Geometric Point Research Articles

3D CITY MODELS FOR URBAN MINING: POINT CLOUD BASED SEMANTIC ENRICHMENT FOR SPECTRAL VARIATION IDENTIFICATION IN HYPERSPECTRAL IMAGERY

Abstract. Urban mining aims at reusing building materials enclosed in our cities. Therefore, it requires accurate information on the availability of these materials for each separate building. While recent publications have demonstrated that such information can be obtained using machine learning and data fusion techniques applied to hyperspectral imagery, challenges still persist. One of these is the so-called ’salt-and-pepper noise’, i.e. the oversensitivity to the presence of several materials within one pixel (e.g. chimneys, roof windows). For the specific case of identifying roof materials, this research demonstrates the potential of 3D city models to identify and filter out such unreliable pixels beforehand. As, from a geometrical point of view, most available 3D city models are too generalized for this purpose (e.g. in CityGML Level of Detail 2), semantic enrichment using a point cloud is proposed to compensate missing details. So-called deviations are mapped onto a 3D building model by comparing it with a point cloud. Seeded region growing approach based on distance and orientation features is used for the comparison. Further, the results of a validation carried out for parts of Rotterdam and resulting in KHAT values as high as 0.7 are discussed.

Differential Geometry of Identity Maps: A Survey

An identity map idM:M→M is a bijective map from a manifold M onto itself which carries each point of M return to the same point. To study the differential geometry of an identity map idM:M→M, we usually assume that the domain M and the range M admit metrics g and g′, respectively. The main purpose of this paper is to provide a comprehensive survey on the differential geometry of identity maps from various differential geometric points of view.

Two-dimensional elastic Bloch waves in helical periodic structures

The goal of this paper is to investigate the propagation of two-dimensional elastic Bloch waves in helical periodic structures, obeying two discrete screw symmetries about the same axis. First, a three-dimensional coordinate system is built from the two helical directions of periodicity of the problem and the radial coordinate originating from the symmetry axis. The existence of Bloch waves in bi-helical structures can be justified owing to the independence of the metric tensor of the coordinate system on both helical coordinates. Considering the elastodynamic equilibrium equations, Bloch theorem is expressed in appropriate bases to project the vector wavefields, namely the covariant/contravariant bases of the bi-helical coordinate system (or, alternatively, the cylindrical basis). From a geometrical point of view, the three-dimensional unit cell is delimited by non-plane boundaries, which must be carefully parametrized. The so-called wave finite element method is then applied to numerically solve the Bloch wave eigenproblem and the implementation of the numerical method in a bi-helical system is detailed. Owing to the cylindrical nature of the geometry, the two-dimensional propagation constants are not independent to each other. The relationship between both constants is established. The calculation of wave mode properties (wavenumbers, group and energy velocities) is performed along the helical propagation directions, as well as the straight axial and circumferential directions. Numerical validations of the overall approach are carried out for cylindrical uniform tubes and a chiral nanotube. Finally, the method is applied to a complex multi-wire structure, often encountered in energy cables, consisting of two layers of helical wires twisted in opposite directions.

Lung Nodule Classification on CT Images Using Deep Convolutional Neural Network Based on Geometric Feature Extraction

Lung cancer detection in the earlier stage is essential to improve the survival rate of the cancer patient. Computed Tomography [CT] is a first and preferred modality of imaging for detecting cancer with an enhanced rate of diagnosis accuracy owing to its function as a single scan process. Visual inspections of the CT images are prone to error, as it is more complex to distinguish lung nodules from the background tissues which are subjective to intra and interobserver variability. Hence, computer-aided diagnosis is essential to support radiologists for accurate lung nodule prediction. To overcome this issue, we propose a deep learning approach for automatic lung cancer detection from a low dose CT images. We also propose image pre-processing using Efficient Adaptive Histogram Equalization based Region of Interest [EAHE-ROI] to enhance the CT scan and to eliminate artefacts which occur due to noise and variations of the image. The ROI is extracted from CT scans using morphological operators, thus reducing the number of false positives. We chose geometric features as they extract more geometric elements like curves, lines and points of cancer nodules. Our Non-Gaussian Convolutional Neural Networks [NG-CNN] architecture contains feature extractor and classifier, which has been applied on training, validation and test dataset. Our proposed methodology offers better-classified outcome and effectual cancer detection by outperforming the other competing methods and gives a test accuracy of 94.97% and AUC 0.896.

