Geometric Mapping Research Articles

Semantic Mapping for Mobile Robots in Indoor Scenes: A Survey

Sensing and mapping its surroundings is an essential requirement for a mobile robot. Geometric maps endow robots with the capacity of basic tasks, e.g., navigation. To co-exist with human beings in indoor scenes, the need to attach semantic information to a geometric map, which is called a semantic map, has been realized in the last two decades. A semantic map can help robots to behave in human rules, plan and perform advanced tasks, and communicate with humans on the conceptual level. This survey reviews methods about semantic mapping in indoor scenes. To begin with, we answered the question, what is a semantic map for mobile robots, by its definitions. After that, we reviewed works about each of the three modules of semantic mapping, i.e., spatial mapping, acquisition of semantic information, and map representation, respectively. Finally, though great progress has been made, there is a long way to implement semantic maps in advanced tasks for robots, thus challenges and potential future directions are discussed before a conclusion at last.

Tuned hybrid nonuniform subdivision surfaces with optimal convergence rates

AbstractThis article presents an enhanced version of our previous work, hybrid nonuniform subdivision (HNUS) surfaces, to achieve optimal convergence rates in isogeometric analysis (IGA). We introduce a parameter () to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid nonuniform subdivision (tHNUS). Thus, HUNS is a special case of tHNUS when . While introducing in hybrid subdivision significantly complicates the theoretical proof of G1 continuity around extraordinary vertices, reducing can recover optimal convergence rates when tHNUS functions are used as a basis in IGA. From the geometric point of view, tHNUS retains comparable shape quality as HNUS under nonuniform parameterization. Its basis functions are refinable and the geometric mapping stays invariant during refinement. Moreover, we prove that a tHNUS surface is globally G1‐continuous. From the analysis point of view, tHNUS basis functions form a nonnegative partition of unity, are globally linearly independent, and their spline spaces are nested. In the end, we numerically demonstrate that tHNUS basis functions can achieve optimal convergence rates for the Poisson's problem with nonuniform parameterization around extraordinary vertices.

On mapping irregular plates without four corners into a regular domain

In structural analysis, the technique of mapping an irregular plate into a regular domain is commonly used. When the irregular plate does not have four corners, some important issues on the geometric mapping should be taken care of and are clearly pointed out herein for the first time. Besides, general shape functions of 12-node Serendipity finite element with nodes of any type are proposed to improve the accuracy of geometric mapping.

Damage and failure analyses of 3D4d braided composite shafts under torsional load and the effects of braid processing parameters on their torsional properties

AbstractThis paper presented the numerical and experimental studies on the torsional properties of 3D braided composite shafts. The torsion test was first conducted, then a parametric tubular unit cell model was constructed based on geometric mapping relations to detail the micro geometries of the shafts. The local yarn orientations were derived using finite deformation theory, and the 3d Hashin failure criterions were adopted to simulate the progressive damage behaviors of the shafts. The predicted results were in good agreements with the experimental ones, which validated the FE model. Based on the FE results, the damage was analyzed in detail, it was found that the transverse shear‐tension damage of longitudinally compressive yarns was critical for the failures of 3D4d braided composite shafts under torsional load. The surface damage initiated first, and then propagated into the internal structure, while the internal damage was much severe in the final failure morphology. The effects of braid processing parameters (M, N, γr, and r1,) on the torsional properties were also reported. A dependency of increasing then decreasing was confirmed by the simulation results for all four parameters, and it was found that the peak values could be achieved when the average braiding angle was around 45o.

Study of beam shaped of large-aperture top-emitting laser device

The output beam of the large-aperture top emitting laser is a kind of annular beam, the beam quality of which is poor and the spot energy distribution is not uniform. This characteristic of large-aperture top-emitting laser restricts its application in many fields. In order to improve the annular light profile to flat-top beam, a beam shaped DOE designed by modified G–S algorithm which based geometric mapping is applied on the surface of the output aperture. The simulation results show that the designed diffractive optical elements have good shaping effect and high light energy utilization. The output characteristics of the devices with and without DOE are tested in the lab. It found that the beam of the device with DOE appears more uniform than the device without DOE and as the injected current increased the light intensity of the center maintain a good uniformity.

