A mesh generation method for geometric features based on knowledge-based engineering

The reconstruction of 3D shapes from a single view has been a longstanding challenge. Previous methods have primarily focused on learning either geometric features that depict overall shape contours but are insufficient for occluded regions, local features that capture details but cannot represent the complete structure, or structural features that encode part relationships but require predefined semantics. However, the fusion of geometric, local, and structural features has been lacking, leading to inaccurate reconstruction of shapes with occlusions or novel compositions. To address this issue, we propose a two-stage approach for achieving 3D shape reconstruction. In the first stage, we encode the hierarchical structure features of the 3D shape using an encoder-decoder network. In the second stage, we enhance the hierarchical structure features by fusing them with global and point features and feed the enhanced features into a signed distance function (SDF) prediction network to obtain rough SDF values. Using the camera pose, we project arbitrary 3D points in space onto different depth feature maps of the CNN and obtain their corresponding positions. Then, we concatenate the features of these corresponding positions together to form local features. These local features are also fed into the SDF prediction network to obtain fine-grained SDF values. By fusing the two sets of SDF values, we improve the accuracy of the model and enable it to reconstruct other object types with higher quality. Comparative experiments demonstrate that the proposed method outperforms state-of-the-art approaches in terms of accuracy.

Optical Character Recognition (OCR) research includes computer vision, artificial intelligence, and pattern recognition. Character recognition has garnered a lot of attention in the last decade due to its broad variety of uses and applications, including multiple-choice test data, business documents (e.g., ID cards, bank notes, passports, etc.), and automatic number plate recognition. This paper introduces an automatic recognition system for printed numerals. The automatic reading system is based on extracting local statistical and geometrical features from the text image. Those features are represented by eight vectors extracted from each digit. Two of these features are local statistical (A, A th), and six are local geometrical (P1, P2, P3, P4, P5, and P6). Thus, the database created consists of 1120 statistical and geometrical features. For the purpose of recognition, the features of the test image are compared with the features of all the images saved in the database depending on the value of the Minimum Distance (MD). All digits (0–9) were identified with 100% accuracy. The average computational time required to recognize a numeral at any font size is 0.06879 seconds.

As 3D acquisition technology develops and 3D sensors become increasingly affordable, large quantities of 3D point cloud data are emerging. How to effectively learn and extract the geometric features from these point clouds has become an urgent problem to be solved. The point cloud geometric information is hidden in disordered, unstructured points, making point cloud analysis a very challenging problem. To address this problem, we propose a novel network framework, called Tree Graph Network (TGNet), which can sample, group, and aggregate local geometric features. Specifically, we construct a Tree Graph by explicit rules, which consists of curves extending in all directions in point cloud feature space, and then aggregate the features of the graph through a cross-attention mechanism. In this way, we incorporate more point cloud geometric structure information into the representation of local geometric features, which makes our network perform better. Our model performs well on several basic point clouds processing tasks such as classification, segmentation, and normal estimation, demonstrating the effectiveness and superiority of our network. Furthermore, we provide ablation experiments and visualizations to better understand our network.

Automatic object detection and tracking has been widely applied in the video surveillance systems for homeland security and data fusion in the remote sensing and airborne imagery. The typical applications include human motion analysis and the vehicle detection. Here we implement object detection and tracking under shape graphs of interesting objects integrating local contextual information (corner/point features, etc) of the objects. On the top layer, shapes/sketches provide a discrimination measure to describe the global status of the interesting objects. This kind of information is very useful to improve the object tracking performance for occlusion. The shape can be modeled as a graph or hyper graph through its local geometric features. On the bottom layer, local geometric features are used to capture local properties of objects and perform correspondence estimation of high-level shapes. The local features provide a way to conquer inaccurate object segmentation and extraction. The experiments were implemented on human face tracking and vehicle detection and tracking.

For the existing 3D point cloud model classification method PointNet only extracts global feature information, but for the problem of insufficient local feature information extraction, a network that can take into account the combination of global features and local features is proposed, so as to realize 3D point Classification of cloud models. This paper proposes a classification network based on local location information. First, the point cloud model is sampled in multiple groups to obtain the center point of each group of samples, and then the radius is set to obtain its spherical neighborhood, and the points in the neighborhood and their center points are used as local location features. In information fusion, the acquired local information features are used as high-dimensional features of the neighborhood space through feature mapping. By analogy, multiple sets of sampled local features are integrated to realize the classification of the point cloud model. The experimental results show that the classification network can achieve a classification accuracy of 92.5% on the ModelNet40 data set, which is higher than the current mainstream algorithm.

Coarse pose registration is a crucial step in 6DOF pose estimation. Assuming the objects to be estimated are regular and their 3D models are known, this paper presents local geometric features (LGFs) to estimate the poses of objects in point cloud. Coordinate frames describing the object's pose are defined according to geometric information. Pose estimation are performed by calculating the transformation between the frames in the scene point cloud and the reference model. Two kinds of LGFs are proposed: one is the corner edge feature (CEF) which exploits corner and radiating edges, and the other is the circle normal feature (CNF) which exploits circle center and normal vector of the plane where the circle is located. Included angle sequence of adjacent edges and circle radius, which are invariant to SE (3) transformation, are selected to identify CEF and CNF, respectively. Simulation is performed to verify the feasibility of the proposed features.

