Sparse Mesh Research Articles

Efficient quadrature rules for subdivision surfaces in isogeometric analysis

We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process generates a sequence of finer and finer quad meshes that in the limit defines a smooth subdivision surface, which can be of any manifold topology. Traditional approaches to quadrature on such surfaces rely on per-quad integration, which is inefficient and typically also inaccurate near vertices where other than four quads meet. Instead, we explore the space of possible groupings of quads and identify the optimal macro-quads in terms of the number of quadrature points needed. We show that macro-quads consisting of quads from one or several consecutive levels of subdivision considerably reduce the cost of numerical integration. Our rules possess a tensor product structure and the underlying univariate rules are Gaussian, i.e., they require the minimum possible number of integration points in both univariate directions.The optimal quad groupings differ depending on the particular application. For instance, computing surface areas, volumes, or solving the Laplace problem lead to different spline spaces with specific structures in terms of degree and continuity. We show that in most cases the optimal groupings are quad-strips consisting of (1×n) quads, while in some cases a special macro-quad spanning more than one subdivision level offers the most economical integration.Additionally, we extend existing results on exact integration of subdivision splines. This allows us to validate our approach by computing surface areas and volumes with known exact values. We demonstrate on several examples that our quadratures use fewer quadrature points than traditional quadratures. We illustrate our approach to subdivision spline quadrature on the well-known Catmull–Clark scheme based on bicubic splines, but our ideas apply also to subdivision schemes of arbitrary bidegree, including non-uniform and hierarchical variants. Specifically, we address the problems of computing areas and volumes of Catmull–Clark subdivision surfaces, as well as solving the Laplace and Poisson PDEs defined over planar unstructured quadrilateral meshes in the context of isogeometric analysis.

Real-Time, Curvature-Sensitive Surface Simplification Using Depth Images

With the rising popularity of handheld virtual reality (VR) devices and depth sensing RGB-D cameras, a variety of VR applications merging these two technologies has been suggested. However, immersive quality of experience in such VR applications is constrained mainly by the large data size and the hardware limitations to handle it. The depth data captured by RGB-D cameras provide a dense sampling of the surface, resulting in a high-poly mesh, which is difficult to be rendered on handheld VR devices due to their limited processing power. To improve the immersive VR experience, a sparse approximation of the depth data is needed. Traditional mesh and point cloud simplification methods are iterative and so are unsuitable for real-time applications. In this paper, we introduce a depth-image-based approach that is capable of generating a good quality sparse mesh for visualization in real time. We propose a curvature-sensitive surface simplification— $\text{CS}^3$ operator that assigns an importance measure to each point in the depth image, based on the local curvature. Further, it applies an importance-order-based restrictive sampling to generate a sparse representation that retains the overall shape as well as the finer features of the object. We also modify the 2-D sweep-line-based constrained Delaunay triangulation to generate 3-D meshes from the sparse point sampling obtained using $\text{CS}^3$ . In addition, the proposed approach preserves key surface properties, such as texture coordinates and materials. We used three different datasets containing dense 3-D models with and without texture, which are scanned using various sensors to validate and compare the robustness, real-time performance, and accuracy of the proposed method over existing approaches. Based on the experimental results, we show that the proposed $\text{CS}^3$ operator and modified 2-D sweep-line-based triangulation generate sparse meshes from depth image in real time, performing significantly faster than current state-of-the-art methods while maintaining similar visual quality.

Ancient Chinese architecture 3D preservation by merging ground and aerial point clouds

Ancient Chinese architecture 3D digitalization and documentation is a challenging task for the image based modeling community due to its architectural complexity and structural delicacy. Currently, an effective approach to ancient Chinese architecture 3D reconstruction is to merge the two point clouds, separately obtained from ground and aerial images by the SfM technique. There are two understanding issues should be specially addressed: (1) it is difficult to find the point matches between the images from different sources due to their remarkable variations in viewpoint and scale; (2) due to the inevitable drift phenomenon in any SfM reconstruction process, the resulting two point clouds are no longer strictly related by a single similarity transformation as it should be theoretically. To address these two issues, a new point cloud merging method is proposed in this work. Our method has the following characteristics: (1) the images are matched by leveraging sparse mesh based image synthesis; (2) the putative point matches are filtered by geometrical consistency check and geometrical model verification; and (3) the two point clouds are merged via bundle adjustment by linking the ground-to-aerial tracks. Extensive experiments show that our method outperforms many of the state-of-the-art approaches in terms of ground-to-aerial image matching and point cloud merging.