Models for representing limit states in geomechanics

A new paradigm of scientific knowledge enabling to display the ultimate stress-strain states in geomechanics is presented in the article. In this case, distortion serves as a natural science theory. The main results concerning the development of distortion theory in natural systems are presented. Geometrical models for representing limiting states and determining distortion invariance during the materials deformation are shown. The format for forming a “strength certificate” of organic mineral soils for solving power and energy problems in the design of executive working bodies of mining machines is given. The technique for representing deformation processes in a reduced square system is described. The proposed methodology and criteria for the stress-strain state are a further development of the E.I. Shemyakin’s synthetic theory of strength. Areas of mutual influence of the main parameters of the soils strength certificate are as follows: specific adhesion and angle of internal friction and their compliance with the experiments of Buisman. The universality of the models under consideration is shown. This enables to give a mathematical description of the limiting parameters and criteria of stress-strain states in an invariant form and a clear geometric mapping.

Automatic structural mapping and semantic optimization from indoor point clouds

Indoor map plays an important role in the fields of indoor position and navigation, location-based services and emergency response. In this study, we address the issue of how to automatically generate indoor geometric maps from laser point clouds, in a manner that is not restricted to the Manhattan-world assumptions. The proposed method comprises two main contributions, namely, (i) indoor geometric structure extraction by the M-RSC (Modified Ring-Stepping Clustering) method and (ii) semantic-constrained optimization models. In the extraction phase, the extracted lines are usually irregular and incomplete because of missing data, object occlusions, and density change of point clouds, etc. Therefore, feature points of initial structural lines are extracted and introduced into the optimization models by different semantic constraints. Additionally, four indoor datasets are tested to demonstrate our approach. Experimental results show that the proposed method is effective and can make the final indoor maps more accurate in terms of the geometry.

The Event Detection System in the NEXT-White Detector.

This article describes the event detection system of the NEXT-White detector, a 5 kg high pressure xenon TPC with electroluminescent amplification, located in the Laboratorio Subterráneo de Canfranc (LSC), Spain. The detector is based on a plane of photomultipliers (PMTs) for energy measurements and a silicon photomultiplier (SiPM) tracking plane for offline topological event filtering. The event detection system, based on the SRS-ATCA data acquisition system developed in the framework of the CERN RD51 collaboration, has been designed to detect multiple events based on online PMT signal energy measurements and a coincidence-detection algorithm. Implemented on FPGA, the system has been successfully running and evolving during NEXT-White operation. The event detection system brings some relevant and new functionalities in the field. A distributed double event processor has been implemented to detect simultaneously two different types of events thus allowing simultaneous calibration and physics runs. This special feature provides constant monitoring of the detector conditions, being especially relevant to the lifetime and geometrical map computations which are needed to correct high-energy physics events. Other features, like primary scintillation event rejection, or a double buffer associated with the type of event being searched, help reduce the unnecessary data throughput thus minimizing dead time and improving trigger efficiency.

Deep Dense Multi-Scale Network for Snow Removal Using Semantic and Depth Priors.

Images captured in snowy days suffer from noticeable degradation of scene visibility, which degenerates the performance of current vision-based intelligent systems. Removing snow from images thus is an important topic in computer vision. In this paper, we propose a Deep Dense Multi-Scale Network (DDMSNet) for snow removal by exploiting semantic and depth priors. As images captured in outdoor often share similar scenes and their visibility varies with depth from camera, such semantic and depth information provides a strong prior for snowy image restoration. We incorporate the semantic and depth maps as input and learn the semantic-aware and geometry-aware representation to remove snow. In particular, we first create a coarse network to remove snow from the input images. Then, the coarsely desnowed images are fed into another network to obtain the semantic and depth labels. Finally, we design a DDMSNet to learn semantic-aware and geometry-aware representation via a self-attention mechanism to produce the final clean images. Experiments evaluated on public synthetic and real-world snowy images verify the superiority of the proposed method, offering better results both quantitatively and qualitatively. https://github.com/HDCVLab/Deep-Dense-Multi-scale-Network https://github.com/HDCVLab/Deep-Dense-Multi-scale-Network.

Not Only Look But Infer: Multiple Hypothesis Clustering of Data Association Inference for Semantic SLAM

In semantic visual simultaneous localization and mapping (VSLAM), accurate data association of semantic measurement from visual sensor is very crucial for robot state estimation and scene reconstruction. However, most of the related works assume a simple world for semantic association. It is still a challenge to deal with the ambiguity of data association in a cluttered environment. In this article, we propose a novel approach to reduce the uncertainty of data association via multiple hypothesis Dirichlet process (MHDP). The posterior distribution of data association is inferred by Dirichlet process (DP) first. Ambiguous associations from the distribution are tackled by a hypothesis tree, and hypothesis testing-based ambiguity judgment is then proposed for each object measurement to provide a strategy for branch growing of the hypothesis tree. Moreover, the proposed data association approach is integrated with a geometric featured-based simultaneous localization and mapping (SLAM) system in a tightly coupled way. The qualitative and quantitative evaluation on simulated and real-world public data sets demonstrates the robustness and effectiveness of our approach compared to other data association methods and the state-of-the-art SLAM system.

