Geometric Details Research Articles

NeRF-based Polarimetric Multi-view Stereo

In this paper, we introduce NeRF-based Polarimetric Multi-view Stereo (NPMVS), a novel 3D reconstruction method that combines the advantages of neural radiance field (NeRF) and shape-from-polarization (SfP) to address the challenge posed by textureless areas while preserving the fine-scale geometric details. Our method first leverages neural rendering to yield depth priors for each input view, subsequently estimates more accurate depths and normals using polarimetric refinement. We further introduce a pixel-wise depth rectification process to address the scaling problem inherent to the polarimetric refinement procedure. In addition, we contribute a new realistic pBRDF-based multi-view synthetic dataset, comprised of RGB and polarization images rendered under real-world lighting conditions, which will serve as a valuable resource for future research in this field. Experimental evaluations on both synthetic and real-world datasets validate the superiority of NPMVS, demonstrating its advantage over other state-of-the-art multi-view stereo and shape-from-polarization methods.

Fast flow field prediction based on E(2)-equivariant steerable convolutional neural networks

In the field of flow field reconstruction, traditional deep learning models predominantly rely on standard convolutions, but their predictive accuracy remains limited. To address this issue, we explore the potential of E(2)-equivariant convolutions to enhance the predictive accuracy of deep learning models for fast flow field prediction. Unlike conventional convolutions, E(2)-equivariant convolutions offer a richer representation capability by better capturing geometric and structural information. Our neural network integrates an attention mechanism that leverages the signed distance function (SDF) to encode geometric details and an indicator matrix to incorporate boundary conditions. The model predicts velocity and pressure fields as outputs. We conducted experiments specifically targeting non-uniform steady laminar flows, and the results show a 16.1% reduction in overall error compared to models based on traditional convolutions while maintaining high efficiency. These findings indicate that E(2)-equivariant convolution, coupled with an attention mechanism, significantly improves flow field prediction by focusing on critical information and better representing complex geometries.

On the compilation of the bathymetric data of the bay of Bengal domain in the nodal points of triangular mesh to be compatible for the implementation of finite element method

This study focuses on the compilation of bathymetric data for the Bay of Bengal domain, specifically for the area between 15°N to 23°N latitudes and 85°E to 95°E longitudes, to ensure compatibility with the Finite Element Method (FEM). A high-resolution color map of the region was generated using ArcGIS software, which served as the basis for discretizing the domain into a triangular mesh. Bathymetric data for the Bay of Bengal, including the Meghna River, was then compiled using a combination of recent data from the Bangladesh Inland Water Transport Authority (BIWTA) and generated data, which were interpolated using a two-way cubic spline interpolation method. The Modified Inverse Distance Weighted Interpolation (MIDWI) method was employed to map this bathymetric data to the nodal points of the triangular mesh, ensuring accurate representation of the seafloor’s varying depths. This work is essential for developing a reliable storm surge prediction model for the Bay of Bengal using FEM, as it provides the necessary geometric and bathymetric details required for precise numerical modeling.

Machine learning and numerical investigation on drag coefficient of arbitrary polygonal particles

AbstractThe drag coefficient, as the most important parameter that characterizes particle dynamics in flows, has been the focus of a large number of investigations. Although good predictability is achieved for simple shapes, it is still challenging to accurately predict drag coefficient of complex‐shaped particles even under moderate Reynolds number (Re). The problem is that the small‐scale shape details of particles can still have considerable impact on the drag coefficient, but these geometrical details cannot be described by single shape factor. To address this challenge, we leverage modern deep‐learning method's ability for pattern recognition, take multiple shape factors as input to better characterize particle‐shape details, and use the drag coefficient as output. To obtain a high‐precision data set, the discrete element method coupled with an improved velocity interpolation scheme of the lattice Boltzmann method is used to simulate and analyze the sedimentation dynamics of polygonal particles. Four different machine‐learning models for predicting the drag coefficient are developed and compared. The results show that our model can well predict the drag coefficient with an average error of less than 5% for particles. These findings suggest that data‐driven models can be an attractive option for the drag‐coefficient prediction for particles with complex shapes.