Invariant conservation law-preserving discretizations of linear and nonlinear wave equations

Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils using the theory of Lie point symmetries of difference equations and the discrete direct multiplier method of conservation law construction. In particular, for the linear wave equation, an explicit five-point scheme is presented that preserves the discrete analogs of its basic geometric point symmetries and six of the corresponding conservation laws. For a class of nonlinear wave equations arising in hyperelasticity, a nine-point implicit scheme is constructed, preserving four-point symmetries and three local conservation laws. Other discretizations of the nonlinear wave equations preserving different subsets of conservation laws are discussed.

C7 sacral tilt (C7ST): a novel spinopelvic parameter reveals the relationship between pelvic parameters and global spinal sagittal balance and converts pelvic parameters into spinal parameters.

The aim is to propose a novel spinopelvic parameter C7 sacral tilt (C7ST), of which its sum with global tilt (GT) is equal to pelvic incidence (PI), from a geometrical point of view. A cohort of 198 patients was recruited and the whole lateral spine and pelvic radiographs were performed. The following sagittal parameters were measured: sagittal vertical axis (SVA), C7 vertical tilt (C7VT), sacral slope (SS), pelvic tilt (PT), PI, GT and C7ST. The correlations between them were analyzed using the Pearson or Spearman correlation coefficient, and simple linear regressions were simultaneously conducted. P < 0.05 was set as the level of significance. Geometric construction by complementary angles revealed that PI = C7ST + GT, GT = PT + C7VT, and C7ST = SS - C7VT. Both C7ST and GT were moderately correlated with PI (R = 0.52 and 0.596, respectively), strongly correlated with SS and PT, respectively (SS = 0.9 * C7ST + 1.15, R = 0.955; PT = 0.87 * GT + 3.86, R = 0.96). The correlation coefficients of the SVA and C7VT, SVA and SS - C7ST, and SVA and GT - PT were 0.935, 0.925 and 0.863, respectively. The novel proposed spinopelvic parameter C7ST has the advantages of convenient measurement, reduced error, and extrapolation of other parameters. The greatest significance of proposing C7ST is that pelvic parameters (PI, PT and SS) are converted into spinal parameters (C7ST and GT), which is very helpful for a more intuitive understanding of the progression of spinal sagittal imbalance.

Stable Robotic Grasping of Multiple Objects using Deep Neural Networks

SUMMARYOptimal grasping points for a robotic gripper were derived, based on object and hand geometry, using deep neural networks (DNNs). The optimal grasping cost functions were derived using probability density functions for each local cost function of the normal distribution. Using the DNN, the optimum height and width were set for the robot hand to grasp objects, whose geometric and mass centre points were also considered in obtaining the optimum grasping positions for the robot fingers and the object. The proposed algorithm was tested on 10 differently shaped objects and showed improved grip performance compared to conventional methods.

Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values

In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic fuzzy values. In this study, we further investigate the problem of ranking intuitionistic fuzzy values from a geometric point of view, and we produce related applications to decision-making. We present Minkowski score functions of intuitionistic fuzzy values, which are natural generalizations of the expectation score function and other useful score functions in the literature. The rationale for Minkowski score functions lies in the geometric intuition that a better score should be assigned to an intuitionistic fuzzy value farther from the negative ideal intuitionistic fuzzy value. To capture the subjective attitude of decision makers, we further propose the Minkowski weighted score function that incorporates an attitudinal parameter. The Minkowski score function is a special case corresponding to a neutral attitude. Some fundamental properties of Minkowski (weighted) score functions are examined in detail. With the aid of the Minkowski weighted score function and the maximizing deviation method, we design a new algorithm for solving decision-making problems based on intuitionistic fuzzy soft sets. Moreover, two numerical examples regarding risk investment and supplier selection are employed to conduct comparative analyses and to demonstrate the feasibility of the approach proposed in this article.

A new solution to the discontinuity problem on metric spaces

We study on the Rhoades' question concerning the discontinuity problem at fixed point for a self-mapping T of a metric space. We obtain a new solution to this question. Our result generalizes some recent theorems existing in the literature and implies the uniqueness of the fixed point. However, there are also cases where the fixed point set of a self-mapping contains more than 1 element. Therefore, by a geometric point of view, we extend the Rhoades' question to the case where the fixed point set is a circle. We also give a solution to this extended version.