Multi-pose 3D facial texture refinement for face recognition

In this paper, we propose a novel approach for 3D face reconstruction from multi-facial images. Given original pose-variant images, coarse 3D face templates are initialized to reconstruct a refined 3D face mesh in an iteration manner. Then, we warp original facial images to the 2D meshes projected from 3D using Sparse Mesh Affine Warp (SMAW). Finally, we weight the face patches in each view respectively and map the patch with higher weight to a canonical UV space. For facial images with arbitrary pose, their invisible regions are filled with the corresponding UV patches. Poisson editing is applied to blend different patches seamlessly. We evaluate the proposed method on LFW dataset in terms of texture refinement and face recognition. The results demonstrate competitive performance compared to state-of-the-art methods.

Image-guided regularization of marine electromagnetic inversion

Marine electromagnetic (EM) inverse methods have recently been rapidly developed for offshore exploration. However, inverted resistivity results with low resolution are provided by the EM method. To improve this quality of the results, we have developed an image-guided regularization method for inversion of the marine EM data. The method incorporates seismic constraints into EM inversion. Information is extracted from seismic/geologic images and consists of the metric tensor field and sampling on the geologic structure. In addition to the regularization, geologic horizons picked from the seismic images and samplings on the structure can be used to generate an irregular sparse mesh. Compared with an unstructured regular dense mesh, a coherence-based irregular sparse mesh can reduce computational costs. Furthermore, image-guided regularization represents an improvement compared with traditional regularization that are structurally based on seismic images by following geologic features more closely and handling anomalies better. We have determined that image-guided regularization improves the results of EM inversions with irregular sparse meshes. The image-guided regularized inversion can be applied to marine controlled-source electromagnetic (CSEM) data and magnetotelluric (MT) data, and it can be used for joint inversion of CSEM and MT data. Regarding its application to real data, image-guided inversion was successfully applied to CSEM data on the Troll area, using an anisotropic model.

Supercritical flow simulation at a right channel junction. Comparison between a uniform and a sparse mesh

This technical note studies the supercritical junction flow occurring at the right-angled confluence of four equal-width channels in which two upstream channels carry flow towards the junction. The note seeks to investigate, firstly, the pertinence of a 2D shallow water equation model to reproduce the typical flow structures at the junction. The second objective is to build a computationally efficient model with more resolution applied at critical point i.e. junction and less in areas where the flow is primarily 1D i.e. channels and compare such model, named, ‘sparse’ with a uniformly meshed model regarding solution accuracy and computational efficiency. The results indicate that the sparse model is able to reproduce typical flow structures appearing at the channel junction in an adequate manner. The discharge distribution is fairly well predicted. The jump angles are almost the same in the two models as well as the location and size of the recirculation zones and the flow depth super-elevation areas. However, the two models diverge in the prediction of very small depths in the recirculation zone where the sparse model overestimates the depths. As regards, computational efficiency, the sparse model is found to be 61% more efficient than the uniform mesh model.

Sparse CSEM inversion driven by seismic coherence

Marine controlled source electromagnetic (CSEM) data inversion for hydrocarbon exploration is often challenging due to high computational cost, physical memory requirement and low resolution of the obtained resistivity map. This paper aims to enhance both the speed and resolution of CSEM inversion by introducing structural geological information in the inversion algorithm. A coarse mesh is generated for Occam's inversion, where the parameters are fewer than in the fine regular mesh. This sparse mesh is defined as a coherence-based irregular (IC) sparse mesh, which is based on vertices extracted from available geological information. Inversion results on synthetic data illustrate that the IC sparse mesh has a smaller inversion computational cost compared to the regular dense (RD) mesh. It also has a higher resolution than with a regular sparse (RS) mesh for the same number of estimated parameters. In order to study how the IC sparse mesh reduces the computational time, four different meshes are generated for Occam's inversion. As a result, an IC sparse mesh can reduce the computational cost while it keeps the resolution as good as a fine regular mesh. The IC sparse mesh reduces the computational cost of the matrix operation for model updates. When the number of estimated parameters reduces to a limited value, the computational cost is independent of the number of parameters. For a testing model with two resistive layers, the inversion result using an IC sparse mesh has higher resolution in both horizontal and vertical directions. Overall, the model representing significant geological information in the IC mesh can improve the resolution of the resistivity models obtained from inversion of CSEM data.

