Surface Representation Research Articles

Orders-of-coupling representation achieved with a single neural network with optimal neuron activation functions and without nonlinear parameter optimization

Orders-of-coupling representations (representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates corresponding to different orders of coupling) are useful in many applications, for example, in computational chemistry and other applications, especially where integration is needed. Examples include N-mode approximations and many-body expansions. Such representations can be conveniently built with machine learning methods, and previously, methods building the lower-dimensional terms of such representations with neural networks [e.g. Comput. Phys. Commun. 180 (2009) 2002] and Gaussian process regressions [e.g. Mach. Learn. Sci. Technol. 3 (2022) 01LT02] were proposed. Here, we show that neural network models of orders-of-coupling representations can be easily built by using a recently proposed neural network with optimal neuron activation functions computed with a first-order additive Gaussian process regression [arXiv:2301.05567] and avoiding non-linear parameter optimization. Examples are given of representations of molecular potential energy surfaces.

Diffusion of tangential tensor fields: numerical issues and influence of geometric properties

Abstract We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose, several finite-element-based numerical methods are collected and used to solve a tangential surface n-tensor heat flow problem. These methods differ with respect to the surface representation used, the geometric information required, and the treatment of the tangentiality condition. We emphasize the importance of geometric properties and their increasing influence as the tensorial degree changes from n = 0 to n ≥ 1. A specific example is presented that illustrates how curvature drastically affects the behavior of the solution.

Pyrolysis of Spherical Wood Particles in a Packed Bed – Comparison between Resolved and Unresolved Discrete Element Method/Computational Fluid Dynamics

AbstractThe combined discrete element method/computational fluid dynamics (DEM/CFD) approach allows for the description of reacting granular assemblies passed by a gas flow. Especially for thermally thick particles, the spatial resolution of the solid object volumes, their surfaces, and of the interstitial flow domain controls the quality of results while at the same time driving computational costs. To evaluate the differences between resolved and unresolved DEM/CFD approaches, pyrolysis of a bulk of spherical wood particles enclosed by a cylindrical heating surface and passed by hot nitrogen is numerically examined. The unresolved simulation is based on the averaged volume method (AVM). For the resolved simulation, the so‐called blocked‐off (BO) method is applied. The results show that the total mass conversion rate of solid particles into gaseous volatiles is faster when employing the resolved BO approach. The better spatial resolution of local flow field and particle surface representation leads to a more detailed prediction of convective and radiative heat transfer to the particles, but is associated with the penalty of a six‐fold computing time.

Fitting Potential Energy Surfaces by Learning the Charge Density Matrix with Permutationally Invariant Polynomials.

The electronic energy in the Hartree-Fock (HF) theory is the trace of the product of the charge density matrix (CDM) with the one-electron and two-electron matrices represented in an atomic orbital basis, where the two-electron matrix is also a function of the same CDM. In this work, we examine a formalism of analytic representation of a generic molecular potential energy surface (PES) as a sum of a linearly parameterized HF and a correction term, the latter formally representing the electron correlation energy, also linearly parameterized, by expressing the elements of CDM using permutationally invariant polynomials (PIPs). We show on a variety of numerical examples, ranging from exemplary two-electron systems HeH+ and H3+ to the more challenging cases of methanium (CH5+) fragmentation and high-energy tautomerization of formamide to formimidic acid that such a formulation requires significantly fewer, 10-20% of PIPs, to accomplish the same accuracy of the fit as the conventional representation at practically the same computational cost.

Technical variability of cornea parameters derived from anterior segment OCT fitted with Fringe Zernike polynomials.

This study uses bootstrapping to evaluate the technical variability (in terms of model parameter variation) of Zernike corneal surface fit parameters based on Casia2 biometric data. Using a dataset containing N = 6953 Casia2 biometric measurements from a cataractous population, a Fringe Zernike polynomial surface of radial degree 10 (36 components) was fitted to the height data. The fit error (height - reconstruction) was bootstrapped 100 times after normalisation. After reversal of normalisation, the bootstrapped fit errors were added to the reconstructed height, and characteristic surface parameters (flat/steep axis, radii, and asphericities in both axes) extracted. The median parameters refer to a robust surface representation for later estimates of elevation, whereas the SD of the 100 bootstraps refers to the variability of the surface fit. Bootstrapping gave median radius and asphericity values of 7.74/7.68 mm and -0.20/-0.24 for the corneal front surface in the flat/steep meridian and 6.52/6.37 mm and -0.22/-0.31 for the corneal back surface. The respective SD values for the 100 bootstraps were 0.0032/0.0028 mm and 0.0093/0.0082 for the front and 0.0126/0.0115 mm and 0.0366/0.0312 for the back surface. The uncertainties for the back surface are systematically larger as compared to the uncertainties of the front surface. As measured with the Casia2 tomographer, the fit parameters for the corneal back surface exhibit a larger degree of variability compared with those for the front surface. Further studies are needed to show whether these uncertainties are representative for the situation where actual repeat measurements are possible.