Automatic high-detailed building reconstruction workflow for urban microscale simulations

Reconstructing urban scenarios for computational fluid dynamics simulations typically requires significant manual effort, especially when higher geometrical details are required. To address this issue, we present a workflow to automatically reconstruct buildings in three levels of detail (LoDs): LoD1.2, LoD1.3, and LoD2.2, tailored to urban microscale simulations. The workflow uses a combination of building footprints and a point cloud to segment roof planes, create partitions, optimise planes, and finally assemble roof planes into 3D building models. Reconstructed buildings are seamlessly integrated into the terrain together with different surface layers such as water, low vegetation, and paved surfaces. Apart from three general LoDs, building footprints can be simplified as a part of the 2D generalisation; additionally, smaller surfaces such as chimneys and ventilation shafts can be removed using a graph-cut optimisation. The integrated geometry validator can report on validity of building models, such as watertightness, manifoldness, or occurrences of self-intersections. In the case of invalid geometries, we can generate an approximation: geometry repair the with alpha wrapping algorithm, or reconstruction in lower LoD. We tested our implementation on two different real-world datasets — one in The Netherlands, and another one in the USA. The results showed that 95% (Dutch dataset) and 90% (US dataset) buildings were valid according to the ISO 19107 standard. Generated grids showed satisfactory quality as we observed monotonous convergence in simulations with grid convergence indices up to 3.8% for pressure and velocity variables. These results indicate that the workflow is suitable for typical urban microscale simulations.

Digital toy design: A doll head modeling method based on model matching and texture generation

With the development of technology and the improvement of living standards, consumer demand for toy products has also changed. More people are showing strong interest and demand for digital toy products. However, in the current digital toy design process, extracting the hairstyle features of the doll’s head is still a challenge. Therefore, this study extracts the two-dimensional contour of the target hairstyle and matches it with the template hairstyle in the database. Then, combining hair texture information and hairstyle structural features, fine geometric texture details are generated on the hairstyle mesh surface. Finally, a doll head modeling method based on model matching and texture generation is proposed. The results showed that the hairstyle of the Generative model was almost the same as the real hairstyle. Compared with the modeling methods based on interactive genetic algorithm and digital image, the average F1 value of this method was 0.95, and the mean absolute error was the smallest. The accuracy of the target model modeling was 95.4%, and the area enclosed by the receiver operating characteristic curve and coordinate axis was 0.965. In summary, the doll head modeling method based on model matching and texture generation proposed in this study can generate high-precision and realistic hairstyle models corresponding to the hairstyle. The overall shape and local geometric details of the hairstyle can meet the needs of 3D printing, providing certain reference significance for hairstyle reconstruction.

Guldborgsund Arson House Fire Experiment and Numerical Investigation

AbstractThis paper describes the Guldborgsund arson house fire experiment performed in Denmark and the subsequent numerical investigation. Gas temperatures were measured with four thermocouple trees, and smoke detector activation times were recorded in all rooms. A two-step approach was used to perform the numerical modelling for reproduction of the fire scene. The measured temperatures in the room of fire origin were used as an input for back calculating the Heat Release Rate (HRR) with the two-zone model Argos. As a next step, this HRR was used in the Fire Dynamic Simulator (FDS) to predict the temperatures and the smoke detectors’ activation times in other rooms. The FDS model was partly build using output files from the laser scanning. A sensitivity analysis is presented, where the effect of nine input parameters was investigated, including HRR, the material properties, the height of the fuel bed, the fire area, level of geometrical detail of the first item ignited etc. This study showed that the measured soot deposition heights on the walls differed from the heights of measured sharp temperature gradients used to indicate the hot smoke layer. The numerical simulations resulted in less than 50% error for most of the temperature measurement points during the fuel-controlled stage of the fire and results were the most sensitive to the input HRR. Material properties in FDS had a significant influence on the computed upper-layer gas temperatures at late stages of the fire.

