Surface Representation Research Articles

LGSur‐Net: A Local Gaussian Surface Representation Network for Upsampling Highly Sparse Point Cloud

AbstractWe introduce LGSur‐Net, an end‐to‐end deep learning architecture, engineered for the upsampling of sparse point clouds. LGSur‐Net harnesses a trainable Gaussian local representation by positioning a series of Gaussian functions on an oriented plane, complemented by the optimization of individual covariance matrices. The integration of parametric factors allows for the encoding of the plane's rotational dynamics and Gaussian weightings into a linear transformation matrix. Then we extract the feature maps from the point cloud and its adjoining edges and learn the local Gaussian depictions to accurately model the shape's local geometry through an attention‐based network. The Gaussian representation's inherent high‐order continuity endows LGSur‐Net with the natural ability to predict surface normals and support upsampling to any specified resolution. Comprehensive experiments validate that LGSur‐Net efficiently learns from sparse data inputs, surpassing the performance of existing state‐of‐the‐art upsampling methods. Our code is publicly available at https://github.com/Rangiant5b72/LGSur-Net.

The isolated effect of yield stress in viscoplastic turbulent flow

Turbulent flows of viscoplastic fluids are present in several industrial and natural applications. The effects of yield stress on this problem have always been studied as a part of a larger physical context, because real viscoplastic materials have many properties that cannot be easily isolated. Direct numerical simulations have recently emerged as a viable tool for investigating non-Newtonian fluid flow in turbulent regimes. In the present work, we solve the turbulent flow of an ideal Bingham fluid, focusing on the isolated effect of yield stress. A numerical scheme for viscoplastic flows was implemented based on the lattice Boltzmann method. An outstanding characteristic of this scheme is the possibility of representing infinite viscosity by setting the relaxation frequency to zero, enabling the representation of the Bingham constitutive equation without artifacts, and producing a more accurate representation of the yield surfaces. In the turbulent channel flow simulations, the friction Reynolds number was fixed at 180, while the Bingham number varied from 0 (Newtonian) to 0.15. It is shown that unyielded portions of material travel along with the flow near the centerline. These unyielded spots do not disappear quickly, but rather have a significant lifetime. Another interesting outcome is that the yield stress increases the turbulence anisotropy, by lowering the spanwise and normal velocity fluctuations, while the streamwise component becomes higher. Reynolds stresses and budgets of turbulent kinetic energy have been analyzed regarding the increased bulk velocities that were found by increasing the yield stress.

Fast Building Instance Proxy Reconstruction for Large Urban Scenes.

Digitalization of large-scale urban scenes (in particular buildings) has been a long-standing open problem, which attributes to the challenges in data acquisition, such as incomplete scene coverage, lack of semantics, low efficiency, and low reliability in path planning. In this paper, we address these challenges in urban building reconstruction from aerial images, and we propose an effective workflow and a few novel algorithms for efficient 3D building instance proxy reconstruction for large urban scenes. Specifically, we propose a novel learning-based approach to instance segmentation of urban buildings from aerial images followed by a voting-based algorithm to fuse the multi-view instance information to a sparse point cloud (reconstructed using a standard Structure from Motion pipeline). Our method enables effective instance segmentation of the building instances from the point cloud. We also introduce a layer-based surface reconstruction method dedicated to the 3D reconstruction of building proxies from extremely sparse point clouds. Extensive experiments on both synthetic and real-world aerial images of large urban scenes have demonstrated the effectiveness of our approach. The generated scene proxy models can already provide a promising 3D surface representation of the buildings in large urban scenes, and when applied to aerial path planning, the instance-enhanced building proxy models can significantly improve data completeness and accuracy, yielding highly detailed 3D building models.