Neural Representation of Open Surfaces

AbstractNeural implicit surfaces have emerged as an effective, learnable representation for shapes of arbitrary topology. However, representing open surfaces remains a challenge. Different methods, such as unsigned distance fields (UDF), have been proposed to tackle this issue, but a general solution remains elusive. The generalized winding number (GWN), which is often used to distinguish interior points from exterior points of 3D shapes, is arguably the most promising approach. The GWN changes smoothly in regions where there is a hole in the surface, but it is discontinuous at points on the surface. Effectively, this means that it can be used in lieu of an implicit surface representation while providing information about holes, but, unfortunately, it does not provide information about the distance to the surface necessary for e.g. ray tracing, and special care must be taken when implementing surface reconstruction. Therefore, we introduce the semi‐signed distance field (SSDF) representation which comprises both the GWN and the surface distance. We compare the GWN and SSDF representations for the applications of surface reconstruction, interpolation, reconstruction from partial data, and latent vector analysis using two very different data sets. We find that both the GWN and SSDF are well suited for neural representation of open surfaces.

Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids

We present two major improvements over the Compressible High-ORder Unstructured Spectral difference (CHORUS) code published in Wang et al., “A compressible high-order unstructured spectral difference code for stratified convection in rotating spherical shells,” J. Comput. Phys. 290, 90–111 (2015). The new code is named CHORUS++ in this paper. Subsequently, we perform a series of efficient simulations for rotationally constrained convection (RCC) in spherical shells. The first improvement lies in the integration of the high-order spectral difference method with a boundary-conforming transfinite mapping on cubed-sphere grids, thus ensuring exact geometric representations of spherical surfaces on arbitrary sparse grids. The second improvement is on the adoption of higher-order elements (sixth-order) in CHORUS++ vs third-order elements for the original CHORUS code. CHORUS++ enables high-fidelity RCC simulations using sixth-order elements on very coarse grids. To test the accuracy and efficiency of using elements of different orders, CHORUS++ is applied to a laminar solar benchmark, which is characterized by columnar banana-shaped convective cells. By fixing the total number of solution degrees of freedom, the computational cost per time step remains unchanged. Nevertheless, using higher-order elements in CHORUS++ resolves components of the radial energy flux much better than using third-order elements. To obtain converged predictions, using sixth-order elements is 8.7 times faster than using third-order elements. This significant speedup allows global-scale fully compressible RCC simulations to reach equilibration of the energy fluxes on a small cluster of just 40 cores. In contrast, CHORUS simulations were performed by Wang et al. on supercomputers using approximately 10 000 cores. Using sixth-order elements in CHORUS++, we further carry out global-scale solar convection simulations with decreased rotational velocities. Interconnected networks of downflow lanes emerge and surround broader and weaker regions of upflow fields. A strong inward kinetic energy flux compensated by an enhanced outward enthalpy flux appears. These observations are all consistent with those published in the literature. Furthermore, CHORUS++ can be extended to magnetohydrodynamic simulations with potential applications to the hydromagnetic dynamo processes in the interiors of stars and planets.

Integrated deep learning-based online layer-wise surface prediction of additive manufacturing

Additive manufacturing (AM) is growing tremendously through its introduction into various industries over recent years, because of its capability of fabricating objects with complex designs. Despite its great successes, AM still has to deal with its main challenge, which is the quality assurance of the printed object. Although extensive studies have been conducted, there are still several critical gaps facing this technology. Due to layer-wise fabrication, one important aspect of quality assurance is to capture the surface morphology of the layer being printed online, which can help to better understand the process dynamics and greatly benefit the promotion of in-process quality control. Thus, this study developed an integrated deep learning model to achieve online layer-wise surface prediction of AM. The proposed deep learning model integrates the convolution autoencoder for surface representation learning and a long short-term memory (LSTM) network for layer-wise prediction. The proposed method is validated by a real-world case study in a common AM process, fused filament fabrication (FFF). The comparison with the benchmarks demonstrates that the developed method has great potential for online layer-wise prediction in AM.

