A Delaunay-based region-growing approach to surface reconstruction from unorganized points

This paper presents a Delaunay-based region-growing (DBRG) surface reconstruction algorithm that holds the advantages of both Delaunay-based and region-growing approaches. The proposed DBRG algorithm takes a set of unorganized sample points from the boundary surface of a three-dimensional object and produces an orientable manifold triangulated model with a correct geometry and topology that is faithful to the original object. Compared with the traditional Delaunay-based approach, the DBRG algorithm requires only one-pass Delaunay computation and needs no Voronoi information because it improves the non-trivial triangle extraction by using a region-growing technique. Compared with the traditional region-growing methods, the proposed DBRG algorithm makes the surface reconstruction more systematic and robust because it inherits the structural characteristics of the Delaunay triangulation, which nicely complements the absence of geometric information in a set of unorganized points. The proposed DBRG algorithm is capable of handling surfaces with complex topology, boundaries, and even non-uniform sample points. Experimental results show that it is highly efficient compared with other existing algorithms.     

Optimized triangle mesh reconstruction from unstructured points

A variety of approaches have been proposed for polygon mesh reconstruction from a set of unstructured sample points. Suffering from severe aliases at sharp features and having a large number of unnecessary faces, most resulting meshes need to be optimized using input sample points in a postprocess. In this paper, we propose a fast algorithm to reconstruct high-quality meshes from sample data. The core of our proposed algorithm is a new mesh evaluation criterion which takes full advantage of the relation between the sample points and the reconstructed mesh. Based on our proposed evaluation criterion, we develop necessary operations to efficiently incorporate the functions of data preprocessing, isosurface polygonization, mesh optimization and mesh simplification into one simple algorithm, which can generate high-quality meshes from unstructured point clouds with time and space efficiency. Published online: 28 January 2003 Correspondence to: Y.-J. Liu     

A mesh optimization algorithm based on neural networks

We have developed a mesh simplification method called GNG3D which is able to produce high quality approximations of polygonal models. This method consists of two distinct phases: an optimization phase and a reconstruction phase. The optimization phase is developed by applying an extension algorithm of the growing neural gas model, which constitutes an unsupervised incremental clustering algorithm. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces obtaining the optimized mesh as a result. We study the model theoretically, analyzing its main components, and experimentally, using for this purpose some 3D objects with different topologies. To evaluate the quality of approximations produced by the method proposed in this paper, three existing error measurements are used. The ability of the model to establish the number of vertices of the final simplified mesh is demonstrated in the examples.     

Automatic mesh generation and transformation for topology optimization methods

This paper presents automatic tools aimed at the generation and adaptation of unstructured tetrahedral meshes in the context of composite or heterogeneous geometry. These tools are primarily intended for applications in the domain of topology optimization methods but the approach introduced presents great potential in a wider context. Indeed, various fields of application can be foreseen for which meshing heterogeneous geometry is required, such as finite element simulations (in the case of heterogeneous materials and assemblies, for example), animation and visualization (medical imaging, for example). Using B-Rep concepts as well as specific adaptations of advancing front mesh generation algorithms, the mesh generation approach presented guarantees, in a simple and natural way, mesh continuity and conformity across interior boundaries when trying to mesh a composite domain. When applied in the context of topology optimization methods, this approach guarantees that design and non-design sub-domains are meshed so that finite elements are tagged as design and non-design elements and so that continuity and conformity are guaranteed at the interface between design and non-design sub-domains. The paper also presents how mesh transformation and mesh smoothing tools can be successfully used when trying to derive a functional shape from raw topology optimization results.     

A general framework for analysis and comparison of surface mesh optimization techniques

Many different algorithms for surface mesh optimization (including smoothing, remeshing, simplification and subdivision), each giving different results, have recently been proposed. All these approaches affect vertices of the mesh. Vertex coordinates are modified, new vertices are added and some original ones are removed, with the result that the shape of the original surface is changed. The important question is how to evaluate the differences in shape between the input and output models. In this paper, we present a novel and versatile framework for analysis of various mesh optimization algorithms in terms of shape preservation. We depart from the usual strategy by measuring the changes in the approximated smooth surfaces rather than in the corresponding meshes. The proposed framework consists of two error metrics: normal-based and physically based. We demonstrate that our metrics allow more subtle changes in shape to be captured than is possible with some commonly used measures. As an example, the proposed tool is used to compare three different techniques, reflecting basic ideas on how to solve the surface mesh improvement problem.     

Continuous global optimization in surface reconstruction from an oriented point cloud

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based data-fit measures and a regularization term. A continuous convex relaxation scheme assures the global minima of the geometric surface functional. The reconstructed surface is implicitly represented by the binary segmentation of vertices of a 3D uniform grid and a triangulated surface can be obtained by extracting an appropriate isosurface. Unlike the discrete graph-cut solution, the continuous global optimization entails advantages like memory requirements, reduction of metrication errors for geometric quantities, and allowing globally optimal surface reconstruction at higher grid resolutions. We demonstrate the performance of the proposed method on several oriented point clouds captured by laser scanners. Experimental results confirm that our approach is robust to noise, large holes and non-uniform sampling density under the condition of very coarse orientation information.     