GS‐Octree: Octree‐based 3D Gaussian Splatting for Robust Object‐level 3D Reconstruction Under Strong Lighting

AbstractThe 3D Gaussian Splatting technique has significantly advanced the construction of radiance fields from multi‐view images, enabling real‐time rendering. While point‐based rasterization effectively reduces computational demands for rendering, it often struggles to accurately reconstruct the geometry of the target object, especially under strong lighting conditions. Strong lighting can cause significant color variations on the object's surface when viewed from different directions, complicating the reconstruction process. To address this challenge, we introduce an approach that combines octree‐based implicit surface representations with Gaussian Splatting. Initially, it reconstructs a signed distance field (SDF) and a radiance field through volume rendering, encoding them in a low‐resolution octree. This initial SDF represents the coarse geometry of the target object. Subsequently, it introduces 3D Gaussians as additional degrees of freedom, which are guided by the initial SDF. In the third stage, the optimized Gaussians enhance the accuracy of the SDF, enabling the recovery of finer geometric details compared to the initial SDF. Finally, the refined SDF is used to further optimize the 3D Gaussians via splatting, eliminating those that contribute little to the visual appearance. Experimental results show that our method, which leverages the distribution of 3D Gaussians with SDFs, reconstructs more accurate geometry, particularly in images with specular highlights caused by strong lighting. The source code can be downloaded from https://github.com/LaoChui999/GS-Octree.

Neural Vector Fields for Implicit Surface Representation and Inference

AbstractNeural implicit fields have recently shown increasing success in representing, learning and analysis of 3D shapes. Signed distance fields and occupancy fields are still the preferred choice of implicit representations with well-studied properties, despite their restriction to closed surfaces. With neural networks, unsigned distance fields as well as several other variations and training principles have been proposed with the goal to represent all classes of shapes. In this paper, we develop a novel and yet a fundamental representation considering unit vectors in 3D space and call it Vector Field (VF). At each point in $$\mathbb {R}^3$$ R 3 , VF is directed to the closest point on the surface. We theoretically demonstrate that VF can be easily transformed to surface density by computing the flux density. Unlike other standard representations, VF directly encodes an important physical property of the surface, its normal. We further show the advantages of VF representation, in learning open, closed, or multi-layered surfaces. We show that, thanks to the continuity property of the neural optimization with VF, a separate distance field becomes unnecessary for extracting surfaces from the implicit field via Marching Cubes. We compare our method on several datasets including ShapeNet where the proposed new neural implicit field shows superior accuracy in representing any type of shape, outperforming other standard methods. Codes are available at https://github.com/edomel/ImplicitVF.

Backward Rauzy-Veech algorithm and horizontal saddle connections

The goal of this note is to study the action of the backward Rauzy-Veech algorithm on the translation surfaces with horizontal saddle connections. In particular, we prove that the orbit of a translation surface via the aforementioned algorithm is $\infty$-complete if and only if the surface does not posses horizontal saddle connections. Moreover, we show that appearance of all saddle connections as sides of the polygonal representations of the translations surface along the backward Rauzy-Veech induction orbit is equivalent to the minimality of the horizontal translation flow.

Dy-SheHeRASADe: A representation of the [formula omitted] sheet dynamics through surface descriptors

Molecular dynamics (MD) simulations are important tools for studying the dynamic motions of macromolecules at the atomic level. With the increasing capabilities of high performance computing, MD simulations are becoming more widely used. This allows molecular modelers to simulate the molecular behavior of large molecular architectures for much longer trajectories. Appropriate visualization of MD trajectories is becoming essential to provide an immediate and intuitive understanding of a molecule’s dynamics and function. In this study, we implement a novel 3D graphical representation, Dynamical Sheets Helper for RepresentAtion of SurfAce Descriptors (Dy-SheHeRASADe), to visualize the β sheet secondary structures of proteins in the context of molecular dynamics. Dy-SheHeRASADe is developed in UnityMol, an open source molecular viewer and prototyping platform. We considered β sheet fluctuations and hydrogen bond formation during molecular dynamics simulations to characterize the parts of β sheets with large motions or with labile bonds. We propose two visualization modes based on a surface representation of the β sheets calculated according to the positions of the α carbons and the hydrogen bonds between the β strands. The volumetric mode, in which this surface is enclosed in a semi-transparent volume that represents the fluctuation zone of the sheet during dynamics. The heatmap mode, in which the surface is colored according to the amplitude values of the α carbons. In addition, we quantify the β sheet fluctuations by displaying the values of the largest and smallest movements of the β sheets, the surface area of the sheets, and the number of hydrogen bonds.