Three-dimensional shape generation via variational autoencoder generative adversarial network with signed distance function

<span lang="EN-US">Mesh-based 3-dimensional (3D) shape generation from a 2-dimensional (2D) image using a convolution neural network (CNN) framework is an open problem in the computer graphics and vision domains. Most existing CNN-based frameworks lack robust algorithms that can scale well without combining different shape parts. Also, most CNN-based algorithms lack suitable 3D data representations that can fit into CNN without modification(s) to produce high-quality 3D shapes. This paper presents an approach that integrates a variational autoencoder (VAE) and a generative adversarial network (GAN) called 3 dimensional variational autoencoder signed distance function generative adversarial network (3D-VAE-SDFGAN) to create a 3D shape from a 2D image that considerably improves scalability and visual quality. The proposed method only feeds a single 2D image into the network to produce a mesh-based 3D shape. The network encodes a 2D image of the 3D object into the latent representations, and implicit surface representations of 3D objects corresponding to those 2D images are subsequently generated. Hence, a signed distance function (SDF) is proposed to maintain object inside-outside information in the implicit surface representation. Polygon mesh surfaces are then produced using the marching cubes algorithm. The ShapeNet dataset was used in the experiments to evaluate the proposed 3D-VAE-SDFGAN. The experimental results show that 3D-VAE-SDFGAN outperforms other state-of-the-art models.</span>

A Multirobot System for 3-D Surface Reconstruction With Centralized and Distributed Architectures

In this article, we propose an original solution to the problem of surface reconstruction of large-scale unknown environments, with multiple cooperative robots. As they progress through the 3-D environment, the robots rely on volumetric maps obtained via a TSDF representation to extract discrete incomplete surface elements (ISEs), and a list of candidate viewpoints is generated to cover them. A next-best-view planning approach, which approximately solves a traveling salesman problem (TSP) via greedy allocation, is then used to iteratively assign these viewpoints to the robots. Two multiagent architectures, a centralized one (TSP-Greedy Allocation or TSGA) and a distributed one (dist-TSGA), in which the robots locally compute their maps and share them, are developed and compared. Extensive numerical and real-world experiments with multiple aerial and ground robots in challenging 3-D environments show the flexibility and effectiveness of our surface representation of a volumetric map. The experiments also shed light on the nexus between reconstruction accuracy and surface completeness, and between total distance traveled and execution time.

Still never at the top: representation of Asian and Black characters in Sony/Marvel Studios’ Spider-Man trilogy

ABSTRACT This article examines the portrayal of Asian and Black characters in Sony/Marvel Studios’ Spider-Man trilogy. We analyze Ned Leeds, Brad Davis, Liz Allan, and M.J. “Michelle Jones-Watson,” as well as minor characters, through the lens of racial triangulation (Kim, 1999). We focus not only on traditional white/Asian/Black comparisons across racial groups, but also on sub-triangulations within groups, such as positioning Black women in comparison to other Black women or Black men, or Asian men to other Asian men or Asian women, along with comparisons to white representations. Despite the trilogy’s diverse cast, Ned, Brad, Liz, and M.J. remain separated from and in opposition to one another, with their existence and purpose constructed around their relationship and/or relevance to Peter Parker (Spider-Man), the white main character. The trilogy furthermore employs long-standing stereotypes about people of Asian and Black descent to help maintain whiteness at the top of all triangulations. We argue for a greater need to push beyond surface representations of “diversity” to consider how media actually represent different groups.

Survey of new applications of geometric algebra

This survey introduces 101 new publications on applications of Clifford's geometric algebras (GAs) newly published during 2022 (until mid‐January 2023). The selection of papers is based on a comprehensive search with Dimensions.ai, followed by detailed screening and clustering. Readers will learn about the use of GA for mathematics, computation, surface representations, geometry, image, and signal processing, computing and software, quantum computing, data processing, neural networks, medical science, physics, electric engineering, control and robotics.

An integrated design approach for simultaneous shape and topology optimization of shell structures

In this work, a novel design approach is developed to carry out shape and topology optimization of shell structures simultaneously. This approach effectively integrates the IsoGeometric Analysis (IGA) method, the Adaptive Bubble Method (ABM) and the Finite Cell Method (FCM) to make full use of their respective advantages in shell structure optimization. To be specific, the IGA method using Non-Uniform Rational B-Splines (NURBS) elements is adopted to analyze the shell structure and realize shape optimization with merits of exact shell surface representation geometrically and rotation-free shell formulation physically; the ABM is utilized to insert deformable holes adaptively in the parametric domain of the NURBS surface for topology optimization of the shell structure; the FCM is employed to facilitate the optimization process by simplifying significantly the discrimination and the numerical integration processes of trimmed elements involved in fixed-mesh analysis of the holed shell structure. Based on this integrated design approach of IGA/ABM/FCM, shape optimization can be implemented by directly optimizing the control-point coordinates of the NURBS surface in the physical space, while topology optimization could be carried out simultaneously in the parametric domain as easily as for 2D planar structures. Finally, representative examples are investigated to demonstrate the effectiveness and advantages of the proposed design approach.