Automatic reconstruction of B-spline surfaces with constrained boundaries

The aim of this study is to present an automatic surface reconstruction method that can take practical restrictions on scanned points into consideration and efficiently and reliably output a group of G¹ surfaces. The proposed method is mainly composed of three phases: quadrangle frame generation, point and curve networks planning, and surface patches reconstruction. In the first phase, the original triangle mesh is reduced and converted into a quadrangle mesh, the edges of which serve as the frame of the surfaces. In the second phase, the boundary data of the surfaces are prepared. These include a network of serial points, frame curves and surface normals which are also expressed as curves. In the final phase, surface initialization, harmonization mapping and surface warping are presented to yield the desired surfaces. The main advantage of the proposed method is that it can relax the pre-processing of a scanned triangle mesh, and hence, increase the efficiency and quality of the surface reconstruction. Several examples of various types of air bags are presented to demonstrate the feasibility of the proposed method.     

Genetic algorithms in mesh optimization for visualization and finite element models

This paper investigates the use of a genetic algorithm (GA) to perform the large-scale triangular mesh optimization process. This optimization process consists of a combination of mesh reduction and mesh smoothing that will not only improve the speed for the computation of a 3D graphical or finite element model, but also improve the quality of its mesh. The GA is developed and implemented to replace the original mesh with a re-triangulation process. The GA features optimized initial population, constrained crossover operator, constrained mutation operator and multi-objective fitness evaluation function. While retaining features is important to both visualization models and finite element models, this algorithm also optimizes the shape of the triangular elements, improves the smoothness of the mesh and performs mesh reduction based on the needs of the user.     

On topology optimization of linear and nonlinear plate problems

In this paper we propose a new restriction method based on employing C ⁰-continuous fields of density defined on a set of meshes different from the one used for the finite element analysis. The optimization procedure starts with using a coarse density-mesh compared to the finite element one. Once the convergence is obtained in the optimization steps, a finer density-mesh is nominated for the further steps. Linear and nonlinear plate behaviors are considered and formulated by Kirchhoff or Mindlin–Reissner hypothesis. Comparison is made with element/nodal based approaches using filter. The results show excellent and robust performance of the proposed method.     

三维重建系统下的特征点处理与位姿恢复优化算法

基于SIFT算法原理,构建了一个全新的算法框架,使用FCN（fully convolutional networks,全卷积神经网络）和BP（back propagation,反向传播）神经网络,综合考虑图像主目标的语义分割、图像灰度共生矩阵等方面的影响,实现了自适应的特征点检测范围、数量调整,并在特征点匹配阶段利用相机位姿偏移稳定性剔除误匹配,同时采用基于图优化的方法对位姿恢复结果进行非线性优化,得到了更加精确的相机位姿。最后与现有主流算法进行分析比对,实验结果验证了该算法的有效性,提高了特征点检测的场景自适应程度与特征点匹配、位姿恢复的精度,实现了更加高效的三维重建。     

Surface and normal ensembles for surface reconstruction

The majority of the existing techniques for surface reconstruction and the closely related problem of normal reconstruction are deterministic. Their main advantages are the speed and, given a reasonably good initial input, the high quality of the reconstructed surfaces. Nevertheless, their deterministic nature may hinder them from effectively handling incomplete data with noise and outliers. An ensemble is a statistical technique which can improve the performance of deterministic algorithms by putting them into a statistics based probabilistic setting. In this paper, we study the suitability of ensembles in normal and surface reconstruction. We experimented with a widely used normal reconstruction technique [Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W. Surface reconstruction from unorganized points. Computer Graphics 1992;71-8] and Multi-level Partitions of Unity implicits for surface reconstruction [Ohtake Y, Belyaev A, Alexa M, Turk G, Seidel H-P. Multi-level partition of unity implicits. ACM Transactions on Graphics 2003;22(3):463-70], showing that normal and surface ensembles can successfully be combined to handle noisy point sets.     

A crossing sensitivity filter for structural topology optimization with chamfering,rounding, and checkerboard-free patterns

Chamfering and rounding are the most common features of structures and mechanisms. Introducing these features is another way to make material usage more efficient by lowering or avoiding stress con centrations and making the structure even stronger. In this brief note, a new crossing sensitivity filter is proposed for structural topology optimization with chamfering and rounding. This method also ensures the final optimal solution without checkerboard patterns or mesh-dependency. It can also partially prevent one-node hinges. Numerical examples that include both design of stiffest/strongest structures and synthesis of compliant mechanisms are provided.     