Analysis of the electrodynamic model of a biologically active point of animal skin

Flat-layered dielectric structure was considered as an electrodynamic model of bioactive point (BAP). This structure is formed by three flat dielectric layers and eventual cylinder filled by a dielectric (by the albumen of collagen). The upper layer designs burly cages, middle layer is blood and lymphatic vessels and an understratum is formed by nervous fibres that conduct and pass management signals from BAP to the central nervous system.Such electrodynamic structure is the dielectric resonator (eventual cylinder) located in a dielectric environment.We will examine affecting of informative electromagnetic radiation on bioactive point, the wave-length of which considerably excels geometrical sizes bioactive point. This fact allows averaging of material parameters on a coordinate . Therefore, it was assumed further, that material parameters (dielectric constant) of flat layered structure (model of bioactive point) does not depend on a coordinate , i.e. the electromagnetic field is axisymmetric.Such electromagnetic field can be excited by the circular electric current located at some distance from the external surface of bioactive point. It was supposed that this current excited harmonic oscillation with circular frequency and modulated on amplitude with frequency of modulation .The problem of the interaction of radio-pulse waves with a biologically active point is an unsteady diffraction problem. Using the complex amplitude method, this problem was reduced to the diffraction problem for electromagnetic fields that depend exponentially on time.By virtue of the principle of superposition, the solution to the original problem can be obtained as a superposition of the solutions of three problems using the complex amplitude method.Such electrodynamic structure allows defining the necessary parameters of the informative electromagnetic field for treatment of dyspepsia of newborn calves.

Preserving Location Privacy in UASN through Collaboration and Semantic Encapsulation

UASN has gained much attention during the past decades. Based on fruitful research and development, UASN could be a compelling component of the global IoT in the future. From the view of location privacy preservation, state-of-the-art investigations mainly concentrate on UASN infrastructures and focus on the location privacy preserving of the source location privacy of the infrastructures, such as anchor nodes, positioning nodes, and communication channel security. However, in the IoT scenario, the underwater positioning service provided by UASN becomes pervasive, and the location privacy of the end-user of this service will come into sight. On the other hand, the presentation model of underwater semantic location is still in use of traditional terrestrial coordinates and geometric points, the concept of underwater semantic location could be further adopted to improve the location privacy. In this article, both these two location privacy issues are concerned. From the view of a UASN positioning service user, we discuss location privacy-related problems and propos a UASN nodes collaboration method to prevent the adversary from learning the precise location of the user when they intercept the communication or hack the central node. Then a concept of "semantic envelope" is designed to encapsulate the location information, which could further strengthen the location privacy.

Variation of complex structures and variation of Lie algebras II: new Lie algebras arising from singularities

Finite dimensional Lie algebras are semi-direct product of the semi-simple Lie algebras and solvable Lie algebras. Brieskorn gave the connection between simple Lie algebras and simple singularities. Simple Lie algebras have been well understood, but not the solvable (nilpotent) Lie algebras. It is extremely important to establish connections between singularities and solvable (nilpotent) Lie algebras. In this article, a new natural connection between the set of complex analytic isolated hypersurface singularities and the set of finite dimensional solvable (nilpotent) Lie algebras has been constructed. We construct finite dimensional solvable (nilpotent) Lie algebras naturally from isolated hypersurface singularities. These constructions help us to understand the solvable (nilpotent) Lie algebras from the geometric point of view. Moreover, it is known that the classification of nilpotent Lie algebras in higher dimensions ($\gt 7$) remains to be a vast open area. There are one-parameter families of non-isomorphic nilpotent Lie algebras (but no two-parameter families) in dimension seven. Dimension seven is the watershed of the existence of such families. It is well-known that no such family exists in dimension less than seven, while it is hard to construct one-parameter family in dimension greater than seven. In this article, we construct an one-parameter family of solvable (resp. nilpotent) Lie algebras of dimension $11$ (resp. $10$) from $\tilde{E}_7$ singularities and show that the weak Torelli-type theorem holds. We shall also construct an one-parameter family of solvable (resp. nilpotent) Lie algebras of dimension $12$ (resp. $11$) from $\tilde{E}_8$ singularities and show that the Torelli-type theorem holds. Moreover, we investigate the numerical relation between the dimensions of the new Lie algebras and Yau algebras. Finally, the new Lie algebras arising from fewnomial isolated singularities are also computed.

Trifectas for TN in 5d

The trinions TN are a class of 5d mathcal{N} = 1 superconformal field theories (SCFTs) realized as M-theory on ℂ3/ℤN× ℤN . We apply to TN , as well as closely-related SCFTs that are obtained by mass deformations, a multitude of recently developed approaches to studying 5d SCFTs and their IR gauge theory descriptions. Thereby we provide a complete picture of the theories both on the Coulomb branch and Higgs branch, from various geometric points of view — toric and gluing of compact surfaces as well as combined fiber diagrams — to magnetic quivers and Hasse diagrams.

