Discrete Surface Model Research Articles

THE SUPERPOSITION COEFFICIENTS OF THE COORDINATES OF FOUR POINTS’ DETERMINATION ON THE TWO VARIABLES POLYNOMIALS EXAMPLE

The article suggests a general approach to determining the values of superposition coefficients of two-dimensional point sets based on given calculation schemes, which allows solving the problems of continuous discrete interpolation and extrapolation by numerical sequences of any two-dimensional functional dependencies at four randomly specified nodal points. One of the tasks of this work were the continuation of research on the modeling of discrete geometric images (GI) based on the classical method of finite differences, the static-geometric method and the geometric apparatus of superposition. The one-dimensional GI model (a curved line presented discretely or continuously) is much easier to comprehensively study than the two-dimensional GI model (a surface presented discretely or continuously). It should be expected that a number of properties that a discrete line model has can be transferred to a surface model formed according to the same laws, if this line is considered to be a component of the surface framework. Other properties of the discrete surface model can be obtained as a result of generalization of the corresponding properties of the line model. Consequently, this work is based on the authors' previous research on determining the regularities of changes in the values of the superposition coefficients of the three nodal points of the polynomial function for the selected calculation scheme. The process of construction of discrete analogues of two-dimensional GI was studied using the example of polynomial functional dependencies and based on the given calculation schemes. In the procedure of research, the regularities of changes in the values of the superposition coefficients of the four nodal points of the polynomial function of two variables were determined in the form of graphs of numerical sequences for the selected calculation scheme. The follow-on regularities make it possible to form two-dimensional geometric images in the form of polynomials of two variables on the selected calculation scheme based on the coordinates of the four nodal points. The investigated data determine a general approach to obtaining similar regularities of changes in the values of the superposition coefficients of the four nodal points of the selected calculation scheme for determining applications of n points of modeled any two-dimensional functional dependencies and arbitrary two-dimensional sets of points.

Three-Dimensional Face Recognition Using Solid Harmonic Wavelet Scattering and Homotopy Dictionary Learning.

Data representation has been one of the core topics in 3D graphics and pattern recognition in high-dimensional data. Although the high-resolution geometrical information of a physical object can be well preserved in the form of metrical data, e.g., point clouds/triangular meshes, from a regular data (e.g., image/audio) processing perspective, they also bring excessive noise in the course of feature abstraction and regression. For 3D face recognition, preceding attempts focus on treating the scan samples as signals laying on an underlying discrete surface (mesh) or morphable (statistic) models and by embedding auxiliary information, e.g., texture onto the regularized local planar structure to obtain a superior expressive performance to registration-based methods, but environmental variations such as posture/illumination will dissatisfy the integrity or uniform sampling condition, which holistic models generally rely on. In this paper, a geometric deep learning framework for face recognition is proposed, which merely requires the consumption of raw spatial coordinates. The non-uniformity and non-grid geometric transformations in the course of point cloud face scanning are mitigated by modeling each identity as a stochastic process. Individual face scans are considered realizations, yielding underlying inherent distributions under the appropriate assumption of ergodicity. To accomplish 3D facial recognition, we propose a windowed solid harmonic scattering transform on point cloud face scans to extract the invariant coefficients so that unrelated variations can be encoded into certain components of the scattering domain. With these constructions, a sparse learning network as the semi-supervised classification backbone network can work on reducing intraclass variability. Our framework obtained superior performance to current competing methods; without excluding any fragmentary or severely deformed samples, the rank-1 recognition rate (RR1) achieved was 99.84% on the Face Recognition Grand Challenge (FRGC) v2.0 dataset and 99.90% on the Bosphorus dataset.

Effect of plasticity and coalescing for neighboring asperities in contact with a rigid flat

The contact behaviors of rough surfaces, which consist of asperities with random geometric properties at small length scale, have been extensively investigated on contact behaviors in engineering and scientific research. Due to the complexity of loading condition and surface topography, the limitation of traditional statistical model leads to the inaccuracy of prediction for rough surface contact behaviors. Starting from the multi-asperity contact theory, we release the restrictions of classical GW model and propose an elastic-plastic interacting model to investigate the coalescence effect of neighboring asperities in this paper. Through numerous simulations and analyses, the results show that the plasticity can be measured by material and morphology parameters. With the increasing of plasticity and the decreasing of asperity peak distance, the contact interface transits from interaction dominated to coalescence dominated contact relationships. With the increasing of loading, the shape of contact zone changes from two independent circles with expanding radius to a joint point, and finally the contact zone becomes a single ellipse. The coalescence status of neighboring asperities is influenced by the plasticity and the initial distance between asperity peaks. Our study provides some basis for establishing a statistical or discrete rough surface model considering merging, predicting the contact behaviors between solids, and revealing the evolution of contact spot information.

