Compression of 2D Vector Fields Under Guaranteed Topology Preservation

In this paper we introduce a new compression technique for 2D vector fields which preserves the complete topology, i.e., the critical points and the connectivity of the separatrices. As the theoretical foundation of the algorithm, we show in a theorem that for local modifications of a vector field, it is possible to decide entirely by a local analysis whether or not the global topology is preserved. This result is applied in a compression algorithm which is based on a repeated local modification of the vector field ‐ namely a repeated edge collapse of the underlying piecewise linear domain. We apply the compression technique to a number of data sets with a complex topology and obtain significantly improved compression ratios in comparison to pre‐existing topology‐preserving techniques.     

Topology Preservation Within Digital Surfaces

Given two connected subsets Y⊂X of the set of the surfels of a connected digital surface, we propose three equivalent ways to express Y being homotopic to X. The first characterization is based on sequential deletion of simple surfels. This characterization enables us to define thinning algorithms within a digital Jordan surface. The second characterization is based on the Euler characteristics of sets of surfels. This characterization enables us, given two connected sets Y⊂X of surfels, to decide whether Y is n-homotopic to X. The third characterization is based on the (digital) fundamental group.     

面向3D打印体积极小的拓扑优化技术

与传统制造所生产的产品相比,3D打印产品的成本仍相对较高.因此,如何能在不牺牲打印物体表面质量的前提下通过模型优化来减少打印材料消耗,对于降低打印成本至关重要.针对这一问题,借鉴传统渐进结构优化方法,结合Von Mises应力计算,给出一种面向3D打印体积极小的拓扑优化算法.该算法通过模型力学计算所得的最大Von Mises应力与材料允许应力之比来引导模型体积减小进化,直至最大Von Mises应力达到允许应力值为止.同时,引入多分辨率技术,由粗网格再到细网格进行优化计算,有效地提高了计算效率.与现有其他给定结构模式的方法相比,该优化结果能更好地体现模型荷载受力的传递路径.     

基于重新检测过程的三维细化算法的改进

现有的基于简单点判断的三维细化算法不能保证提取骨架的连续性,容易产生断裂。针对该问题,提出了一组各向同性模板,该模板能够使得算法具有90°旋转不变性;在此基础上,进一步提出了一种新的重新检测的方法,通过判断被删除的目标点的26邻域的连通性,来决定该目标点是否应该被还原,从而逐点检测3D物体的连通性,达到 保持整体连通性的目的。该方法可以应用于大多数基于模板的三维细化算法,能够修复断裂,保证其拓扑结构,避免产生空洞;同时,与同类算法相比,本算法由于利用了各向同性模板,在物体旋转的情况下亦能得到最佳的细化结果。     

A Fully Parallel 3D Thinning Algorithm and Its Applications

A thinning algorithm is a connectivity preserving process which is applied to erode an object layer by layer until only a “skeleton” is left. Generally, it is difficult to prove that a 3D parallel thinning algorithm preserves connectivity. Sufficient conditions which can simplify such proofs were proposed recently inCVGIP: Image Understanding(59, No. 3 (1994), 328–339). One of the purposes of this paper is to propose a connectivity preserving fully parallel 3D thinning algorithm. The other purpose is to show how to use the sufficient conditions to prove a 3D parallel thinning algorithm to be connectivity preserving. By this demonstration, a new generation of 3D parallel thinning algorithms can be designed and proved to preserve connectivity relatively easily.     

Thinning combined with iteration-by-iteration smoothing for 3D binary images

In this work we present a new thinning scheme for reducing the noise sensitivity of 3D thinning algorithms. It uses iteration-by-iteration smoothing that removes some border points that are considered as extremities. The proposed smoothing algorithm is composed of two parallel topology preserving reduction operators. An efficient implementation of our algorithm is sketched and its topological correctness for (26, 6) pictures is proved.     