Second order analysis of geometric anisotropic point processes revisited

Various methods for directional analysis of spatial point patterns have been introduced in the literature. In this paper, we formulate a unifying framework for methods based on integral transforms of the second order product density. Examples include directional versions of Ripley’s K-function, wavelet transforms, and spectral analysis. Furthermore, we propose an additional method based on the projection of the Fry points of the point pattern on the unit sphere. This method solves some of the practical problems appearing in the application of the integral transform. In particular, it can be easily applied in 3D and provides a definition of an isotropy test without the need of replicated data. The method is evaluated in a simulation study.

Geometric Gibbs theory

Geometric models and Teichm\"uller structures have been introduced for the space of smooth expanding circle endomorphisms and for the space of uniformly symmetric circle endomorphisms. The latter one is the completion of the previous one under the Techm\"uller metric. Moreover, the spaces of geometric models as well as the Teichm\"uller spaces can be described as the space of H\"older continuous scaling functions and the space of continuous scaling functions on the dual symbolic space. The characterizations of these scaling functions have been also investigated. The Gibbs measure theory and the dual Gibbs measure theory for smooth expanding circle dynamics have been viewed from the geometric point of view. However, for uniformly symmetric circle dynamics, an appropriate Gibbs measure theory is unavailable, but a dual Gibbs type measure theory has been developed for the uniformly symmetric case. This development extends the dual Gibbs measure theory for the smooth case from the geometric point of view. In this survey article, We give a review of these developments which combines ideas and techniques from dynamical systems, quasiconformal mapping theory, and Teichm\"uller theory. There is a measure-theoretical version which is called $g$-measure theory and which corresponds to the dual geometric Gibbs type measure theory. We briefly review it too.

Geometrical constrained independent component analysis for hyperspectral unmixing

ABSTRACT One of the limitations of the hyperspectral remote sensing application is the existence of mixed pixels in image data. Spectral decomposition, which separates the mixed pixels into a set of endmember spectra and abundance fractions, is the most effective way to solve the mixed pixel problem. Due to the independence of source signals, independent component analysis (ICA) has been developed for hyperspectral unmixing by adding auxiliary constraints. Abundance sum-to-one and nonnegative constraints are two obvious features for hyperspectral data. In this paper, by processing these two constraints sequentially from the geometrical point of view to restrain the sum-to-one constraint thoroughly at each iteration, geometrical constrained ICA (GCICA) is proposed based on treating the abundance distribution as the independent signal. To validate the proposed algorithm, the synthetic data, and real image data are used for unmixing, respectively. Synthetic data are generated based on spectra from the ENVI (Environment for Visualizing Images) software spectral library. The real images are used with three hyperspectral datasets, AVIRIS (Airborne Visible Infrared Imaging Spectrometer) Cuprite dataset, AVIRIS Indiana Pine dataset and HYDICE (Hyperspectral Digital Imagery Collection Experiment) dataset. Results, in comparison with previously proposed algorithms, show that the proposed method has better performance for the decomposition of hyperspectral data in abundance and endmember spectral extraction, thus providing a new and effective method for spectral unmixing and signal separation without prior information.

Identification of a new acoustic sound field trend in modern catholic churches

This work describes the sound field transformation in catholic churches up today, focusing on a new possible acoustic trend in modern buildings.In the past, the sacred sense inside a church was greatly reinforced by the surrounding atmosphere of a very reverberant space, with possible echoes, that infatuated the perception of God and his presence. On the contrary, nowadays, concentration and intimacy are preferred.Modern Church buildings have become acoustically complex places. They are complex from the geometric point of view, because their dimensions and shapes may be extremely varied, passing from simple auditorium-like churches to complicated ones characterized by curved walls, side chapels, vaults which often act as partially coupled volumes. The range of the possible sound messages is also extremely varied passing from the spoken word to congregational singing and sometimes to organ music during the same liturgical service.In this paper some main recommendations to follow in the acoustic design of new catholic churches are presented, explaining two case studies in detail: the Santa Gianna Beretta Molla Church in Trezzano, Milan (IT) and the Massimiliano Kolbe Church in Bergamo (IT).Room Acoustics procedures and implementations of computer simulation techniques are included. A new approach for the acoustic design is proposed in which the acoustic response is suitable for both speech and music as recent room acoustics’ studies for other typologies of building such as theatres and multipurpose auditoria suggest.