Lattice Boltzmann simulations of unsteady Bingham fluid flows

Transient flows of viscoplastic fluids have very peculiar characteristics. The startup and cessation flows of viscoplastic materials have been subject to many theoretical and numerical investigations. The most challenging aspect of numerical solutions of viscoplastic fluids is the viscosity singularity during the transition from yielded to unyielded material. Hence, the proper representation of yield surfaces is the most critical aspect of numerical methods in viscoplastic fluid flow. In the present work, we use a lattice Boltzmann scheme to solve an ideal Bingham fluid’s startup and cessation flows. This numerical scheme advantage is that can represent infinite viscosity without noticeable numerical instabilities, producing yield surfaces with more accuracy and quality. Theoretical solutions for the startup flow are available in the literature. However, it is unclear which is more accurate and what their validity ranges are. Nonetheless, these solutions served as a reference for the present simulations. The overall aspect of the numerical solutions agreed with the theoretical models. The cessation flow of the Bingham fluid was also simulated. Unlike a Newtonian fluid, this type of flow is known to have a finite period until cessation. The simulations correctly reproduced this behavior. The transient yield surfaces matched very well with augmented Lagrangian solutions.

Factors Affecting Stimulus Duration Threshold for Depth Discrimination of Asynchronous Targets in the Intermediate Distance Range.

Binocular depth discrimination in the near distance range (< 2 m) improves with stimulus duration. However, whether the same response-pattern holds in the intermediate distance range (approximately 2-25 m) remains unknown because the spatial coding mechanisms are thought to be different. We used the two-interval forced choice procedure to measure absolute depth discrimination of paired asynchronous targets (3, 6, or 16 arc min). The paired targets (0.2 degrees) were located over a distance and height range, respectively, of 4.5 to 7.0m and 0.15 to 0.7 m. Experiment 1 estimated duration thresholds for binocular depth discrimination at varying target durations (40-1610 ms), in the presence of a 2 × 6 array of parallel texture-elements spanning 1.5 × 5.83 m on the floor. The texture-elements provided a visible background in the light-tight room (9 × 3 m). Experiment 2 used a similar setup to control for viewing conditions: binocular versus monocular and with versus without texture background. Experiment 3 compared binocular depth discrimination between brief (40, 80, and 125 ms) and continuous texture background presentation. Stimulus duration threshold for depth discrimination decreased with increasing disparity in experiment 1. Experiment 2 revealed depth discrimination performance with texture background was near chance level with monocular viewing. Performance with binocular viewing degraded without texture background. Experiment 3 showed continuous texture background presentation enhances binocular depth discrimination. Absolute depth discrimination improves with target duration, binocular viewing, and texture background. Performance further improved with longer background duration underscoring the role of ground surface representation in spatial coding.

Enhancing 3D Models with Spectral Imaging for Surface Reflectivity.

The increasing demand for accurate and detailed 3D modeling in fields such as cultural heritage preservation, industrial inspection, and scientific research necessitates advanced techniques to enhance model quality. This paper addresses this necessity by incorporating spectral imaging data to improve the surface detail and reflectivity of 3D models. The methodology integrates spectral imaging with traditional 3D modeling processes, offering a novel approach to capturing fine textures and subtle surface variations. The experimental results of this paper underscore the advantages of incorporating spectral imaging data in the creation of 3D models, particularly in terms of enhancing surface detail and reflectivity. The achieved experimental results demonstrate that 3D models generated with spectral imaging data exhibit significant improvements in surface detail and accuracy, particularly for objects with intricate surface patterns. These findings highlight the potential of spectral imaging in enhancing 3D model quality. This approach offers significant advancements in 3D modeling, contributing to more precise and reliable representations of complex surfaces.