Geometric-aware RGB-D representation learning for hand–object reconstruction

Reconstructing hand–object interaction from single images, crucial for interactive applications, is challenging due to the diversity of hand–object poses and shapes. Depth maps effectively complement RGB data in understanding these interactions geometrically within challenging scenes. However, most existing methods do not fully utilize the potential benefits of RGB-D information fused at different feature levels for reconstruction, limiting their capability to capture the geometric details of hand–object interaction. To address this, we propose an implicit geometric-aware RGB-D representation learning approach using adaptive bidirectional RGB-D feature fusion (ABF) and geometric Fourier feature encoding (GFFE). This method innovatively leverages the hierarchical and complementary high-level features of RGB-D information to enhance the neural implicit representations of hand–object interaction during the feature extraction and encoding stages of RGB-D data. Initially, a two-stream RGB-point cloud encoder, combining CNN and Transformer architectures, extracts appearance and geometric information from RGB and point cloud data. Subsequently, ABF fuses this information, generating dense RGB-D features by leveraging the complementary of appearance and geometric features along with the varying sensitivities of different layers. Finally, GFFE introduces frequency domain information to capture both high-frequency and low-frequency features of objects equally to precisely capture the geometric details of hand–object interaction. Experiments conducted on the real-world DexYCB and the synthetic ObMan benchmarks demonstrate that our approach significantly outperforms existing approaches.

Neural-IMLS: Self-Supervised Implicit Moving Least-Squares Network for Surface Reconstruction.

Surface reconstruction is a challenging task when input point clouds, especially real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual representation of the underlying surface, we introduce Neural-IMLS, a novel approach that directly learns a noise-resistant signed distance function (SDF) from unoriented raw point clouds in a self-supervised manner. In particular, IMLS regularizes MLP by providing estimated SDFs near the surface and helps enhance its ability to represent geometric details and sharp features, while MLP regularizes IMLS by providing estimated normals. We prove that at convergence, our neural network produces a faithful SDF whose zero-level set approximates the underlying surface due to the mutual learning mechanism between the MLP and the IMLS. Extensive experiments on various benchmarks, including synthetic and real scans, show that Neural-IMLS can reconstruct faithful shapes even with noise and missing parts. The source code can be found at https://github.com/bearprin/Neural-IMLS.

SketchMetaFace: A Learning-Based Sketching Interface for High-Fidelity 3D Character Face Modeling.

Modeling 3D avatars benefits various application scenarios such as AR/VR, gaming, and filming. Character faces contribute significant diversity and vividity as a vital component of avatars. However, building 3D character face models usually requires a heavy workload with commercial tools, even for experienced artists. Various existing sketch-based tools fail to support amateurs in modeling diverse facial shapes and rich geometric details. In this article, we present SketchMetaFace - a sketching system targeting amateur users to model high-fidelity 3D faces in minutes. We carefully design both the user interface and the underlying algorithm. First, curvature-aware strokes are adopted to better support the controllability of carving facial details. Second, considering the key problem of mapping a 2D sketch map to a 3D model, we develop a novel learning-based method termed "Implicit and Depth Guided Mesh Modeling" (IDGMM). It fuses the advantages of mesh, implicit, and depth representations to achieve high-quality results with high efficiency. In addition, to further support usability, we present a coarse-to-fine 2D sketching interface design and a data-driven stroke suggestion tool. User studies demonstrate the superiority of our system over existing modeling tools in terms of the ease to use and visual quality of results. Experimental analyses also show that IDGMM reaches a better trade-off between accuracy and efficiency.

PCDNF: Revisiting Learning-Based Point Cloud Denoising via Joint Normal Filtering.