A Heuristic Algorithm for the Heath–Jarrow–Morton Model

Heath–Jarrow–Morton [1990, 1991, and 1992] presented a general, intuitively appealing, term structure model for pricing interest rate claims. However, in discrete time, the model results in a non-recombining tree for many general deterministic volatility structures, which can be relatively computationally expensive when the number of time steps is large. This article provides a technique that combines interpolation with sparse ad-hoc mesh generation for valuing interest rate claims in the Heath–Jarrow–Morton framework. When this approach is used, the number of nodes in the mesh is significantly reduced without sacrificing accuracy. This article shows that with proper choice of nodes, the method will converge.

Selectively densified 3D object modeling based on regions of interest detection using neural gas networks

The paper discusses automated solutions for 3D object modeling at multiple resolutions in the context of virtual reality. An original solution, based on an unsupervised neural network, is proposed to guide the creation of selectively densified meshes. A neural gas network, applied over a sparse density object mesh, adapts its nodes during training to capture the embedded shape of the object. Regions of interest are then identified as areas with higher density of nodes in the adapted neural gas map. Meshes at different level of detail for an object, which preserve these regions of interest, are constructed by adapting a classical simplification algorithm, the QSlim. The simplification process will therefore only affect the regions of lower interest, ensuring that the characteristics of an object are preserved even at lower resolutions. Various interest point detectors are incorporated in selectively densified meshes in a similar manner to enable the comparison with the proposed neural gas approach. A novel solution based on learning is proposed to select the number of faces for the discrete models of an object at different resolutions. Finally, selectively densified object meshes are incorporated in a discrete level-of-detail method for presentation in virtual reality applications.

Hybrid optimization methodology of variable densities mesh model for the axial supporting design of wide-field survey telescope

The optimization of a primary mirror support system is one of the most critical problems in the design of large telescopes. Here, we propose a hybrid optimization methodology of variable densities mesh model (HOMVDMM) for the axial supporting design, which has three key steps: (1) creating a variable densities mesh model, which will partition the mirror into several sparse mesh areas and several dense mesh areas; (2) global optimization based on the zero-order optimization method for the support of primary mirror with a large tolerance; (3) based on the optimization results of the second step, further optimization with first-order optimization method in dense mesh areas by a small tolerance. HOMVDMM exploits the complementary merits of both the zero- and first-order optimizations, with the former in global scale and the latter in small scale. As an application, the axial support of the primary mirror of the 2.5-m wide-field survey telescope (WFST) is optimized by HOMVDMM. These three designs are obtained via a comparative study of different supporting points including 27 supporting points, 39 supporting points, and 54 supporting points. Their residual half-path length errors are 28.78, 9.32, and 5.29 nm. The latter two designs both meet the specification of WFST. In each of the three designs, a global optimization value with high accuracy will be obtained in an hour on an ordinary PC. As the results suggest, the overall performance of HOMVDMM is superior to the first-order optimization method as well as the zero-order optimization method.

Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method

We present here a fast and easily realized computational approach based on the finite element methods with consistent and lumped mass matrices (CM-FEM and LM-FEM, respectively), and the Bloch’s theorem, to calculate the elastic band structures of phononic crystals. Two improvements, the adjustment of the introduction of Bloch’s theorem as well as weighting treatment of consistent and lumped mass matrices, are performed. Numerical simulations show that convergence speed is accelerated obviously. Furthermore, the method is verified by analytical solutions in specified homogeneous cases. It is concluded that compared with CM-FEM or LM-FEM, the present method gives higher precision results with sparser mesh and takes less time.

Cholestasis-induced adaptive remodeling of interlobular bile ducts.