Optimizing algorithm for high-precision imaging stitching systems based on spline surfaces

As optical systems continue to advance, non-uniform rational B-spline (NURBS) surfaces increasingly being considered in asymmetric optical systems due to their localized control characteristics. However, the representation of NURBS surfaces has complicated the analysis of these systems, leading to a significant computational burden. To address this challenge, we propose an optimizing algorithm for imaging optical systems based on high-precision ray tracing of NURBS surfaces. This method initiates with getting a knot grid as prior information, in conjunction with the Newton-Raphson algorithm, to obtain high-precision numerical solutions for the intersection of rays with a NURBS surface. Building upon this methodology, we introduce an optimization technique that includes shape evaluation to generate an evaluation function specific to NURBS surfaces. This approach is then applied within a rapid optimization process that accounted for the region of ray influence. Under consistent control point grids and sampling ray conditions, we present an off-axis four-mirror system to showcase that our algorithm has achieved a computational efficiency improvement of approximately 14 times compared to the previous method. This high-precision imaging design based on spline surfaces fulfills the need for efficient and accurate algorithms for NURBS surface applications in various imaging systems, providing guidance for practical applications.

Turkish spelling errors by Turkish-Dutch bilingual children

The current pilot study adds to the small body of work focusing on Turkish-Dutch children's Turkish literacy attainment by investigating their spelling errors. This study deviates from the previous studies by attempting to find patterns behind the surface representation of errors (i.e. omission, substitution and addition). Fifty-three 10 to 12 year-old Turkish-Dutch bilingual children were asked to write Turkish narratives. The participants misspelled about half of the words. The errors in order of frequency were diacritic errors (i.e. confusing the graphemes with and without diacritics), orthographic ambiguity errors (i.e. phonetically spelling a word though it is not orthographically transparent), punctuation errors, capitalization errors, morphological errors (e.g. using a wrong allomorph of a suffix), spacing errors (e.g. writing two words as one), code-switching (i.e. utilizing Dutch words in Turkish sentences) and Dutch-influenced errors (i.e. using Dutch orthographic rules in Turkish such as spelling /j/ as <j> or /u/ as <oe>). The rest of the errors, which lacked a discernible pattern, were categorized as “other”. These results differed from the findings on Turkish monolingual children's spelling errors in the literature in some notable ways (e.g. the very high rate of misspelled words and the prevalence of diacritic errors).

Comparative Study on the Interest in Non-Uniform Rational B-Splines Representation versus Polynomial Surface Description in a Freeform Three-Mirror Anastigmat

Novel freeform optical design methods can be classified in two categories, depending on whether they focus on the generation of a starting point or the development of new optimization tools. In this paper, we design a freeform three-mirror anastigmat (TMA) and compare different surface representations using either a differential ray tracer as a new optimization tool or a commercial ray tracer (ANSYS-ZEMAX OpticStudio). For differential ray tracing, we used FORMIDABLE (Freeform Optics Raytracer with Manufacturable Imaging Design cApaBiLitiEs), an optical design library with differential ray tracing and Non-Uniform Rational B-Splines (NURBS) optimization capabilities, available under the European Software Community License (ESCL). NURBS allow a freeform surface to be represented without needing any prior knowledge of the surface, such as the polynomial degree in polynomial descriptions. OpticStudio and other commercial optical design software are designed to optimize polynomial surfaces but are not well-suited to optimize NURBS surfaces, requiring a custom optical design library. In order to demonstrate the interest in using NURBS representation, we designed and independently optimized two freeform telescopes over different iteration cycles; with NURBS using FORMIDABLE or with XY polynomials using OpticStudio. We then compared the resulting systems using their root mean square field maps to assess the optimization quality of each surface representation. We also provided a full-system comparison, including mirror freeform departures. This study shows that NURBS can be a relevant alternative to XY polynomials for the freeform optimization of reflective three-mirror telescopes as it achieves more a uniform imaging quality in the field of view.

