Vertex Position Research Articles

A <formula formulatype="inline"><tex Notation="TeX">$z$</tex></formula>-Vertex Trigger for Belle II

The Belle II experiment will go into operation at the upgraded SuperKEKB collider in 2016. SuperKEKB is designed to deliver an instantaneous luminosity $\mathcal{L}=8\times10^{35}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$. The experiment will therefore have to cope with a much larger machine background than its predecessor Belle, in particular from events outside of the interaction region. We present the concept of a track trigger, based on a neural network approach, that is able to suppress a large fraction of this background by reconstructing the $z$ (longitudinal) position of the event vertex within the latency of the first level trigger. The trigger uses the hit information from the Central Drift Chamber (CDC) of Belle II within narrow cones in polar and azimuthal angle as well as in transverse momentum ("sectors"), and estimates the $z$-vertex without explicit track reconstruction. The preprocessing for the track trigger is based on the track information provided by the standard CDC trigger. It takes input from the 2D track finder, adds information from the stereo wires of the CDC, and finds the appropriate sectors in the CDC for each track. Within the sector, the $z$-vertex is estimated by a specialized neural network, with the drift times from the CDC as input and a continuous output corresponding to the scaled $z$-vertex. The neural algorithm will be implemented in programmable hardware. To this end a Virtex 7 FPGA board will be used, which provides at present the most promising solution for a fully parallelized implementation of neural networks or alternative multivariate methods. A high speed interface for external memory will be integrated into the platform, to be able to store the $\mathcal{O}(10^9)$ parameters required. The contribution presents the results of our feasibility studies and discusses the details of the envisaged hardware solution.

Anisotropic adaptive method for triangular meshes smoothing

Even with the advancing laser scanner technology, the digital objects are inevitably corrupted with random noise during the acquisition process. Many algorithms, regardless of principle, share the same basic idea of noise reduction through mesh smoothing. Smoothing can be performed locally, as in the anisotropic filtering by calculus of variations; or by smoothing mesh attributes such as normal vector and then adjusting vertex positions. In this study, the authors propose a novel algorithm based on the statistical distribution noise for anisotropic mesh smoothing. In this approach, the probability density function of the noise is first estimated, and then the anisotropic smoothing operation is performed through the diffusion tensor that allows to preserve mesh characteristics like edges, corner and ridges. The proposed algorithm is easy to implement and is thus suitable for real-time noise reduction application.

Clip space sample culling for motion blur and defocus blur

Motion blur and defocus blur are two common visual effects for rendering realistic camera images. This paper presents a novel clip space culling for stochastic rasterization to render motion and defocus blur effects. Our proposed algorithm reduces the sample coverage using the clip space information in camera lens domain (UV) and time domain (T). First, samples outside the camera lens were culled in stage I using the linear relationship between camera lens and vertex position. Second, samples outside the time bounds were culled in stage II using the triangle similarity in clip space to find the intersection time. Each pixel was computed within two linear bounds only once. Our method achieves good sample test efficiency with low computation cost for real-time stochastic rasterization. Finally, the proposed method is demonstrated by means of various experiments, and a comparison is made with previous works. Our algorithm was able to handle these two blur effects simultaneously and performed better than others did.

A neural network z-vertex trigger for Belle II

We present the concept of a track trigger for the Belle II experiment, based on a neural network approach, that is able to reconstruct the z (longitudinal) position of the event vertex within the latency of the first level trigger. The trigger will thus be able to suppress a large fraction of the dominating background from events outside of the interaction region. The trigger uses the drift time information of the hits from the Central Drift Chamber (CDC) of Belle II within narrow cones in polar and azimuthal angle as well as in transverse momentum (sectors), and estimates the z-vertex without explicit track reconstruction. The preprocessing for the track trigger is based on the track information provided by the standard CDC trigger. It takes input from the 2D (r — φ) track finder, adds information from the stereo wires of the CDC, and finds the appropriate sectors in the CDC for each track in a given event. Within each sector, the z-vertex of the associated track is estimated by a specialized neural network, with a continuous output corresponding to the scaled z-vertex. The input values for the neural network are calculated from the wire hits of the CDC.