Cholestasis is a common complication in liver diseases that triggers a proliferative response of the biliary tree. Bile duct ligation (BDL) is a frequently used model of cholestasis in rodents. To determine which changes occur in the three‐dimensional (3D) architecture of the interlobular bile duct during cholestasis, we used 3D confocal imaging, surface reconstructions, and automated image quantification covering a period up to 28 days after BDL. We show a highly reproducible sequence of interlobular duct remodeling, where cholangiocyte proliferation initially causes corrugation of the luminal duct surface, leading to an approximately five‐fold increase in surface area. This is analogous to the function of villi in the intestine or sulci in the brain, where an expansion of area is achieved within a restricted volume. The increase in surface area is further enhanced by duct branching, branch elongation, and loop formation through self‐joining, whereby an initially relatively sparse mesh surrounding the portal vein becomes five‐fold denser through elongation, corrugation, and ramification. The number of connections between the bile duct and the lobular bile canalicular network by the canals of Hering decreases proportionally to the increase in bile duct length, suggesting that no novel connections are established. The diameter of the interlobular bile duct remains constant after BDL, a response that is qualitatively distinct from that of large bile ducts, which tend to enlarge their diameters. Therefore, volume enhancement is only due to net elongation of the ducts. Because curvature and tortuosity of the bile duct are unaltered, this enlargement of the biliary tree is caused by branching and not by convolution. Conclusion: BDL causes adaptive remodeling that aims at optimizing the intraluminal surface area by way of corrugation and branching. (Hepatology 2016;63:951–964)

Delayed-State Nonparametric Filtering in Cooperative Tracking

This paper presents a novel nonparametric approach toward delayed-state filtering for cooperative tracking. Standard parametric cooperative localization/tracking approaches are generally aimed at problems that can be easily parameterized and/or are limited to incorporate only real-time measurements. This paper provides a nonparametric yet computationally tractable alternative that is suitable for tracking cases where real-time observations are not always possible, e.g., in a sparse mesh network. The proposed delayed-state cooperative particle filter features forward filtering and backward smoothing to incorporate measurements that are received with time delays. A record of historical marginal states is kept for each mobile node within a sliding time window, instead of the high-dimensional joint state. Essentially, it replaces the importance sampling in traditional particle filters by a Gibbs sampler, which is a Markov chain Monte Carlo method, to fuse all available egocentric and internode relative observations into the global position estimate, thus alleviating the high-dimensionality problems in cooperative tracking. The performance of the proposed approach is evaluated in a multiagent simulation, and experimental results from a large-scale multivehicle industrial operation clearly demonstrate that the proposed approach effectively facilitates the tracking of mobile nodes without position awareness, through the use of relative range, negative detection, and time-delayed measurements.

FACE IDENTIFICATION ALGORITHM BASED ON MESH-DERIVED SYNTHETIC LINEAR DESCRIPTORS

This paper presents appearance-based face identification algorithm by means of synthetic linear filters. The objective of our research is to construct facial descriptor in the form of linear filter, which should produce high and low outputs for intra- and inter-class recognition problem correspondingly. This filter can be synthesized from 2,5D sparse mesh derived from a given set of images of a person. As ever the filter is created it is then used as facial descriptor, i.e. serves as personal ID for face identification.

A sparse mesh for Compact Finite Difference—Fourier solvers with radius-dependent spectral resolution in circular domains

This paper presents a new method for the resolution of elliptic and parabolic equations in circular domains. It can be trivially extended to cylindrical domains. The algorithm uses a mixed Fourier-Compact Finite Difference method. The main advantage of the method is achieved by a new concept of mesh. The topology of the new grid keeps constant the aspect ratio of the cells, avoiding the typical clustering for radial structured meshes at the center. The reduction of the number of nodes has as a consequence the reduction in memory consumption. In the case of fluid mechanics problems, this technique also increases the time step for a constant Courant number. Several examples are given in the paper which show the potential of the method.