Impact of Atomic Defects on Water Contact Angle of 2D Molybdenum Disulfide Surfaces.

Interfacial dynamics within nanofluidic systems are crucial for applications like water desalination and osmotic energy harvesting. Understanding these dynamics can inform the rational optimization of two-dimensional (2D) materials and devices for such applications. This study explores the wetting behavior of realistic 2D MoS2 surfaces incorporating vacancies and atomic steps, known as atomic defects. We employ a combined density functional theory (DFT) and molecular dynamics (MD) computational approach to elucidate the influence of atomic defects on the MoS2-water interface. DFT calculations are utilized to determine the charge distribution within MoS2. Subsequently, free energy calculations are obtained through MD simulations of the MoS2-water interface. Our findings underscore the importance of incorporating atomic defects into MoS2 surfaces for accurate water contact angle (WCA) predictions in nanofluidic simulations, particularly when using Abal et al. force field parameters. However, the force field developed by Liu et al. yielded more accurate results for pristine MoS2 surfaces. While these parameters provide reliable outcomes for pristine MoS2 surfaces, their application to surfaces with defects may lead to underestimation of WCA. This highlights the critical need for realistic surface representations in nanofluidic modeling to accurately capture the complex interactions between water and MoS2 materials.

A semi-automatic method for block-structured hexahedral meshing of aortic dissections.

The article presents a semi-automatic approach to generating structured hexahedral meshes of patient-specific aortas ailed by aortic dissection. The condition manifests itself as a formation of two blood flow channels in the aorta, as a result of a tear in the inner layers of the aortic wall. Subsequently, the morphology of the aorta is greatly impacted, making the task of domain discretization highly challenging. The meshing algorithm presented herein is automatic for the individual lumina, whereas the tears require user interaction. Starting from an input (triangle) surface mesh, we construct an implicit surface representation as well as a topological skeleton, which provides a basis for the generation of a block-structure. Thereafter, the mesh generation is performed via transfinite maps. The meshes are structured and fully hexahedral, exhibit good quality and reliably match the original surface. As they are generated with computational fluid dynamics in mind, a fluid flow simulation is performed to verify their usefulness. Moreover, since the approach is based on valid block-structures, the meshes can be made very coarse (around 1000 elements for an entire aortic dissection domain), and thus promote using solvers based on the geometric multigrid method, which is typically reliant on the presence of a hierarchy of coarser meshes.

The Human Cerebellum: A Digital Anatomical Atlas at the Level of Individual Folia.

Scientific interest in the cerebellum has surged in the last few decades with an emerging consensus on a multifaceted functionality and intricate, but not yet fully understood, functional topography over the cerebellar cortex. To further refine this structure-function relationship and quantify its inter-subject variability, a high-resolution digital anatomical atlas is fundamental. Using a combination of manual labeling and image processing, we turned a recently published reconstruction of the human cerebellum, the first such reconstruction fine enough to resolve the individual folia, into a digital atlas with both surface and volumetric representations. Its unprecedented granularity (0.16 mm) and detailed expert labeling make the atlas usable as an anatomical ground truth, enabling new ways of analyzing and visualizing cerebellar data through its digital format.