An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

In this paper we present a new and efficient quadrature-free formulation for the family of cell-centered high order accurate direct arbitrary-Lagrangian---Eulerian one-step ADER-WENO finite volume schemes on unstructured triangular and tetrahedral meshes that has been developed by the authors in a recent series of papers (Boscheri et al. in J Comput Phys 267:112---138, 2014; Boscheri and Dumbser in Commun Comput Phys 14:1174---1206, 2013; Boscheri and Dumbser in J Comput Phys 275:484---523, 2014; Dumbser and Boscheri in Comput Fluids 86:405---432, 2013). High order of accuracy in time is obtained by using a local space---time Galerkin predictor on moving curved meshes, while a high order accurate nonlinear WENO method is adopted to produce high order essentially non-oscillatory reconstruction polynomials in space. The mesh is moved at each time step according to the solution of a node solver algorithm that assigns a unique velocity vector to each node of the mesh. A rezoning procedure can also be applied when mesh distortions and deformations become too severe. The space---time mesh is then constructed by straight edges connecting the vertex positions at the old time level $$t^n$$tn with the new ones at the next time level $$t^{n+1}$$tn+1, yielding closed space---time control volumes, on the boundary of which the numerical flux must be integrated. This is done here with a new and efficient quadrature-free approach: the space---time boundaries are split into simplex sub-elements, i.e. either triangles in 2D or tetrahedra in 3D. This leads to space---time normal vectors as well as Jacobian matrices that are constant within each sub-element. Within the space---time Galerkin predictor stage that solves the Cauchy problem inside each element in the small, the discrete solution and the flux tensor are approximated using a nodal space---time basis. Since these space---time basis functions are defined on a reference element and do not change, their integrals over the simplex sub-surfaces of the space---time reference control volume can be integrated once and for all analytically during a preprocessing step. The resulting integrals are then used together with the space---time degrees of freedom of the predictor in order to compute the numerical flux that is needed in the finite volume scheme. We apply the high order algorithm presented in this paper to the equations of hydrodynamics obtaining convergence rates up to fourth order of accuracy in space and time. A set of classical Lagrangian test problems has been solved and the results have been compared with the ones given by the original formulation of the algorithm (Boscheri and Dumbser 2013, 2014). The efficiency has been monitored and measured for each test case and the new quadrature-free schemes were up to 3.7 times faster than the ones based on Gaussian quadrature.

The MuPix high voltage monolithic active pixel sensor for the Mu3e experiment

Mu3e is a novel experiment searching for charged lepton flavor violation in the rare decay μ → eee. In order to reduce background by up to 16 orders of magnitude, decay vertex position, decay time and particle momenta have to be measured precisely. A pixel tracker based on 50 μm thin high voltage monolithic active pixel sensors (HV-MAPS) in a magnetic field will deliver precise vertex and momentum information. Test beam results like an excellent efficiency of >99.5% and a time resolution of better than 16.6 ns obtained with the MuPix HV-MAPS chip developed for the Mu3e pixel tracker are presented.

Numerical analysis of multi-parallelized swirling flow inside a circular pipe

The flow field of multi-parallelized swirling flow inside a circular pipe was investigated numerically. Two types of swirling flow configuration are considered. One type is the co-rotating type. Four co-rotating swirls are arranged at the vertex position of square in this type. The other type is the counter-rotating type which consists of two pairs of swirls having opposite swirl rotations. Each pair is arranged diagonally at the vertex position of a square. By coupling the discrete vortex method and boundary element method, unsteady flow simulation is performed. Swirl modeling with vortex elements is used in this simulation and its validity is confirmed. From the simulation results, in the co-rotating type, the four swirls interact and their shape is deformed. Each vortex motion vanishes rapidly in the downstream region. Finally, they are turned into a single swirling flow. In counter-rotating type, each vortex motion is maintained a little bit longer than co-rotating type, and their shape is not so deformed. However, the flow patterns are changed completely in the downstream region. The swirling velocity of each swirl mostly vanishes. Finally, they are turned into an axial flow. For the investigation of the mixing promoting effect due to parallelizing swirls, particle tracking simulations are performed in the co-rotating type and the counter-rotating type. As a comparison, the simulation for single swirl flow is also performed. In these simulations, the particles are introduced in the vicinity of pipe inner wall. In addition, the assumption that particles follow the flow motion absolutely is used. From the results, the motion of particles in these three cases is completely different. For the co-rotating and counter-rotating type, the particle entrainment into the main axial flow is clearly observed. This indicates the mixing is improved compared to single swirl flow. The difference of particle entrainment motion between co-rotating and counter-rotating type is slight.