Solid-State Nanopore Modifications for Improved Resolution of DNA Translocations

Nanopores extend electrophoretic detection to the single molecule level, where they provide a versatile platform for analysis of nucleic acids and proteins. The primary advantage of the technique relies upon the size of the nanopore, which should be only slightly larger than the cross-section of the molecule it detects. In the case of long biopolymers, a sufficiently small nanopore can only accommodate one section at a time, uncoiling and scanning the biopolymer as it enters and translocates through the pore. Small variations in size or chemical composition along the length of the DNA - such as the location of bound small molecules, proteins, or even the nucleic acid sequence - can be detected by monitoring changes in the blocked current level during translocation. A critical determinant of nanopore sensing resolution is the speed at which molecules translocate through the nanopore. Slower translocation speeds provide better temporal resolution of small changes in current blockage level, improving detection of local features along the DNA. We have recently developed two novel nanopore modifications to slow DNA translocation through solid-state nanopores fabricated in thin silicon nitride membranes, both of which do not permanently alter the nanopore itself, and which are functionally orthogonal to other nanopore modifications: 1) With just a few mW of visible laser light, we induce high negative surface charge density at the nanopore, creating an electro-osmotic flow which moves in opposition to negatively charged analytes such as DNA, increasing drag and slowing translocation. 2) Electrospinning a sparse nanofiber mesh onto the volume directly outside the nanopore creates interactions with translocating molecules that increase dwell time and are tunable by varying the fiber chemical composition. These techniques enable detection of small proteins and local features along DNA.

Complex fluid simulations with the parallel tree-based Lattice Boltzmann solver Musubi

We present the open source Lattice Boltzmann solver Musubi. It is part of the parallel simulation framework APES, which utilizes octrees to represent sparse meshes and provides tools from automatic mesh generation to post-processing. The octree mesh representation enables the handling of arbitrarily complex simulation domains, even on massively parallel systems. Local grid refinement is implemented by several interpolation schemes in Musubi. Various kernels provide different physical models based on stream-collide algorithms. These models can be computed concurrently and can be coupled with each other. This paper explains our approach to provide a flexible yet scalable simulation environment and elaborates its design principles and implementation details. The efficiency of our approach is demonstrated with a performance evaluation on two supercomputers and a comparison to the widely used Lattice Boltzmann solver Palabos.

A model-based tracking framework for textureless 3D rigid curved objects

This paper addresses the problem of tracking texturelessrigid curved objects. A common approach uses polygonalmeshes to represent curved objects inside an edge-based trackingsystem. However, in order to accurately recover their shape,high quality meshes are required, creating a trade-off betweencomputational efficiency and tracking accuracy. To solve thisissue, we suggest the use of quadrics calculated for each patchin the mesh to give local approximations of the object contour.This representation reduces considerably the level of detail of thepolygonal mesh while maintaining tracking accuracy. The noveltyof our research lies in using curves to represent the quadrics’projection in the current viewpoint for distance evaluation insteadof comparing directly the edges from the mesh and detectededges in the video image. In our tracking framework, we alsoinclude a method to calculate the measurable Degrees of Freedom(DoF) of the target object. This is used to recover the poseparameters when the object has less than 6DoF. Experimentalresults compare our approach to the traditional method ofusing sparse and dense meshes. Finally, we present a potentialAugmented Reality application of the proposed method.

Dynamic Stochastic Superresolution of sparsely observed turbulent systems

Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a fashion elucidated here. The DSS technique exploiting a simple Gaussian closure of the nonlinear stochastic forecast model emerges as the most suitable trade-off between the superresolution skill and computational complexity associated with estimating the cross-correlations between the aliasing modes of the sparsely observed turbulent signal. Such techniques offer a promising and efficient approach to constraining unresolved turbulent fluxes through stochastic superparameterization and a subsequent improvement in coarse-grained filtering and prediction of the next generation atmosphere–ocean system (AOS) models.

A Thermohydrodynamic Sparse Mesh Model of Bump-Type Foil Bearings

A numerical model for 3D thermohydrodynamic analysis of bump-type foil bearings with a sparse mesh across the air film is described. The model accounts for heat convection into cooling air, thermal expansion of the bearing components, and material property variations due to temperature rise. Deflection of the compliant foil strip, described as a link-spring structure, is coupled to the solution of the generalized Reynolds equation and the energy equation to account for the effect of foil deformation on the film thickness. The variation in bump stiffness with the thermal growth of bumps is also considered in the model. The unique airflow in foil bearings created by the top foil detachment in the subambient region is analyzed for use in modifying the thermal boundary condition. The Lobatto point quadrature algorithm is used to represent the model on a sparse mesh and thereby reduce the computational effort. The calculated bearing temperatures are in remarkable agreement with both the published test data with the use of cooling air and that without the use of cooling air. The change of bearing radial clearance due to thermal growth of the bearing components was found to significantly affect the bearing load and to be a likely cause of the obvious drop in load capacity with a rise in ambient temperature.