A simple and practical representation of compatibility condition derived using a QR decomposition of the deformation gradient

This paper examines a condition for the existence and uniqueness of a finite deformation field whenever a Gram–Schmidt (QR) factorization of the deformation gradient $${\mathbf {F}}$$ is used. First, a compatibility condition is derived, provided that a right Cauchy–Green tensor $${\mathbf {C}} = {\mathbf {F}}^T {\mathbf {F}}$$ is prescribed. It is well-known that under this condition a vanishing of the Riemann curvature tensor $${\mathbb {R}}$$ ensures compatibility of a finite deformation field. We derive a restriction imposed on Laplace stretch $$\varvec{{\mathcal {U}}}$$ , arising from a QR decomposition of the deformation gradient, through this compatibility condition. The derived condition on Laplace stretch is unambiguous, because a Cholesky factorization of the right Cauchy–Green tensor ensures the existence of a unique Laplace stretch. Although a vanishing of the Riemann curvature tensor provides a necessary and sufficient compatibility condition from a purely geometric point of view, this condition lacks a direct physical interpretation in a sense that one cannot identify the restrictions imposed by this condition on a quantity that can be readily measured from experiments. On the other hand, our compatibility condition restricts dependence of components of a Laplace stretch on certain spatial variables in a reference configuration. Unlike the symmetric right Cauchy–Green stretch tensor $${\mathbf {U}}$$ obtained from a traditional polar decomposition of $${\mathbf {F}}$$ , the components of Laplace stretch can be measured from experiments. Thus, this newly derived compatibility condition provides a physical meaning to the somewhat abstract idea of the traditionally used compatibility condition, viz., a vanishing of the Riemann curvature tensor. Couplings between certain components of the Laplace stretch representing shear and elongation play a crucial role in deriving this condition. Finally, implications of this compatibility condition are discussed.

Atom scattering off a vibrating surface: An example of chaotic scattering with three degrees of freedom

We study the classical chaotic scattering of a He atom off a harmonically vibrating Cu surface. The three degree of freedom (3-dof) model is studied by first considering the non-vibrating 2-dof model for different values of the energy. The set of singularities of the scattering functions shows the structure of the tangle between the stable and unstable manifolds of the fixed point at an infinite distance to the Cu surface in the Poincaré map. These invariant manifolds of the 2-dof system and their tangle can be used as a starting point for the construction of the stable and unstable manifolds and their tangle for the 3-dof coupled model. When the surface vibrates, the system has an extra closed degree of freedom and it is possible to represent the 3-dof tangle as deformation of a stack of 2-dof tangles, where the stack parameter is the energy of the 2-dof system. Also for the 3-dof system, the resulting invariant manifolds have the correct dimension to divide the constant total energy manifold. By this construction, it is possible to understand the chaotic scattering phenomena for the 3-dof system from a geometric point of view. We explain the connection between the set of singularities of the scattering function, the Jacobian determinant of the scattering function, the relevant invariant manifolds in the scattering problem, and the cross-section, as well as their behavior when the coupling due to the surface vibration is switched on. In particular, we present in detail the relation between the changes as a function of the energy in the structure of the caustics in the cross-section and the changes in the zero level set of the Jacobian determinant of the scattering function.

On local active contour model for automatic detection of tumor in MRI and mammogram images

Tumor segmentation in medical images is an important step to determine and predict the stage, size and progression of tumors in realistic geometries and may be used for diagnosis and treatment follow-up in MRI and mammogram images. Automating this challenging task helps radiologists to reduce the high manual workload of brain or breast cancer analysis. Detecting tumor in medical images means to quantify the structure contents of the tumor. In this paper, we propose a model for quantifying the structure contents of the tumor in MRI and mammogram images. The proposed model is based on optimized Laplacian of Gaussian, which is useful in smoothing the homogeneous region and highlight the boundaries of the tumor structure. The proposed model uses local intensity information in later stage of segmentation as image data fitting. For this purpose, local Gaussian distribution is used for fitting image data and is combined with level set function. Due to usage of local intensities and level set, the proposed model is able to deal with intensity inhomogeneity and capture different topologies. To stop the leakage of contour at the boundary of tumor, we take some geometrical points near the tumor's boundary and introduce a distance constraint in model. The gradient flow equation and other optimal values are obtained through minimization of the energy functional. The gradient flow equation is solved by using additive operator splitting method. The experimental results of the proposed model are validated by comparing it with existing state of the art models both qualitatively and quantitatively. The proposed model achieves average values of 99.96%, 99.88%, 99.91%, 99.91%, 99.95% for Jaccard similarity, dice coefficient, accuracy, sensitivity and specificity respectively, which are better than the existing models in comparison.