Study on the influence of the fetus head molding on the biomechanical behavior of the pelvic floor muscles, during vaginal delivery

Pelvic floor injuries during vaginal delivery are considered a significant risk factor to develop pelvic floor dysfunction. The molding of the fetus head during vaginal delivery facilitates the labor progress, since it adjusts to the birth canal geometry.In this work, a finite element model was used to represent the effects induced by the passage of the fetus head on the pelvic floor. The numerical model used for this simulation included the pelvic floor muscles attached to the bones, and a fetus body. The model of the fetus head included the skin and soft tissues, the skull with sutures and fontanelles, and the brain. The fetus head movements during birth in vertex position were simulated: descent, internal rotation and extension. Two models of the fetus head were compared: a rigid and a deformable one, with the inclusion of the cranial sutures. The influence of the fetus head molding on the pelvic floor muscles was analyzed by evaluating their reaction forces, stretch, and stress and strain fields. Additionally, anatomical indices for the molding of the fetal skull were obtained and compared with clinical data.The passage of the deformable fetus head through the birth canal leads to a reduction of 17.3% on the reaction forces on the pelvic floor muscles when compared to the ones of a rigid head. Furthermore, the fetus head molding implies inferior resistance to rotation resulting in a reduction of 1.86% in muscle stretching. Quantitative evaluation of the fetus head molding showed good agreement with clinical experiments.

Does midtrimester cervical length aid in predicting vaginal birth after cesarean?

A longer midtrimester cervical length (CL) is associated with an increased chance of cesarean delivery, but CL has not been used to predict the chance of successful trial of labor after cesarean delivery (TOLAC). The objective of this study was to identify whether midtrimester CL improves the prediction of vaginal birth after cesarean delivery (VBAC) among women undergoing a TOLAC. Women with 1 prior cesarean and a singleton gestation in the vertex position who had a routine CL assessment between 18 and 24 weeks and chose to undergo a TOLAC were identified. Midtrimester CL and characteristics identifiable in early prenatal care that have been used in a validated predictive model for VBAC (ie, age, body mass index, race/ethnicity, prior vaginal delivery, prior VBAC, and indication for prior cesarean delivery) were abstracted from the medical record. Multivariable regressions with VBAC as the dependent variable, with and without CL, were created and their predictive capacity compared using receiver-operating characteristic curves and reclassification tables. Of the 678 women who met inclusion criteria, 517 (76.3%) experienced a VBAC. Mean midtrimester CL was lower in women who achieved a VBAC compared with those who required a cesarean delivery in labor (4.3 ± 0.8 cm vs 4.7 ± 0.8 cm, P < .001). In a multivariable logistic regression, midtrimester CL (centimeters) was significantly associated with a reduced chance of VBAC (adjusted odds ratio [aOR], 0.60; 95% confidence interval [CI], 0.47-0.76). Although the addition of CL improved the area under the receiver-operating characteristic curve (aOR, 0.695 [95% CI, 0.648-0.743] vs aOR, 0.727 [95% CI, 0.681-0.773]; P= .03), it did not significantly enhance the clinical value of the model, as quantified by net reclassification improvement (P= .11). Shorter midtrimester CL is associated with a greater chance of vaginal birth after a TOLAC. However, midtrimester CL does not significantly improve the clinical value of a previously developed VBAC prediction model.

