomical measurements as described by Camp et al1 and Frangiamore et al2 produced better ligament isometry through 120 degrees of flexion (ligament length changes of 3.9% and 9.4%, respectively) when compared to using the geometric cloud technique (46.4% length change). Humeral anchor deviations produced a statistically significant increase in ligament excursion when compared to ulnar anchor deviations (p < 0.001).Conclusions:When performing UCL repair, small deviations in humeral anchor position may significantly influence graft and ligament isometry. Anchor position was most isometric while using the quantitative measurements as described in Camp et al1. Particularly when addressing detachments of the humeral footprint, surgeons should be critical of the humeral anchor position in order to restore native anatomy and optimal biomechanics.

Geological feature driven 3D geological modeling

In 3D geological modeling, it is generally difficult to effectively integrate geometric data and attribute data due to their different characteristics. In order to realize the integration of geological features, we propose a 3D geological modeling technology driven by geological features. We construct the geometric structure model based on 3D spatial data. By solving the geometric mapping and topological correlation of geological features, we establish the topological relationship between attribute data of various geological features and graphic elements of geometric model, and realize the effective constraints of attribute data and geometric data. Finally, we obtain a 3D geological model driven by geological features satisfying the unique topological relationship. The experimental verification is carried out through the actual engineering data located in the slope zone between Yunnan Guizhou Plateau and Guangxi basin. This technology solves the effective fusion of geometric data and attribute data, provides a comprehensive 3D model for geological comprehensive analysis and engineering application.

Quantum geometric maps and their properties

Quantum geometric maps, which relate SU(2) spin networks and Lorentz covariant projected spin networks, are an important ingredient of spin foam models (and tensorial group field theories) for four-dimensional quantum gravity. We give a general definition of such maps, that encompasses all current spin foam models, and we investigate their properties at such general level. We then specialize the definition to see how the precise implementation of simplicity constraints affects features of the quantum geometric maps in specific models.

EFEKTIFITAS KINERJA SIMPANG TAK BERSINYAL BUNDARAN KELAPA GADING DENGAN SIMPANG BERSINYAL

The Kelapa Gading roundabout junction, North Jakarta is one of the unsignalized intersections with the roundabout. Traffic conditions that have a density in every arm, trigger traffic jams during rush hours. In this study, an analysis of the performance of the Kelapa Gading roundabout will be presented.Primary data includes geometric, environmental conditions, traffic flow and location maps. While secondary data includes population and vehicle growth in DKI Jakarta Province. The research method uses the formula contained in the 1997 MKJI and modeling using the Vissim Student Version softwareAfter evaluating the performance of the roundabout, it is found that the capacity, degree of saturation, delays and opportunities for queuing roundabouts. If the degree of saturation DS&gt;0.75 in one or several parts of the road can be changed to a signalized intersection. Key words: Kelapa Gading Roundabout, Signalized intersection, MKJI,

Einstein Yang-Mills amplitudes from intersections of twisted forms

We present a geometric derivation of all-multiplicity (single-trace) tree-level Einstein Yang-Mills (EYM) amplitudes mathcal{A} (n; r) involving n gluons and r gravitons by a bilinear of two twisted differential forms on the moduli space of Riemann spheres with m := n + r punctures. The differential forms are gained by studying the underlying superstring disk amplitude and proposing an embedding of the disk onto the sphere. This map can be interpreted as a geometrical map from the open superstring to a heterotic or ambitwistor string structure. Then, the twisted intersection number of the two m-forms, which is obtained by integrating over the moduli space of Riemann sphere with m punctures, reproduces in the infinite inverse string tension limit α′ → ∞ the corresponding CHY formula of the EYM amplitude. To bolster our findings we study the disk amplitude of open and closed strings using the Graßmann description of the underlying superstring amplitude, map it to a closed string amplitude and consider the α′ → ∞ limit. Finally, we present an all-multiplicity decomposition formula of any EYM amplitude mathcal{A} (n; r) as linear combination over (m − 3)! pure m gluon subamplitudes.

A deformation model and draping behavior analysis of plain weave fabric with low-twist yarn on continuous surface

Fiber-reinforced composites have been widely applied in aerospace, transportation and other industrial applications. An effective method shaping the complex performs is draping plain fabrics on the mandrel surface. However, it is a challenge to realize and predict accurately the deformation of fabric. To establish an accurate deformation mode, plain weave fabrics with low-twist yarn were classified into a stable structure that are not easy to deform and an unstable structures with large deformability based on microstructure characteristics. A variable microstructure unit-cell model has been established to analyze the variation of fabric geometry and performance during deformation. To analyze the draping behavior of fabric with large deformation, a four-node unit was used to mesh the fabric, and then each node on the fabric was mapped to the mandrel surface. The deformation of fabric after draping was simulated by the continuous change of the unit mesh. Analysis results showed that the thickness of preform decreases with the increase of the major-axis of the yarn cross-section, and the formability of fabric increases with the increase of fabric pitch. The accuracy and effectiveness of the geometric mapping method are verified by the fabric drape experiment.

A neural refinement network for single image view synthesis

Recent years have seen an increasing interest in single image view synthesis. It remains however a challenging task due to the lack of comprehensive colour and depth information from different views. In this paper, we propose a novel view synthesis approach that incorporates a Neural Image Refinement Network (NIRN) and generates both depth and colour images for the target view in an end-to-end manner. The appearance of the colour image greatly benefits from the generated depth image as it provides an intermediate projection relationship for the object in the 3D world. Since the direct application of geometric projection mapping will result in empty regions and/or distortions, our approach proposes to embed a novel refinement network into the view synthesis pipeline for improved performance. Experimental results on three publicly available datasets demonstrate that our NIRN outperforms other state-of-the-art view synthesis methods.

Robust numerical integration on curved polyhedra based on folded decompositions

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the given parametric surfaces. Each pyramid serves as an integration cell with a geometric mapping from a standard parent domain (e.g., a unit cube), where the tensor-product Gauss quadrature is adopted. As no constraint is imposed on the decomposition, certain resulting pyramids may intersect with themselves, and thus their geometric mappings may present negative Jacobian values. We call such cells folded cells and refer to the corresponding decomposition as a folded decomposition. We show that folded cells do not cause any issues in practice as they are only used to numerically compute certain integrals of interest. The same idea can be applied to planar curved polygons as well. We demonstrate both theoretically and numerically that folded cells can retain the same accuracy as the cells with strictly positive Jacobians. On the other hand, folded cells allow for a much easier and much more flexible decomposition for general curved polyhedra, on which one can robustly compute integrals. In the end, we show that folded cells can flexibly and robustly accommodate real-world complex geometries by presenting several examples in the context of immersed isogeometric analysis, where involved sharp features can be well respected in generating integration cells.