Point cloud denoising is a fundamental and challenging problem in geometry processing. Existing methods typically involve direct denoising of noisy input or filtering raw normals followed by point position updates. Recognizing the crucial relationship between point cloud denoising and normal filtering, we re-examine this problem from a multitask perspective and propose an end-to-end network called PCDNF for joint normal filtering-based point cloud denoising. We introduce an auxiliary normal filtering task to enhance the network's ability to remove noise while preserving geometric features more accurately. Our network incorporates two novel modules. First, we design a shape-aware selector to improve noise removal performance by constructing latent tangent space representations for specific points, taking into account learned point and normal features as well as geometric priors. Second, we develop a feature refinement module to fuse point and normal features, capitalizing on the strengths of point features in describing geometric details and normal features in representing geometric structures, such as sharp edges and corners. This combination overcomes the limitations of each feature type and better recovers geometric information. Extensive evaluations, comparisons, and ablation studies demonstrate that the proposed method outperforms state-of-the-art approaches in both point cloud denoising and normal filtering.

Pose-Driven Compression for Dynamic 3D Human via Human Prior Models.

To cost-effectively transmit high-quality dynamic 3D human images in immersive multimedia applications, efficient data compression is crucial. Unlike existing methods that focus on reducing signal-level reconstruction errors, we propose the first dynamic 3D human compression framework based on human priors. The layered coding architecture significantly enhances the perceptual quality while also supporting a variety of downstream tasks, including visual analysis and content editing. Specifically, a high-fidelity pose-driven Avatar is generated from the original frames as the basic structure layer to implicitly represent the human shape. Then, human movements between frames are parameterized via a commonly-used human prior model, i.e., the Skinned Multi-Person Linear Model (SMPL), to form the motion layer and drive the Avatar. Furthermore, the normals are also introduced as an enhancement layer to preserve fine-grained geometric details. Finally, the Avatar, SMPL parameters, and normal maps are efficiently compressed into layered semantic bitstreams. Extensive qualitative and quantitative experiments show that the proposed framework remarkably outperforms other state-of-the-art 3D codecs in terms of subjective quality with only a few bits. More notably, as the size or frame number of the 3D human sequence increases, the superiority of our framework in perceptual quality becomes more significant while saving more bitrates.

CarvingNet: Point cloud completion by stepwise refining multi-resolution features

In the field of 3D vision, 3D point cloud completion is a crucial task in many practical applications. Current methods use Transformer's Encoder-Decoder framework to predict the missing part of the point cloud features at low resolution, which does not fully utilize the feature information at multiple resolutions and can result in the loss of the object's geometric details. In this paper, we present a novel point cloud completion method, CarvingNet, which, to the best of our knowledge, is the first to apply the U-Net architecture to the point cloud completion task by operating directly on unordered point cloud features at multiple resolutions. Firstly, we gradually expand the receptive field and use cross-attention to purify the features of the missing part of the point cloud at each resolution and to generate the contour features of the complete point cloud at the last obtained resolution. Then, we gradually reduce the receptive field and use cross-attention to refine the features of the complete point cloud at each resolution and to generate the features of the complete point cloud with rich details at the last obtained resolution. To obtain point cloud features at different resolutions, we specifically design the up-sampling module and down-sampling module for disordered point cloud features. Furthermore, we improve the FoldingNet network to make it more suitable for generating high-quality dense point clouds. The experimental results demonstrate that our proposed CarvingNet achieves the performance of existing state-of-the-art methods on the ShapeNet-55, ShapeNet-34, and KITTI benchmarks.