Generating Logistic Characteristic Curves using Discrete Event Simulation and Response Surface Models

Generating Logistic Characteristic Curves using Discrete Event Simulation and Response Surface Models

ОЦЕНКИ ИЗМЕНЕНИЯ РЕЛЬЕФА БЕРЕГОВОЙ ЗОНЫ ПРИ АБРАЗИИ ПО ДАННЫМ ДИСТАНЦИОННОГО ЗОНДИРОВАНИЯ: МЕТОДИЧЕСКИЕ ПОДХОДЫ И ПРЕДВАРИТЕЛЬНЫЕ РЕЗУЛЬТАТЫ

The article offers a method for assessing changes in the relief of the Azov sea coastline and the localization of areas of erosion using discrete surface models obtained from remote sensing of the Earth using unmanned aerial vehicles (UAVs). This problem arises because of the need to monitor the dynamics of the coastline: due to the activation of various natural and man-made processes, there is an intensive destruction of the shores of the seas of Russia. Existing modern methods of land topographic survey do not allow you to quickly get information about changes in the state of the coastline or are expensive, and the large extent of the zone subject to erosion makes the traditional instrumental approach of measuring at reference points very labor-intensive. Also, the data obtained by the instrumental method reflects the problem point-by-point, rather than along the entire coastline. In this paper, we developed an algorithm and software for building a three-dimensional terrain model (using Delaunay triangulation) based on the so-called “dense point cloud” obtained when shooting terrain from an unmanned aerial vehicle (UAV). we proposed and programmatically implemented an algorithm for comparing (subtracting) two 3D models based on surveys performed by the same camera, but at different times of the day, in different seasons, and at different heights with an interval of 2 years, to identify significant changes in terrain in the area of the coastal slope, caused by abrasive and collapse processes. Experimental studies of the developed approach were conducted at the test site (500 by 300 m in size) on the southern shore of the Taganrog Bay. As a result of the considered experimental studies of comparing two 3D terrain models based on dense point clouds, additional working hypotheses (steps) that need to be solved were formulated to identify significant differences due to the destruction of the coast

Discrete geodesic parallel coordinates

Geodesic parallel coordinates are orthogonal nets on surfaces where one of the two families of parameter lines are geodesic curves. We describe a discrete version of these special surface parameterizations and show that they are very useful for specific applications, most of which are related to the design and fabrication of surfaces in architecture. With the new discrete surface model, it is easy to control strip widths between neighboring geodesics. This facilitates tasks such as cladding a surface with strips of originally straight flat material or designing geodesic gridshells and timber rib shells. It is also possible to model nearly developable surfaces. These are characterized by geodesic strips with almost constant strip widths and are used for generating shapes that can be manufactured from materials which allow for some stretching or shrinking like felt, leather, or thin wooden boards. Most importantly, we show how to constrain the strip width parameters to model a class of intrinsically symmetric surfaces. These surfaces are isometric to surfaces of revolution and can be covered with doubly-curved panels that are produced with only a few molds when working with flexible materials like metal sheets.

ERROR OF MODELING ECHO SIGNALS FROM EARTH SURFACE ARISING DUE TO DISCRETE ASSIGNMENT OF REFLECTIVE PROPERTIES

The use of discrete distribution of the earth surface reflective properties to simulate echoes leads inevitably to the errors in setting the parameters of the simulated signal. Therefore, there is a problem of choosing the optimal ratio between the intensity of the errors and the sampling frequency, which affects the speed of subsequent echo calculations based on a discrete surface model. To solve this problem, relations linking the statistical characteristics of the errors in specifying the power of echoes with the sample interval of the surface map are obtained. Two approaches are used. In the first case, dependences between the errors of setting the mean value and the variance of the normalized radar cross section and the sample interval are obtained. In the second case, the averaged error values are obtained after interpolating the sampled values. The paper also presents general relations for calculating the error value for the 0–2π angle sector based on the ratios for the sampling interval.

Construction of Analysis-Suitable Vascular Models Using Axis-Aligned Polycubes.

Image-based modeling is an active and growing area of biomedical research that utilizes medical imaging to create patient-specific simulations of physiological function. Under this paradigm, anatomical structures are segmented from a volumetric image, creating a geometric model that serves as a computational domain for physics-based modeling. A common application is the segmentation of cardiovascular structures to numerically model blood flow or tissue mechanics. The segmentation of medical image data typically results in a discrete boundary representation (surface mesh) of the segmented structure. However, it is often desirable to have an analytic representation of the model, which facilitates systematic manipulation. For example, the model then becomes easier to union with a medical device, or the geometry can be virtually altered to test or optimize a surgery. Furthermore, to employ increasingly popular isogeometric analysis (IGA) methods, the parameterization must be analysis suitable. Converting a discrete surface model to an analysis-suitable model remains a challenge, especially for complex branched structures commonly encountered in cardiovascular modeling. To address this challenge, we present a framework to convert discrete surface models of vascular geometries derived from medical image data into analysis-suitable nonuniform rational B-splines (NURBS) representation. This is achieved by decomposing the vascular geometry into a polycube structure that can be used to form a globally valid parameterization. We provide several practical examples and demonstrate the accuracy of the methods by quantifying the fidelity of the parameterization with respect to the input geometry.

Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling

We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping r from a two-dimensional parameter space M to the three-dimensional Euclidean space R 3 . The metric variable g a b , which is always fixed to the Euclidean metric δ a b , can be extended to a more general non-Euclidean metric on M in the continuous model. The problem we focus on in this paper is whether such an extension is well defined or not in the discrete model. We find that a discrete surface model with a nontrivial metric becomes well defined if it is treated in the context of Finsler geometry (FG) modeling, where triangle edge length in M depends on the direction. It is also shown that the discrete FG model is orientation asymmetric on invertible surfaces in general, and for this reason, the FG model has a potential advantage for describing real physical membranes, which are expected to have some asymmetries for orientation-changing transformations.

MRI-Based Medial Axis Extraction and Boundary Segmentation of Cranial Nerves Through Discrete Deformable 3D Contour and Surface Models

This paper presents a segmentation technique to identify the medial axis and the boundary of cranial nerves. We utilize a 3-D deformable one-simplex discrete contour model to extract the medial axis of each cranial nerve. This contour model represents a collection of two-connected vertices linked by edges, where vertex position is determined by a Newtonian expression for vertex kinematics featuring internal and external forces, the latter of which include attractive forces toward the nerve medial axis. We exploit multiscale vesselness filtering and minimal path techniques in the medial axis extraction method, which also computes a radius estimate along the path. Once we have the medial axis and the radius function of a nerve, we identify the nerve surface using a two-simplex deformable model, which expands radially and can accommodate any nerve shape. As a result, the method proposed here combines the benefits of explicit contour and surface models, while also achieving a cornerstone for future work that will emphasize shape statistics, static collision with other critical structures, and tree-shape analysis.

Realization of NURBS Surface CNC Machining Simulation in Matlab

This paper presents a method of realization of NURBS surface CNC Machining simulation in matlab, including NURBS surface production, tool path generation, discrete surface and simulation model construction and CNC machining simulation realization.

Scaled, patient-specific 3D vertebral model reconstruction based on 2D lateral fluoroscopy

Accurate three-dimensional (3D) models of lumbar vertebrae are required for image-based 3D kinematics analysis. MRI or CT datasets are frequently used to derive 3D models but have the disadvantages that they are expensive, time-consuming or involving ionizing radiation (e.g., CT acquisition). An alternative method using 2D lateral fluoroscopy was developed. A technique was developed to reconstruct a scaled 3D lumbar vertebral model from a single two-dimensional (2D) lateral fluoroscopic image and a statistical shape model of the lumbar vertebrae. Four cadaveric lumbar spine segments and two statistical shape models were used for testing. Reconstruction accuracy was determined by comparison of the surface models reconstructed from the single lateral fluoroscopic images to the ground truth data from 3D CT segmentation. For each case, two different surface-based registration techniques were used to recover the unknown scale factor, and the rigid transformation between the reconstructed surface model and the ground truth model before the differences between the two discrete surface models were computed. Successful reconstruction of scaled surface models was achieved for all test lumbar vertebrae based on single lateral fluoroscopic images. The mean reconstruction error was between 0.7 and 1.6 mm. A scaled, patient-specific surface model of the lumbar vertebra from a single lateral fluoroscopic image can be synthesized using the present approach. This new method for patient-specific 3D modeling has potential applications in spine kinematics analysis, surgical planning, and navigation.

Discrete lattice surface models and their quantum spin counterparts

Discrete lattice surface models and their quantum spin counterparts

Water–Carbon Interactions 2: Calibration of Potentials using Contact Angle Data for Different Interaction Models

Molecular dynamics simulations of water droplets on graphite are carried out to determine the contact angle for different water–carbon potential functions. Following the procedure of Werder et al. [J. Phys. Chem. B, 107 (2003) 1345], the C–O Lennard–Jones well depth is varied to recover the experimental value for the contact angle using a 2000-molecule water droplet and compensating for the line tension effect that lowers the contact angle for increasing droplet size. For the discrete graphite surface model studied by Werder et al., the effects of adding C–H Lennard–Jones interactions and changing the long-range cut-off distance are considered. In addition, a continuum graphite surface model is studied for which the water–graphite interaction energy depends only on the normal distance (z) from the water oxygen to the surface. This new model, with z -10 repulsion and z -4 attraction, is formulated in terms of the standard Lennard–Jones parameters, for which the recommended values are sgr CO=3.19 Å and ε CO=0.3651 kJ/mol.

A 3D deformable surface model for segmentation of objects from volumetric data in medical images

In this paper we present a new 3D discrete dynamic surface model. The model consists of vertices and edges, which connect adjacent vertices. Basic geometry of the model surface is generated by triangle patches. The model deforms by internal and external forces. Internal forces are obtained from local geometry of the model and are related to the local curvature of the surface. External forces, on the other hand, are based on the image data and are calculated from desired image features. We also present a method for generating an initial volume for the model from a stack of initial contours, drawn by the user on cross sections of the volumetric data.