Geometric mapping of the eye lens and its epithelium reveals changes that accompany emmetropia

PurposeTo investigate changes in both lens shape and the epithelial distribution as emmetropia is established in C57Bl6J mice between postnatal weeks 4 to 6.MethodsWe used a computational approach to produce geometrical maps of the mouse lens and its epithelium. Conveniently our approach ulitises data collected from intact lenses imaged using a conventional laser scanning confocal microscope. It delivers cartesian coordinates for every epithelial cell in the lens epithelium. We chose to investigate lenses during postnatal weeks 4 to 6, a time during lens development when emmetropia is established in this inbred strain of mice (Tkatchenko et al., 2010).ResultsGeometric mapping standardises the measurement and analysis of lens epithelial cell densities. Emmetropia is established in C57Bl6J inbred mice, but many other strains exhibit considerable refractive error (Tkatchenko et al., 2019). The eye lens plays its part in the development and establishment of emmetropia in mice (Tkatchenko et al., 2010; Pardue et al., 2013). We record a change in the shape of the eye lens from a spheroid to a lentoid shape between postnatal weeks 4 and 6. The distribution of the epithelial cells in the lens epithelium also changes from a non‐zonal to a zonal distribution, with characteristics that typify the epithelia of adult animals. We correlate these observations regarding lens geometry with genetic mutations in lens cytoskeletal proteins found in those strains that present with refractive error, but which are absent from C57Bl6J (Sandilands et al., 2004). We discuss the potential significance of these observations in the context of the mechanistic basis of the lens contribution to emmetropia.ConclusionsThe development of emmetropia in the C57Bl6J inbred strain of mice correlates with changes in epithelial cell organisation and changes in lens geometry, which when combined with strain‐specific genetic differences offer a mechanistic understanding involving the lintermediate filament cytoskeleton.Pardue, M. T., et al., (2013) Exp Eye Res, 114, 96–105.Sandilands, A., et al (2004). Eye Res. 78, 109–123.Tkatchenko, T. V. et al. (2019). BMC Medical Genomics, 12, 1–24.Tkatchenko, T. V., Shen, Y. and Tkatchenko, A. V. (2010) Invest Ophth Vis Sci, 51, 21–27. https://doi.org/10.1167/iovs.08‐2767

Relativity Isoframes—A Useful and Potentially Unifying Conceptual Framework

This brief note introduces the conceptual framework of special and general relativity isoclocks and isoframes. Isoclocks and isoframes, as defined herein, can be used to create geometrical maps of space and time (“space-time”) with and without matter embedded. They are useful for having a mental picture of space-time relationships without having to picture 4-dimensional manifolds, which very few students and scientists are able to do. With the aid of the optical lensing definition of curvature as inverse radius, a new gravitational force equation is derived, which also incorporates Einstein’s mass/energy relation in the mx term. Thus, one may see how it is that gravitational force correlates with its time-embedded curvature-squared (Cx2) space in a more accurate formulation than could be envisioned by Newton. This becomes more apparent in high gamma fields, such as found near a black hole horizon. It is hoped that probability theories, such as quantum field theories in curved space-time, might be adaptable to the general relativity isoframe concept introduced herein.

Design Optimization of Origami-Tunable Frequency Selective Surfaces

Recent studies demonstrate the benefit of integrating origami in many engineering applications, where computational methods facilitate the origami design process. An emerging concept utilizes origami design for physically and functionally flexible electromagnetic devices. However, coupled mechanical and electromagnetic design tools are needed to systematically navigate the complex spaces of fold topology and electromagnetic performance. In this article, we introduce topology optimization formulations that find origami fold-driven frequency selective surface designs possessing electromagnetic filtering properties at target frequencies. These formulations utilize a nonlinear mechanics analysis to simulate an origami folding process. A geometric mapping relates mechanically-relevant origami substrate properties and electromagnetically-relevant conductive element properties. Both gradient-based and genetic algorithm methods are used to find optimal origami crease patterns and folded configurations by optimizing fold stiffness and force distributions over a prescribed potential fold line network. Using nonlinear manifold learning techniques, we demonstrate the isolated nature of optimal design candidates in the design space and the complex interplay of fold topology and fold path selection through initial perturbation from the flat state. Collectively, this study provides an initial framework to design novel EM origami structures and also provides important insights on the complex nature of the design space, which can be leveraged to refine future tool development.