Walkin’ Robin: Walk on Stars with Robin Boundary Conditions

Numerous scientific and engineering applications require solutions to boundary value problems (BVPs) involving elliptic partial differential equations, such as the Laplace or Poisson equations, on geometrically intricate domains. We develop a Monte Carlo method for solving such BVPs with arbitrary first-order linear boundary conditions---Dirichlet, Neumann, and Robin. Our method directly generalizes the walk on stars (WoSt) algorithm, which previously tackled only the first two types of boundary conditions, with a few simple modifications. Unlike conventional numerical methods, WoSt does not need finite element meshing or global solves. Similar to Monte Carlo rendering, it instead computes pointwise solution estimates by simulating random walks along star-shaped regions inside the BVP domain, using efficient ray-intersection and distance queries. To ensure WoSt produces bounded-variance estimates in the presence of Robin boundary conditions, we show that it is sufficient to modify how WoSt selects the size of these star-shaped regions. Our generalized WoSt algorithm reduces estimation error by orders of magnitude relative to alternative grid-free methods such as the walk on boundary algorithm. We also develop bidirectional and boundary value caching strategies to further reduce estimation error. Our algorithm is trivial to parallelize, scales sublinearly with increasing geometric detail, and enables progressive and view-dependent evaluation.

Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis

While surface-based view synthesis algorithms are appealing due to their low computational requirements, they often struggle to reproduce thin structures. In contrast, more expensive methods that model the scene's geometry as a volumetric density field (e.g. NeRF) excel at reconstructing fine geometric detail. However, density fields often represent geometry in a "fuzzy" manner, which hinders exact localization of the surface. In this work, we modify density fields to encourage them to converge towards surfaces, without compromising their ability to reconstruct thin structures. First, we employ a discrete opacity grid representation instead of a continuous density field, which allows opacity values to discontinuously transition from zero to one at the surface. Second, we anti-alias by casting multiple rays per pixel, which allows occlusion boundaries and subpixel structures to be modelled without using semi-transparent voxels. Third, we minimize the binary entropy of the opacity values, which facilitates the extraction of surface geometry by encouraging opacity values to binarize towards the end of training. Lastly, we develop a fusion-based meshing strategy followed by mesh simplification and appearance model fitting. The compact meshes produced by our model can be rendered in real-time on mobile devices and achieve significantly higher view synthesis quality compared to existing mesh-based approaches. Our interactive webdemo is available at https://binary-opacity-grid.github.io.

A Coupled CFD-DEM Approach to Model Reactive Granular Beds

Packed and moving bed reactors are widely used in process industry to process granular material. Shaft furnaces are one example of this. Due to their counterflow layout, a high thermal efficiency can be achieved. Shaft furnaces have a wide range of length and time scales that makes them challenging to model. Geometric details, like injection nozzles, are smaller than the particle size, which need a computationally highly expensive resolved Discrete Element Method (DEM) approach. To overcome this problem, a computing technique called Volume Fraction Smoother (VFS) was developed. Since the time scales in those systems reach from milliseconds for the particle collisions to hours of process time, the process time scale must be separated to model a quasi-steady state with reasonable computing time. For this, the Time Scale Splitting Method (TSSM) was introduced. This method was also adapted to model the self-heating behaviour of direct reduced iron (DRI).

The role of machine learning for insight into the material behavior of lattices: A surrogate model based on data from finite element simulation

In recent years, lattice structures have gained extensive attention due to their unique properties and great potential in various fields. Their effective material properties can be obtained by several means, e.g., numerical homogenization methods, finite element (FE) simulations, and experiments. Numerical homogenization methods involve certain assumptions, and thus, their applications are limited to those lattice structures satisfying all assumptions. On the contrary, although the FE simulations and experiments can be performed for all lattice structures, they are more time-consuming and tedious than the numerical homogenization methods, especially for lattice structures with complex geometry. In this study, a surrogate model is presented to address all the drawbacks mentioned above. More precisely, the effective elastic modulus of two-dimensional lattice structures with triangular unit cells is predicted by a surrogate model trained with the random forest algorithm. The dataset is generated from FE simulations. Several geometric details along with the elastic modulus of the parent material are selected as input features. These input features are varied to cover a wide range of lattice structures encountered in engineering applications. The correlation between input features is investigated to test their independence. Furthermore, the contribution of each input feature to the prediction of the surrogate models is also thoroughly examined. The accuracy of the proposed surrogate model is evaluated through comparisons with FE simulations, numerical homogenization methods, and experiments for untrained datasets.