Image-consistent patches from unstructured points with J-linkage

Going from unstructured cloud of points to surfaces is a challenging problem. However, as points are produced by a structure-and-motion pipeline, image-consistency is a powerful clue that comes to the rescue. In this paper we present a method for extracting planar patches from an unstructured cloud of points, based on the detection of image-consistent planar patches with J-linkage, a robust algorithm for multiple model fitting. The method integrates several constraints inside J-linkage, optimizes the position of the points with regard to image-consistency and deploys a hierarchical processing scheme that decreases the computational load. With respect to previous work this approach has the advantage of starting from sparse data. Several results show the effectiveness of the proposed approach.     

基于多任务学习CNN辅助Transformer的手部mesh重建

针对当前手势姿态估计算法对于未充分利用2D信息辅助3D手部Mesh重建问题,首次在手部Mask、2D热力图的基础上提出引入RGB图像的HOG特征图,通过多任务学习CNN的框架对2D信息进行特征提取,并针对手的拓扑结构进行信息融合增强。为了解决Transformer encoder中的隐层embeddings维度一致性以及参数过大问题,设计了一种新的 MLP（multi-layer perception）模块嵌入Transformer encoder之间,达到embeddings的数量渐进增加以及其维度渐进减少的目的,从而完成手部mesh精细化的预测。实验结果表明该CNN与Transformer混合的新框架在 FreiHAND 和 RHD 数据集均取得了较好效果。     

Parallelized structural topology optimization and CFD coupling for design of aircraft wing structures

A set of structural optimization tools are presented for topology optimization of aircraft wing structures coupled with Computational Fluid Dynamics (CFD) analyses. The topology optimization tool used for design is the material distribution technique. Because reducing the weight requires numerous calculations, the CFD and structural optimization codes are parallelized and coupled via a code/mesh coupling scheme. In this study, the algorithms used and the results obtained are presented for topology design of a wing cross-section under a given critical aerodynamic loading and two different spar positions to determine the optimum rib topology.     

面向虚拟装配的VRML模型优化重构

对基于Web的虚拟装配中VRML模型优化重构进行了研究.提出了虚拟装配环境中的五层结构信息模型;在此基础上,分析VRML模型的语法结构和语法解析过程,建立了节点重构算法和优化处理算法;实现了VRML模型组织结构和信息描述的优化重构,很好地满足了虚拟装配快速设计与分析的需求.开发了基于Web的交互式虚拟装配原型系统,验证了模型优化重构算法的可行性.     

单幅图像三维表面重建的算法研究与实现

以单幅二维图像为研究对象,应用SFS的基本理论,首先对二维图像进行了光照的倾角和偏角的估计,在光源坐标系下计算出物体每一点的表面梯度;之后,旋转坐标系,在观察坐标系下得到物体的表面梯度;最后采用三点辛普森公式求出物体表面的高度。整个算法流程简单,求解层次分明,重构满意度较高。     

Deformable model with a complexity independent from image resolution

We present a parametric deformable model which recovers image components with a complexity independent from the resolution of input images. The proposed model also automatically changes its topology and remains fully compatible with the general framework of deformable models. More precisely, the image space is equipped with a metric that expands salient image details according to their strength and their curvature. During the whole evolution of the model, the sampling of the contour is kept regular with respect to this metric. By this way, the vertex density is reduced along most parts of the curve while a high quality of shape representation is preserved. The complexity of the deformable model is thus improved and is no longer influenced by feature-preserving changes in the resolution of input images. Building the metric requires a prior estimation of contour curvature. It is obtained using a robust estimator which investigates the local variations in the orientation of image gradient. Experimental results on both computer generated and biomedical images are presented to illustrate the advantages of our approach.     

Capacitated clustering problem in computational biology: Combinatorial and statistical approach for sibling reconstruction

The capacitated clustering problem (CCP) has been studied in a wide range of applications. In this study, we investigate a challenging CCP in computational biology, namely, sibling reconstruction problem (SRP). The goal of SRP is to establish the sibling relationship (i.e., groups of siblings) of a population from genetic data. The SRP has gained more and more interests from computational biologists over the past decade as it is an important and necessary keystone for studies in genetic and population biology. We propose a large-scale mixed-integer formulation of the CCP for SRP that is based on both combinatorial and statistical genetic concepts. The objective is not only to find the minimum number of sibling groups, but also to maximize the degree of similarity of individuals in the same sibling groups while each sibling group is subject to genetic constraints derived from Mendel's laws. We develop a new randomized greedy optimization algorithm to effectively and efficiently solve this SRP. The algorithm consists of two key phases: construction and enhancement. In the construction phase, a greedy approach with randomized perturbation is applied to construct multiple sibling groups iteratively. In the enhancement phase, a two-stage local search with a memory function is used to improve the solution quality with respect to the similarity measure. We demonstrate the effectiveness of the proposed algorithm using real biological data sets and compare it with state-of-the-art approaches in the literature. We also test it on larger simulated data sets. The experimental results show that the proposed algorithm provide the best reconstruction solutions.