Winding number based automatic mesh generation algorithm for hydrogen analysis code GASFLOW-MPI

Purpose Automatic mesh generation is still a challenge problem for combustion fluid dynamics simulations because of the high-quality requirement and complexity of geometries. This paper aims to find an efficient automatic analysis model creation and mesh generation method to save the time for pre-processing in numerical simulations. Design/methodology/approach Based on the previous work, we explore effective model processing and mesh generation methods from practical engineering applications. Considering the automation and high quality requirement, we construct an automatic mesh generation procedure for combustion fluid dynamics problems. Findings The numerical results show that the procedure we proposed in this paper can automatically generate high quality mesh for combustion fluid dynamics simulations. The strategy of fluid model construction is time-saving and with high-precision. The mesh generation method in our procedure is automatic and efficient. Practical implications The procedure proposed in this paper is applicable to the practical engineering application model, such as aircraft simulation, aeroengine simulation and so on. The procedure has been integrated into an numerical simulation software. Originality/value The method proposed in this paper has very practical application value. It can be used in the practical application and saves a lot of manual processing time for numerical stimulation specialists.

This paper presents a new approach to estimate accurate and robust 3D semantic correspondence with the hierarchical neural semantic representation. Our work has three key contributions. First, we design the hierarchical neural semantic representation (HNSR), which consists of a global semantic feature to capture high-level structure and multi-resolution local geometric features to preserve fine details, by carefully harnessing 3D priors from pre-trained 3D generative models. Second, we design a progressive global-to-local matching strategy, which establishes coarse semantic correspondence using the global semantic feature, then iteratively refines it with local geometric features, yielding accurate and semantically-consistent mappings. Third, our framework is training-free and broadly compatible with various pre-trained 3D generative backbones, demonstrating strong generalization across diverse shape categories. Our method also supports various applications, such as shape co-segmentation, keypoint matching, and texture transfer, and generalizes well to structurally diverse shapes, with promising results even in cross-category scenarios. Both qualitative and quantitative evaluations show that our method outperforms previous state-of-the-art techniques.

The present paper is devoted to an in-depth study of ϕ-Ricci symmetric LP-Sasakian manifolds, which represent a significant class of Lorentzian para-Sasakian manifolds with rich geometric structures and distinctive curvature characteristics. The notion of ϕ-Ricci symmetry imposes specific constraints on the Ricci tensor in relation to the structure tensor ϕ, offering deeper insight into the curvature behavior and intrinsic geometry of these manifolds. This investigation aims to explore various fundamental properties of ϕ-Ricci symmetric LP-Sasakian manifolds, examining how these symmetry conditions influence their global and local geometric features. To support and illustrate the theoretical analysis, we construct an explicit example of a three-dimensional ϕ-Ricci symmetric LP-Sasakian manifold. Moreover, we study W1-flat LP-Sasakian manifold.

In industrial environments, steel plate surface inspection plays a crucial role in quality control. However, vibrations during laser scanning can significantly impact measurement accuracy. While traditional vibration compensation methods rely on complex dynamic modeling, they often face challenges in practical implementation and generalization. This paper introduces a novel point cloud vibration compensation algorithm that combines an improved Gaussian–Laplacian filter with adaptive local feature analysis. The key innovations include (1) an FFT-based vibration factor extraction method that effectively identifies vibration trends, (2) an adaptive windowing strategy that automatically adjusts based on local geometric features, and (3) a weighted compensation mechanism that preserves surface details while reducing vibration noise. The algorithm demonstrated significant improvements in signal-to-noise ratio: 15.78% for simulated data, 6.81% for precision standard parts, and 12.24% for actual industrial measurements. Experimental validation confirms the algorithm’s effectiveness across different conditions. This approach achieved a practical, implementable solution for surface inspection in steel plate surface inspection.

On shortened 3D local binary descriptors

In this paper, we present the development and application of a two-dimensional, automatic unstructured mesh generator for shallow water models called Admesh. Starting with only target minimum and maximum element sizes and points defining the boundary and bathymetry/ topography of the domain, the goal of the mesh generator is to automatically produce a high-quality mesh from this minimal set of input. From the geometry provided, properties such as local features, curvature of the boundary, bathymetric/topographic gradients, and approximate flow characteristics can be extracted, which are then used to determine local element sizes. The result is a high-quality mesh, with the correct amount of refinement where it is needed to resolve all the geometry and flow characteristics of the domain. Techniques incorporated include the use of the so-called signed distance function, which is used to determine critical geometric properties, the approximation of piecewise linear coastline data by smooth cubic splines, a so-called mesh function used to determine element sizes and control the size ratio of neighboring elements, and a spring-based force equilibrium approach used to improve the element quality of an initial mesh obtained from a simple Delaunay triangulation. Several meshes of shallow water domains created by the new mesh generator are presented.

MeshONet: A generalizable and efficient operator learning method for structured mesh generation.

Due to the noise accompanied with fault signals, it is challenging to identify the discriminant information and the local geometric feature from the complex fault data for enhancing fault diagnosis accuracy. To address this challenge, this work proposed an anti-noise algorithm based on locally linear embedding integrated with diffusion distance and maximum correntropy criterion (DMLLE). In DMLLE, diffusion distance was adopted instead of the Euclidean distance for neighborhood construction. Meanwhile, the optimal weights were updated to reveal local geometry information based on the loss function of the maximum correntropy criterion. Subsequently, DMLLE is eventually developed to further restrain noise embedding into raw signals and obtain low dimensional features. Furthermore, weighted extreme gradient boosting is used to map the low dimensional features to the types of faults, which easily implements fault pattern recognition. Finally, two synthetic manifold datasets and fault data acquired from the transmit/receive (T/R) module are used to validate the performance of the proposed diagnosis methodology. Compared with the existing methods, the proposed diagnosis methodology generates a smoother flow structure by preserving the local neighborhood of the dataset with noises and realizes a higher accuracy of 94.41% on the T/R module dataset, which outperforms 3%–9% better than other classification models. Therefore, it can be concluded that the proposed diagnosis methodology can effectively extract intrinsic fault features by weakening the influence aroused by noise and achieve superior accuracy in fault diagnosis by addressing the problem of small sample size.