Bridging game theory and the knapsack problem: a theoretical formulation

This paper presents an approach to solving the knapsack problem in which the solution can be derived based on a treatment of the classical bargaining problem. In spatial game theory, all the players form an $$n$$ -polyhedron in space, and the bargaining set of items is positioned such that the geometrical distance of each item from every player reference vertex point is inversely proportional to its utility to the player. The game-theoretical-based distance of an item to a player is defined as the ratio of the geometrical distance referenced from the player’s vertex position to the sum of distances from all the $$n$$ -player vertices of the polyhedron, and its game moment is derived from the product of utility and this distance. Pareto optimality can then be achieved by balancing the effective game-moment contributions from $$n$$ -player subsets of items at equilibrium. The Pareto-optimal solution is defined such that for a given set of consolidated items, further addition of items to the knapsack will result in diminishing returns in their payoffs or profits attained together with the corresponding unwanted increases in constraints or burdens to cause destabilization of this equilibrium. This game-theoretical approach is employed by having the game player entities work cooperatively to maximize profit and minimize burdens in order to arrive at a solution and is the first spatial game representation of the knapsack problem.

Efficient parallel optimization of volume meshes on heterogeneous computing systems

We describe a parallel algorithmic framework for optimizing the shape of elements in a simplicial volume mesh. Using fine-grained parallelism and asymmetric multiprocessing on multi-core CPU and modern graphics processing unit hardware simultaneously, we achieve speedups of more than tenfold over current state-of-the-art serial methods. In addition, improved mesh quality is obtained by optimizing both the surface and the interior vertex positions in a single pass, using feature preservation to maintain fidelity to the original mesh geometry. The framework is flexible in terms of the core numerical optimization method employed, and we provide performance results for both gradient-based and derivative-free optimization methods.

Prediction of Longitudinal Development of Infant Cortical Surface Shape Using a 4D Current-Based Learning Framework.

Understanding the early dynamics of the highly folded human cerebral cortex is still an actively evolving research field teeming with unanswered questions. Longitudinal neuroimaging analysis and modeling have become the new trend to advance research in this field. However, this is challenged by a limited number of acquisition timepoints and the absence of inter-subject matching between timepoints. In this paper, we propose a novel framework that unprecedentedly solves the problem of predicting the dynamic evolution of infant cortical surface shape solely from a single baseline shape based on a spatiotemporal (4D) current-based learning approach. Specifically, our method learns from longitudinal data both the geometric (vertices positions) and dynamic (temporal evolution trajectories) features of the infant cortical surface, comprising a training stage and a prediction stage. In the training stage, we first use the current-based shape regression model to set up the inter-subject cortical surface correspondences at baseline of all training subjects. We then estimate for each training subject the diffeomorphic temporal evolution trajectories of the cortical surface shape and build an empirical mean spatiotemporal surface atlas. In the prediction stage, given an infant, we first warp all training subjects onto its baseline cortical surface. Second, we select the most appropriate learnt features from training subjects to simultaneously predict the cortical surface shapes at all later timepoints from its baseline cortical surface, based on closeness metrics between this baseline surface and the learnt baseline population average surface atlas. We used the proposed framework to predict the inner cortical surface shape at 3, 6 and 9 months from the cortical shape at birth in 9 healthy infants. Our method predicted with good accuracy the spatiotemporal dynamic change of the highly folded cortex.

Bi-Normal Filtering for Mesh Denoising.

Most mesh denoising techniques utilize only either the facet normal field or the vertex normal field of a mesh surface. The two normal fields, though contain some redundant geometry information of the same model, can provide additional information that the other field lacks. Thus, considering only one normal field is likely to overlook some geometric features. In this paper, we take advantage of the piecewise consistent property of the two normal fields and propose an effective framework in which they are filtered and integrated using a novel method to guide the denoising process. Our key observation is that, decomposing the inconsistent field at challenging regions into multiple piecewise consistent fields makes the two fields complementary to each other and produces better results. Our approach consists of three steps: vertex classification, bi-normal filtering, and vertex position update. The classification step allows us to filter the two fields on a piecewise smooth surface rather than a surface that is smooth everywhere. Based on the piecewise consistence of the two normal fields, we filtered them using a piecewise smooth region clustering strategy. To benefit from the bi-normal filtering, we design a quadratic optimization algorithm for vertex position update. Experimental results on synthetic and real data show that our algorithm achieves higher quality results than current approaches on surfaces with multifarious geometric features and irregular surface sampling.