A fibre direction informed continuum damage model with enriched kinematics for modelling matrix cracking in composites

Continuum Damage Mechanics models are widely used for simulation of ply-level damage such as matrix cracking in composites. Although their ease of implementation within the finite element framework is appealing, several limitations exist such as a smeared representation of sharp cracks, mesh orientation bias of crack growth, inaccurate energy dissipation due to approximate definition of characteristic length etc. In this work, a new ‘semi-discrete’ continuum damage model is proposed for matrix cracking, that includes sharp crack kinematics. The mesh orientation bias is eliminated by a fibre-directed growth driving criterion. The crack characteristic length is exactly computed due to an accurate geometric representation of the crack surface. The model also addresses a well-known problem of spurious stress transfer across crack faces when deformation becomes large. Through several challenging benchmark problems, the model is shown to perform nearly as good as discrete crack models while being simpler and more robust.

Conversion from NURBS to Bézier representation

With the help of the Cox-de Boor recursion formula and the recurrence relation of the Bernstein polynomials, two categories of recursive algorithms for calculating the conversion matrix from an arbitrary non-uniform B-spline basis to a Bernstein polynomial basis of the same degree are presented. One is to calculate the elements of the matrix one by one, and the other is to calculate the elements of the matrix in two blocks. Interestingly, the weights in the two most basic recursion formulas are directly related to the weights in the recursion definition of the B-spline basis functions. The conversion matrix is exactly the Bézier extraction operator in isogeometric analysis, and we obtain the local extraction operator directly. With the aid of the conversion matrix, it is very convenient to determine the Bézier representation of NURBS curves and surfaces on any specified domain, that is, the isogeometric Bézier elements of these curves and surfaces.

Fitting of Coupled Potential Energy Surfaces via Discovery of Companion Matrices by Machine Intelligence.

Fitting coupled potential energy surfaces is a critical step in simulating electronically nonadiabatic chemical reactions and energy transfer processes. Analytic representation of coupled potential energy surfaces enables one to perform detailed dynamics calculations. Traditionally, fitting is performed in a diabatic representation to avoid fitting the cuspidal ridges of coupled adiabatic potential energy surfaces at conical intersection seams. In this work, we provide an alternative approach by carrying out fitting in the adiabatic representation using a modified version of the Frobenius companion matrices, whose usage was first proposed by Opalka and Domcke. Their work involved minimizing the errors in fits of the characteristic polynomial coefficients (CPCs) and diagonalizing the resulting companion matrix, whose eigenvalues are adiabatic potential energies. We show, however, that this may lead to complex eigenvalues and spurious discontinuities. To alleviate this problem, we provide a new procedure for the automatic discovery of CPCs and the diagonalization of a companion matrix by using a special neural network architecture. The method effectively allows analytic representation of global coupled adiabatic potential energy surfaces and their gradients with only adiabatic energy input and without experience-based selection of a diabatization scheme. We demonstrate that the new procedure, called the companion matrix neural network (CMNN), is successful by showing applications to LiH, H3, phenol, and thiophenol.

Subword Representations Successfully Decode Brain Responses to Morphologically Complex Written Words

Abstract This study extends the idea of decoding word-evoked brain activations using a corpus-semantic vector space to multimorphemic words in the agglutinative Finnish language. The corpus-semantic models are trained on word segments, and decoding is carried out with word vectors that are composed of these segments. We tested several alternative vector-space models using different segmentations: no segmentation (whole word), linguistic morphemes, statistical morphemes, random segmentation, and character-level 1-, 2- and 3-grams, and paired them with recorded MEG responses to multimorphemic words in a visual word recognition task. For all variants, the decoding accuracy exceeded the standard word-label permutation-based significance thresholds at 350–500 ms after stimulus onset. However, the critical segment-label permutation test revealed that only those segmentations that were morphologically aware reached significance in the brain decoding task. The results suggest that both whole-word forms and morphemes are represented in the brain and show that neural decoding using corpus-semantic word representations derived from compositional subword segments is applicable also for multimorphemic word forms. This is especially relevant for languages with complex morphology, because a large proportion of word forms are rare and it can be difficult to find statistically reliable surface representations for them in any large corpus.