Mining Geometric Constraints From Crowd-Sourced Radio Signals and its Application to Indoor Positioning

Crowd-sourcing has become a promising way to build a feature-based indoor positioning system that has lower labour and time costs. It can make full use of the widely deployed infrastructure as well as built-in sensors on mobile devices. One of the key challenges is to generate the reference feature map (RFM), a database used for localization, by aligning crowd-sourced trajectories according to associations embodied in the data. In order to facilitate the data fusion using crowd-sourced inertial sensors and radio signals, this paper proposes an approach to adaptively mining geometric information. This is the essential for generating spatial associations between trajectories when employing graph-based optimization methods. The core idea is to estimate the functional relationship to map the similarity/dissimilarity between radio signals to the physical space based on the relative positions obtained from inertial sensors and their associated radio signals. Namely, it is adaptable to different modalities of data and can be implemented in a self-supervised way. We verify the generality of the proposed approach through comprehensive experimental analysis: i) qualitatively comparing the estimation of geometric mapping models and the alignment of crowd-sourced trajectories; ii) quantitatively evaluating the positioning performance. The 68% of the positioning error is less than 4.7 m using crowd-sourced RFM, which is on a par with manually collected RFM, in a multi-storey shopping mall, which covers more than 10, 000 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

Variational formulation and differential quadrature finite element for freely vibrating strain gradient Kirchhoff plates

AbstractIn this paper, we apply the energy variational principle to arrive at the differential equation of motion and all appropriate boundary conditions for strain gradient Kirchhoff micro‐plates. The resulting sixth‐order boundary value problem of free vibration is solved by a thirty‐six‐DOF four‐node differential quadrature plate finite element. The C2‐continuity condition of the deflection is guaranteed by devising a sixth‐order differential quadrature‐ based geometric mapping scheme that can transform the displacement parameters at Gauss‐Lobatto quadrature points into those at element nodes. The total potential energy of a generic micro‐plate element is firstly discretized in terms of nodal parameters. It is then minimized to obtain the formulation of element stiffness and mass matrices. For comparison reasons, a Hermite interpolation‐based strain gradient finite element is provided. With the help of the symbolic computation system Maple, the explicit algebraic relationship between the stiffness (or mass) matrices of two types of elements is derived. Convergence and comparison studies are conducted to show the efficacy of our element in the free vibration analysis of macro/micro‐ plates. Finally, we apply the developed method to study the size‐dependent vibration behavior of micro‐plates with uniform or stepped thickness. Numerical examples reveal that strain gradient effects can change the vibration mode shapes, not the vibration frequencies alone.

Prediction accuracy of reservoir break flood simulation model using finite volume method and UAV

Methods for producing high-resolution digital topographic maps using an unmanned aerial vehicle (UAV), and 3D fluid dynamics simulation to estimate the flooded areas caused by a collapsed reservoir, were proposed in this paper. The UAV flight path for photographing damaged areas was divided into two sections considering the drone flight time and overlapping range of the images in the x- and y-directions. The metadata taken by the drone were transferred into world coordinates by tracking the key features of the photographs of nearby areas using a 3D rotation matrix. The point cloud data with a 3D space were extracted from the registered images, and a digital surface map (DSM) was produced using a point cloud classification geometric mapping technique. To amend the serious elevation errors caused by natural or artificial obstacles, a kriging interpolation method was used to reproduce the DSM. A transient computational simulation that considers both the complex geometric topology and hydrodynamic energy of flowing water was conducted using FLOW-3D software to deal with an renormalization group (RNG) turbulence model. The flooded areas calculated through visual reading using images taken by the UAV were compared with the 3D simulation results for verification. The flooded areas estimated through the simulation were approximately 18.3% larger than those found by visual reading. Turbulent flows were mainly observed in obstacles or curved areas of the stream, and the differences in the water depth could be further increased. However, the villagers confirmed that the flooded areas were much greater than what was seen through the visual reading. Therefore, the combination of UAV surveying and the 3D simulation method based on the RNG turbulence model is recommended to accurately estimate flooded areas, and it will support an administrative policy aimed at minimizing the economic costs of damage caused by future reservoir collapses. Keywords: reservoir failure, flooded area, finite volume method, unmanned aerial vehicle, photogrammetric survey, digital surface model DOI: 10.25165/j.ijabe.20201306.4909 Citation: Jeon J, Choi W. Prediction accuracy of reservoir break flood simulation model using finite volume method and UAV. Int J Agric & Biol Eng, 2020; 13(6): 7–15.