一种基于拓扑连接图的三维模型检索方法

提出了一种基于分割技术的拓扑连接图构造方法。并用于三维模型检索．首先构造多层邻域计算用于度量每个三角片平坦度的信号值。根据这些信号值采用一种改进的分水岭方法把模型分割成不同的曲面片．然后利用这些曲面片之间的连接关系构造拓扑连接图．最后通过比较不同模型的拓扑连接图相似性来得到它们的匹配度。根据匹配度进行三维模型检索．     

Complete Tensor Field Topology on 2D Triangulated Manifolds embedded in 3D

This paper is concerned with the extraction of the surface topology of tensor fields on 2D triangulated manifolds embedded in 3D. In scientific visualization topology is a meaningful instrument to get a hold on the structure of a given dataset. Due to the discontinuity of tensor fields on a piecewise planar domain, standard topology extraction methods result in an incomplete topological skeleton. In particular with regard to the high computational costs of the extraction this is not satisfactory. This paper provides a method for topology extraction of tensor fields that leads to complete results. The core idea is to include the locations of discontinuity into the topological analysis. For this purpose the model of continuous transition bridges is introduced, which allows to capture the entire topology on the discontinuous field. The proposed method is applied to piecewise linear three‐dimensional tensor fields defined on the vertices of the triangulation and for piecewise constant two or three‐dimensional tensor fields given per triangle, e.g. rate of strain tensors of piecewise linear flow fields.     

Topology Preserving Simplification of Medial Axes in 3D Models

We propose an efficient method for topology‐preserving simplification of medial axes of 3D models. Existing methods either cannot preserve the topology during medial axes simplification or have the problem of being geometrically inaccurate or computationally expensive. To tackle these issues, we restrict our topology‐checking to the areas around the topological holes to avoid unnecessary checks in other areas. Our algorithm can keep high precision even when the medial axis is simplified to be in very few vertices. Furthermore, we parallelize the medial axes simplification procedure to enhance the performance significantly. Experimental results show that our method can preserve the topology with highly efficient performance, much superior to the existing methods in terms of topology preservation, accuracy and performance.     

三维水下监视传感器网络的拓扑生成算法

当前大多数传感器网络研究假设传感器节点在二维平面部署,然而许多水下传感器网络应用要求节点在三维空间分布。针对三维水下监视应用,提出一种新颖的分布式传感器网络拓扑生成算法（ETG）。基于格理论,ETG算法将节点的移动控制与活动设备的调度相结合。初始时刻监视设备密集部署在二维海平面上,ETG算法根据局部信息选择活动设备,并通过控制其传感器节点在垂直方向的移动,形成一个三维水下网络。仿真实验表明,ETG算法能够以较小的平均节点移动距离覆盖较大的空间,从而有效减少网络建立阶段的能量开销。     

一种基于三维骨架化的人体姿势估计方法

提出了一种基于三维2 步子迭代混合细化算法和启发式搜索的无标记三维人体姿势估计方法.其主要思想是首先通过一种新的2 步子迭代混合细化算法,对由Shape-from-Silhouette(SFS)算法从多幅二维图像中重建出的人体三维模型进行骨架化,然后通过一种启发式的方法进行模型匹配.实验结果表明,该方法不仅思想简单,而且具有较好的鲁棒性,能够很好的去除各种噪声的影响.     

三维模型近刚性保体变形

为保持三维模型表面细节和模型体积,提高模型变形的真实感效果,提出一种基于能量最小化的近刚性保体变形方法.首先对模型进行Laplacian变形,在此基础上,通过极分解求解曲面局部区域三角形的旋转变形,构建模型刚性变形能;然后通过模型体积积分离散化将模型体积变形约束转化为模型曲面变形约束,构建体积变形能;再通过衡量约束点的位置变形误差构建约束变形能.在最小二乘意义下最小化上述加权变形能,获得模型变形结果.实例结果表明,文中方法能够在线性的算法效率下获得近刚性保体变形效果,为模型的真实感变形提供了一条有效的途径.     