Progressive refinement imaging with depth-assisted disparity correction

In recent years, the increasing on-board compute power of mobile camera devices gave rise to a class of digitization algorithms that dynamically fuse a stream of camera observations into a progressively updated scene representation. Previous algorithms either obtain general 3D surface representations, often exploiting range maps from a depth camera, such as, Kinect Fusion, etc.; or they reconstruct planar (or distant spherical, respectively) 2D images with respect to a single (perspective or orthographic) reference view, such as, panoramic stitching or aerial mapping. Our work sets out to combine aspects of both, reconstructing a 2.5-D representation (color and depth) as seen from a fixed viewpoint, at spatially variable resolution. Inspired by previous work on “progressive refinement imaging”, we propose a hierarchical representation that enables progressive refinement of both colors and depths by ingesting RGB-D images from a handheld depth camera that is carried through the scene. We evaluate our system by comparing it against state-of-the-art methods in 2D progressive refinement and 3D scene reconstruction, using high-detail indoor and outdoor data sets comprising medium to large disparities. As we will show, the restriction to 2.5-D from a fixed viewpoint affords added robustness (particularly against self-localization drift, as well as backprojection errors near silhouettes), increased geometric and photometric fidelity, as well as greatly improved storage efficiency, compared to more general 3D reconstructions. We envision that our representation will enable scene exploration with realistic parallax from within a constrained range of vantage points, including stereo pair generation, visual surface inspection, or scene presentation within a fixed VR viewing volume.

A multi-moment finite volume formulation for the interaction between free surface flow and moving bodies with THINC method

A numerical model is developed for fluid-rigid body interaction involving free surfaces on moving unstructured grids using the Arbitrary-Lagrangian–Eulerian (ALE) formulation. The multi-moment finite volume method is used for the spatial discretization of Navier–Stokes equations in which volume integrated average (VIA) and point values (PVs) are defined as prognostic variables and updated by integral and differential form respectively. Given VIA and PV in each cell, a higher-order reconstruction function can be built in a compact stencil which improves the numerical accuracy and robustness on the unstructured grids. More importantly, it facilitates imposing a more accurate Dirichlet–Neumann condition for the partitioned interface between the fluid and solid region. The geometrical conservation law (GCL) is also formulated to govern the spatial volume element under an arbitrary mapping. In order to capture the free surfaces of multiphase flows, the volume-of-fluid (VOF) equation is solved by THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature) scheme in varying mesh, which achieves geometrical faithful interface representation, particularly for curved surfaces in a complex and moving domain. The present model is validated by some benchmark tests in two dimensions for fluid–structure interaction problems with free surfaces. The numerical results show closer agreement with the experimental data than the reference solution of other numerical models. It convinces that the present model provides accurate and robust solutions for the simulation of the complex interaction between the free surface flows and moving bodies.

PERFORMANCE ASSESSMENT OF LANDSAT 8 AND SENTINEL-2 SATELLITE IMAGES FOR THE PRODUCTION OF TIME SERIES LAND USE/LAND COVER (LULC) MAPS

Land use/Land cover (LULC) maps are essential tools used in various disciplines, including geosciences, urban and regional planning, climate, and agriculture. LULC maps provide a visual representation of the Earth's surface, depicting the different types of land use and land cover in a given area. Land use refers to the human activities that take place on the land, such as agriculture, urban development, and mining, while land cover refers to the physical characteristics of the land, such as forests, grasslands, and wetlands. Researchers can gain insights into environmental trends and patterns, such as deforestation, urbanization, and climate change by analysing changes in LULC over time. While Landsat 8 images have been used to create LULC maps for years, the high-resolution images provided by Sentinel-2 since 2017 have allowed for the creation of highly detailed LULC maps. However, it is still necessary to use Landsat 8 images to produce LULC maps for time-series analyses and future predictions. Unsupervised classification is a method used to create LULC maps using Landsat 8 images, but this study found that the resulting maps differed from those created using Sentinel-2 images, with up to a two-fold difference in the classification of classes such as "Bare Ground," "Built Area," "Crops," and "Trees". Especially when using Landsat data, it is suggested that it would be useful to make evaluations for wider areas/regions as the resolution of Landsat 8 satellite images is limited to 30 meters.