Numerical Simulations of Scalar Transport on Rough Surfaces

Numerical simulations provide unfettered access to details of the flow where experimental measurements are difficult to obtain. This paper summarises the progress achieved in the study of passive scalars in flows over rough surfaces thanks to recent numerical simulations. Townsend’s similarity applies to various scalar statistics, implying the differences due to roughness are limited to the roughness sublayer (RSL). The scalar field exhibits a diffusive sublayer that increasingly conforms to the roughness surface as ks+ or Pr increase. The scalar wall flux is enhanced on the windward slopes of the roughness, where the analogy between momentum and scalar holds well; the momentum and scalar fields, however, have very different behaviours downwind of the roughness elements, due to recirculation, which reduces the scalar wall flux. Roughness causes breakdown of the Reynolds analogy: any increase in St is accompanied by a larger increase in cf. A flattening trend for the scalar roughness function, ΔΘ+, is observed as ks+ increases, suggesting the possibility of a scalar fully rough regime, different from the velocity one. The form-induced (FI) production of scalar fluctuations becomes dominant inside the RSL and is significantly different from the FI production of turbulent kinetic energy, resulting in notable differences between the scalar and velocity fluctuations. Several key questions remain open, in particular regarding the existence of a fully rough scalar regime and its characteristics. With the increase in Re and Pr, various quantities such as scalar roughness function, the dispersive fluxes, FI wall flux, etc., appear to trend towards saturation. However, the limited range of Re and Pr achieved by numerical simulations only allows us to speculate regarding such asymptotic behaviour. Beyond extending the range of Re and Pr, systematic coverage of different roughness types and topologies is needed, as the scalar appears to remain sensitive to the geometrical details.

On G2 approximation of planar algebraic curves under certified error control by quintic Pythagorean-hodograph splines

The Pythagorean-Hodograph curve (PH curve) is a valuable curve type extensively utilized in computer-aided geometric design and manufacturing. This paper presents an approach to approximate a planar algebraic curve within a bounding box by employing piecewise quintic PH spline curves, while maintaining G2 smoothness of the approximating curve and preserving second-order geometric details at singularities. The bounding box encompasses all x-coordinates of key topological points, ensuring accurate representation. The paper explores the analysis of the G2 interpolation problem for quintic PH curves with invariant convexity, transforming the quest for interpolation solutions into identifying positive roots within a set of algebraic equations. Through infinitesimal order analysis, it is established that a solution necessarily exists following adequate subdivision, laying the groundwork for practical application. Finally, the paper introduces a novel algorithm that integrates prior research to construct the approximating curve while maintaining control over the desired error levels.

Modality adaptation via feature difference learning for depth human parsing

In the field of human parsing, depth data offers unique advantages over RGB data due to its illumination invariance and geometric detail, which motivates us to explore human parsing with only depth input. However, depth data is challenging to collect at scale due to the specialized equipment required. In contrast, RGB data is readily available in large quantities, presenting an opportunity to enhance depth-only parsing models with semantic knowledge learned from RGB data. However, fully finetuning the RGB-pretrained encoder leads to high training costs and inflexible domain generalization, while keeping the encoder frozen suffers from a large RGB-depth modality gap and restricts the parsing performance. To alleviate the limitations of these naive approaches, we introduce a Modality Adaptation pipeline via Feature Difference Learning (MAFDL) which leverages the RGB knowledge to facilitate depth human parsing. A Difference-Guided Depth Adapter (DGDA) is proposed within MAFDL to learn the feature differences between RGB and depth modalities, adapting depth features into RGB feature space to bridge the modality gap. Furthermore, we also design a Feature Alignment Constraint (FAC) to impose explicit alignment supervision at pixel and batch levels, making the modality adaptation more comprehensive. Extensive experiments on the NTURGBD-Parsing-4K dataset show that our method surpasses previous state-of-the-art approaches.