Mesh improvement by minimizing a weighted sum of squared element volumes

Summary We describe a new mesh smoothing method that consists of minimizing the sum of squared element volumes over the free vertex positions. To the extent permitted by the fixed vertices and mesh topology, the resulting mesh elements have uniformly distributed volumes. In the case of a triangulation, uniform volume implies well-shaped triangles. If a graded mesh is required, the element volumes may be weighted by centroidal values of a sizing function, resulting in a mesh that conforms to the required vertex density. The method has both a local and a global implementation. In addition to smoothing, the method serves as a simple parameter-free means of untangling a mesh with inverted elements. It applies to all types of meshes, but we present test results here only for planar triangle meshes. Our test results show the new method to be fast, superior in uniformity or conformity to a sizing function, and among the best methods in terms of triangle shape quality. We also present a new angle-based method that is simpler and more effective than alternatives. This method is directly aimed at producing well-shaped triangles and is particularly effective when combined with the volume-based method. It also generalizes to anisotropic mesh smoothing. Copyright © 2014 John Wiley & Sons, Ltd.

Fast centroidal Voronoi Delaunay triangulation for unstructured mesh generation

A fast unstructured mesh generation algorithm based on conforming centroidal Voronoi Delaunay triangulation (CfCVDT) algorithm (Ju, 2007) is proposed in this paper. In the new algorithm, the constrained Delaunay triangulation (CDT) algorithm is used only for the generation of the initial mesh. The mesh quality shall be continuously improved by updating the positions of vertices and flipping edges in a number of iterations. Since the most time consuming procedure in CfCVDT algorithm is the CDT in each iteration which has been successfully avoided in this new algorithm the efficiency has been significantly improved. Furthermore, the meshes generated by this algorithm have similar high quality features as that generated by CfCVDT. When complex interfaces are involved, our algorithm can keep the mesh conforming to the interfaces very efficiently. By using various density functions, this algorithm can produce high quality non-uniform meshes for potentially many applications.

Robust surface reconstruction via dictionary learning

Surface reconstruction from point cloud is of great practical importance in computer graphics. Existing methods often realize reconstruction via a few phases with respective goals, whose integration may not give an optimal solution. In this paper, to avoid the inherent limitations of multi-phase processing in the prior art, we propose a unified framework that treats geometry and connectivity construction as one joint optimization problem. The framework is based on dictionary learning in which the dictionary consists of the vertices of the reconstructed triangular mesh and the sparse coding matrix encodes the connectivity of the mesh. The dictionary learning is formulated as a constrained ℓ 2,q -optimization (0 &lt; q &lt; 1), aiming to find the vertex position and triangulation that minimize an energy function composed of point-to-mesh metric and regularization. Our formulation takes many factors into account within the same framework, including distance metric, noise/outlier resilience, sharp feature preservation, no need to estimate normal, etc., thus providing a global and robust algorithm that is able to efficiently recover a piecewise smooth surface from dense data points with imperfections. Extensive experiments using synthetic models, real world models, and publicly available benchmark show that our method outperforms the state-of-the-art in terms of accuracy, robustness to noise and outliers, geometric feature and detail preservation, and mesh connectivity.

Anisotropic simplicial meshing using local convex functions

We present a novel method to generate high-quality simplicial meshes with specified anisotropy. Given a surface or volumetric domain equipped with a Riemannian metric that encodes the desired anisotropy, we transform the problem to one of functional approximation. We construct a convex function over each mesh simplex whose Hessian locally matches the Riemannian metric, and iteratively adapt vertex positions and mesh connectivity to minimize the difference between the target convex functions and their piecewise-linear interpolation over the mesh. Our method generalizes optimal Delaunay triangulation and leads to a simple and efficient algorithm. We demonstrate its quality and speed compared to state-of-the-art methods on a variety of domains and metrics.