Predicting Electronic Structure of Realistic Amorphous Surfaces

AbstractAmorphous materials underlie the functionality of many devices in photocatalysis, electronics, and other technological applications. The performance of such devices is largely altered by the interfacial characteristics of the material motivating better understanding of their structure function relationships. However, open questions remain about how to generate atomistic representations of amorphous surfaces that are realistic while being amenable to computational study using electronic structure methods. Here, model parameters are explored to generate accurate amorphous surface models using prototypical amorphous titanium dioxide and a melt‐quench approach. In particular, non‐standard model considerations such as minimum sample size, unit cell size, and quench conditions are varied to efficiently explore amorphous structural space. The results indicate different modeling parameters have a substantial effect on surface morphology and electronic structure that significantly alters the interpretations gained by computational study of amorphous interfaces. Critically, it is shown that the structural motifs that contribute to such differences are not detectable by short range structural analysis that has traditionally been used to assess the quality of melt‐quench derived amorphous structures.

PySubdiv 1.0: open-source geological modeling and reconstruction by non-manifold subdivision surfaces

Abstract. Sealed geological models are commonly used as an input to process simulations, for example, in hydrogeological or geomechanical studies. Creating these meshes often requires tedious manual work, and it is therefore difficult to adjust a once-created model. In this work, we propose a flexible framework to create and interact with geological models using explicit surface representations. The essence of the work lies in the determination of the control mesh and the definition of semi-sharp-crease values, which, in combination, enable the representation of complex structural settings with a low number of control points. We achieve this flexibility through the adaptation of recent algorithms from the field of computer graphics to the specific requirements of geological modeling, specifically the representation of non-manifold topologies and sharp features. We combine the method with a particle swarm optimization (PSO) approach to enable the automatic optimization of vertex position and crease sharpness values. The result of this work is implemented in an open-source software (PySubdiv) for reconstructing geological structures while resulting in a model which is (1) sealed/watertight, (2) controllable with a control mesh and (3) topologically similar to the input geological structure. Also, the reconstructed model may include a lower number of vertices compared to the input geological structure, which results in reducing the cost of modeling and simulation. In addition to enabling a manual adjustment of sealed geological models, the algorithm also provides a method for the integration of explicit surface representations in inverse frameworks and the consideration of uncertainties.

A Case Study on the Application of 3D Scanning Technology in Deformation Monitoring of Slope Stabilization Structure

Traditional deformation monitoring suffers from issues such as the point-based representation of surfaces and low measurement efficiency. Moreover, the majority of researchers study the deformation of slopes using methods such as 3S technology, synthetic aperture radar interferometry, distributed fiber optic sensing technology, etc. Based on this, a slope stabilization structure deformation monitoring method based on 3D laser scanning technology is proposed. First, with the slope stabilization structure of Caihong Road as the engineering background, point cloud data of the slope stabilization structure is obtained using a Trimble SX10 device. Second, the point deformation, overall deformation, and line deformation of the two-phase slope stabilization structure point cloud data are analyzed. Finally, the measurement accuracy of the 3D laser scanning technology is evaluated. The results show that the deformation analysis of points, lines, and surfaces can complement each other, thereby comprehensively assessing the situation of slope stabilization structure deformation. Moreover, the maximum displacement value in the deformation of points, lines, and surfaces is 8.52 mm, which does not exceed the standard, and 93.61% of the point deformation is between −0.76~0.92 mm, indicating that the slope stabilization structure is in a safe and stable state. The independent sample t-test has a test statistic of t = 2.074, verifying that the 3D laser scanning technology and the total station measurement accuracy are highly consistent and can meet the needs of actual engineering. The results of this study can provide a reasonable theoretical and methodological reference for analyzing similar engineering deformation monitoring in the future.

Learning neural implicit representations with surface signal parameterizations

Neural implicit surface representations have recently emerged as popular alternative to explicit 3D object encodings, such as polygonal meshes, tabulated points, or voxels. While significant work has improved the geometric fidelity of these representations, much less attention is given to their final appearance. Traditional explicit object representations commonly couple the 3D shape data with auxiliary surface-mapped image data, such as diffuse color textures and fine-scale geometric details in normal maps that typically require a mapping of the 3D surface onto a plane, i.e., a surface parameterization; implicit representations, on the other hand, cannot be easily textured due to lack of configurable surface parameterization. Inspired by this digital content authoring methodology, we design a neural network architecture that implicitly encodes the underlying surface parameterization suitable for appearance data. As such, our model remains compatible with existing mesh-based digital content with appearance data. Motivated by recent work that overfits compact networks to individual 3D objects, we present a new weight-encoded neural implicit representation that extends the capability of neural implicit surfaces to enable various common and important applications of texture mapping. Our method outperforms reasonable baselines and state-of-the-art alternatives.