High resolution 3-D modelling of cylinder shape bodies applied to ancient columns of a church

Abstract. The use of Non-Destructive Testing (NDT) applied to construction materials allows to highlight and characterize their features, especially in the case of old buildings. The multi-technique high resolution 3D modelling described here is aimed to investigate the conservation state of the central column of a colonnade in the ancient church of Saints Lorenzo and Pancratio, dating to about the second half of the thirteenth century and located in the old town of Cagliari (Italy). This column was considered of interest because its longitudinal axis deviates from its ideal position and it appears the most deteriorated. In this work we describe the integrated application of 3D diagnostic methods, i.e. Terrestrial Laser Scanner (TLS), close range photogrammetry (CRP) and ultrasonic tomography supported by petrographic investigations. They were used to improve the diagnostic process of the conservation state of the investigated column. The TLS technique was supported by CRP to obtain a natural colour texturized 3D model of the column. The geometrical anomaly maps derived from the data of the TLS-CRP survey show the presence of some anomalies worthy of attention. Starting from the 3D reconstruction with previous techniques we planned and implemented a 3D ultrasonic tomography. Ultrasonic tomography proved to be a successful tool in identifying internal defects, as well as the presence of voids and flaws within the materials through the analysis of the propagation of ultrasonic waves. The integration of the three non-invasive techniques supported by petrographical analyses demonstrates its potential in reducing ambiguities since each technique brings its clue to the overall diagnostic process.

Zagreb Connection Numbers for Cellular Neural Networks

Neural networks in which communication works only among the neighboring units are called cellular neural networks (CNNs). These are used in analyzing 3D surfaces, image processing, modeling biological vision, and reducing nonvisual problems of geometric maps and sensory-motor organs. Topological indices (TIs) are mathematical models of the (molecular) networks or structures which are presented in the form of numerical values, constitutional formulas, or numerical functions. These models predict the various chemical or structural properties of the under-study networks. We now consider analogous graph invariants, based on the second connection number of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for the cellular neural networks (CNNs). In order to find their efficiency, a comparison among the obtained indices of CNN is also performed in the form of numerical tables and 3D plots.

Towards exterior/interior correspondence of black-holes

We describe a simple approach for a possible connection between the exterior and interior of black-holes. According to our result, the Schwarzschild radius determines a [Formula: see text]-dimensional sphere that separates two worlds: the exterior, where ordinary matter moves with velocities less than the light velocity, and the interior, where tachyons move with velocities greater than the light velocity. Moreover, we find a geometric map in the complex plane that connects ordinary matter with faster than light particles. Motivated by these results, we also find that the exterior and the interior structures of black-holes can be unified in a world of [Formula: see text]-dimensions. Finally, we comment about the possibility that superluminal particles in the interior of a black-hole may provide an alternative solution of the rotation curves of spiral galaxies.

Strain gradient differential quadrature finite element for moderately thick micro‐plates

SummaryIn this study, we integrate the advantages of differential quadrature method (DQM) and finite element method (FEM) to construct a C1‐type four‐node quadrilateral element with 48 degrees of freedom (DOF) for strain gradient Mindlin micro‐plates. This element is free of shape functions and shear locking. The C1‐continuity requirements of deflection and rotation functions are accomplished by a fourth‐order differential quadrature (DQ)‐based geometric mapping scheme, which facilitates the conversion of the displacement parameters at Gauss‐Lobatto quadrature (GLQ) points into those at element nodes. The appropriate application of DQ rule to non‐rectangular domains is proceeded by the natural‐to‐Cartesian geometric mapping technique. Using GLQ and DQ rules, we discretize the total potential energy functional of a generic micro‐plate element into a function of nodal displacement parameters. Then, we adopt the principle of minimum potential energy to determine element stiffness matrix, mass matrix, and load vector. The efficacy of the present element is validated through several examples associated with the static bending and free vibration problems of rectangular, annular sectorial, and elliptical micro‐plates. Finally, the developed element is applied to study the behavior of freely vibrating moderately thick micro‐plates with irregular shapes. It is shown that our element has better convergence and adaptability than that of Bogner‐Fox‐Schmit (BFS) one, and strain gradient effects can cause a significant increase in vibration frequencies and a certain change in vibration mode shapes.