Visual salience guided feature-aware shape simplification

In the area of 3D digital engineering and 3D digital geometry processing, shape simplification is an important task to reduce their requirement of large memory and high time complexity. By incorporating the content-aware visual salience measure of a polygonal mesh into simplification operation, a novel feature-aware shape simplification approach is presented in this paper. Owing to the robust extraction of relief heights on 3D highly detailed meshes, our visual salience measure is defined by a center-surround operator on Gaussian-weighted relief heights in a scale-dependent manner. Guided by our visual salience map, the feature-aware shape simplification algorithm can be performed by weighting the high-dimensional feature space quadric error metric of vertex pair contractions with the weight map derived from our visual salience map. The weighted quadric error metric is calculated in a six-dimensional feature space by combining the position and normal information of mesh vertices. Experimental results demonstrate that our visual salience guided shape simplification scheme can adaptively and effectively re-sample the underlying models in a feature-aware manner, which can account for the visually salient features of the complex shapes and thus yield better visual fidelity.

High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics

SUMMARYIn this paper, we present a class of high‐order accurate cell‐centered arbitrary Lagrangian–Eulerian (ALE) one‐step ADER weighted essentially non‐oscillatory (WENO) finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two‐dimensional unstructured triangular meshes. High order of accuracy in space is achieved by a WENO reconstruction algorithm, while a local space–time Galerkin predictor allows the schemes to be high order accurate also in time by using an element‐local weak formulation of the governing PDE on moving meshes. The mesh motion can be computed by choosing among three different node solvers, which are for the first time compared with each other in this article: the node velocity may be obtained either (i) as an arithmetic average among the states surrounding the node, as suggested by Cheng and Shu, or (ii) as a solution of multiple one‐dimensional half‐Riemann problems around a vertex, as suggested by Maire, or (iii) by solving approximately a multidimensional Riemann problem around each vertex of the mesh using the genuinely multidimensional Harten–Lax–van Leer Riemann solver recently proposed by Balsara et al. Once the vertex velocity and thus the new node location have been determined by the node solver, the local mesh motion is then constructed by straight edges connecting the vertex positions at the old time level tn with the new ones at the next time level tn + 1. If necessary, a rezoning step can be introduced here to overcome mesh tangling or highly deformed elements. The final ALE finite volume scheme is based directly on a space–time conservation formulation of the governing PDE system, which therefore makes an additional remapping stage unnecessary, as the ALE fluxes already properly take into account the rezoned geometry. In this sense, our scheme falls into the category of direct ALE methods. Furthermore, the geometric conservation law is satisfied by the scheme by construction.We apply the high‐order algorithm presented in this paper to the Euler equations of compressible gas dynamics as well as to the ideal classical and relativistic magnetohydrodynamic equations. We show numerical convergence results up to fifth order of accuracy in space and time together with some classical numerical test problems for each hyperbolic system under consideration. Copyright © 2014 John Wiley &amp; Sons, Ltd.

The ultra-lightweight support structure and gaseous helium cooling for the Mu3e silicon pixel tracker

The Mu3e experiment searches for charged lepton flavor violation in the rare decay μ→eee. In order to reach a sensitivity of better than 10−16, more than 109 muon decays per second have to be observed over a running time of one year. Precise determination of particle momentum, vertex position and time are necessary for background suppression. These requirements can be met by combining an ultra-lightweight tracker based on High-Voltage Monolithic Active Pixel Sensors (HV-MAPS) with a timing system which consists of a scintillating fiber detector and a tile hodoscope. As the momentum of particles from muon decay at rest is below 53 MeV/c, the silicon pixel tracker resolution is dominated by multiple Coulomb scattering. This leads to extreme requirements for the material budget of the tracking detector of below 0.1% of a radiation length per layer. Even though the target power consumption of the HV-MAPS detector is as low as 150 mW/cm2, the detector cooling must be very efficient and at the same time avoid adding material inside the active tracking volume.