3D Topology Preserving Flows for Viewpoint-Based Cortical Unfolding

We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface with respect to a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. The third is a method that dramatically improves the computational speed of the 3D topology preservation approach by creating a tree structure of the 3D surface and using a recursion technique. Experiments results show that the proposed approach can successfully unfold highly convoluted surfaces such as the cortex while preserving their topology during the evolution.     

三维矢量场的流动拓扑结构抽取

提出一种基于关键点分类的三维矢量场流动拓扑结构抽取算法,可应用于三维曲线网格、结构化网格和分块网格中.在许多计算流体力学计算中,存在非滑移边界,这种边界上流体的速度为0.通过分析流场边界的表面摩擦场的拓扑,展示绕壁面流体的流动结构;使用图标定位关键点,可交互式地标记和显示涡核区域,并通过选择暗示螺旋流动的图标,沿着该关键点的实特征值对应的特征矢量方向积分流线来完成.测试结果清晰地展示了关键特征区域的流体流动特征.     

3D Digital Topology under Binary Transformation with Applications

In this paper we study 3D digital topology under the transformation of an object point to a nonobject point and vice versa. As a result of such a transformation, an object component in the 3 × 3 × 3 neighborhood of the affected point may vanish or split into two or more components or more than one object components may merge into one. Also, cavities or tunnels in the 3 × 3 × 3 neighborhood may be destroyed or created. One of the goals of this paper is to develop an efficient algorithm (topo_para) to compute the change in the numbers of object components, tunnels and cavities in the 3 × 3 × 3 neighborhood of the transformed point. Another important contribution is the classification of different types of points (e.g., arc inner point, arc edge point, surface inner point, surface edge point) and detection of different types of junction points (e.g., junction between arcs, junction between surfaces and arcs, junction between surfaces) on the surface skeleton representation of a 3D digital image. Using these junction points it is possible to segment a 3D digital surface topologically into meaningful parts. Also, we describe an efficient algorithm for computing the Euler number of a 3D digital image using the topological parameters computed bytopo_para.     

A Combinatorial Method for Topology Adaptations in 3D Deformable Models

In this paper we propose an efficient algorithm for topology adaptation of evolving surface meshes in 3D. This system has two novel features: First, a spatial hashing technique is used to detect self-colliding triangles of the evolving mesh. Secondly, for the topology adaptation itself, we use formulas which are derived from homology. In view of this the advantages of our algorithm are that it does not require global mesh re-parameterizations and the topology adaptation can be performed in a stable way via a rather coarse mesh. We apply our algorithm to segmentation of three-dimensional synthetic and ultrasound data.     

三维最优持久编队拓扑生成策略

针对智能体间的通信拓扑优化问题, 结合图论知识研究了三维空间中最优持久图的生成算法. 首先,利用刚度矩阵生成最优刚性图;然后,根据顶点连通度数的不同分别采取有向化操作方法, 通过逐层缩小最优刚性图范围的方式把刚性图持久化,生成了最优持久图;最后, 对三维空间中随机分布的智能体进行仿真实验,其结果验证了该算法的可行性和有效性, 此算法能降低编队拓扑的通信复杂度,减少通信能量消耗.     

Distance-Ordered Homotopic Thinning: A Skeletonization Algorithm for 3D Digital Images

A technique called distance-ordered homotopic thinning (DOHT) for skeletonizing 3D binary images is presented. DOHT produces skeletons that are homotopic, thin, and medial. This is achieved by sequentially deleting points in ascending distance order until no more can be safely deleted. A point can be safely deleted only if doing so preserves topology. Distance information is provided by the chamfer distance transform, an integer approximation to the Euclidean distance transform. Two variations of DOHT are presented that arise from using different rules for preserving points. The first uses explicit rules for preserving the ends of medial axes or edges of medial surfaces, and the second preserves the centers of maximal balls identified from the chamfer distance transform. By thresholding the centers according to their distance values, the user can control the scale of features represented in the skeleton. Results are presented for real and synthetic 2D and 3D data.     

Powerful Parallel and Symmetric 3D Thinning Schemes Based on Critical Kernels

The main contribution of the present article consists of new 3D parallel and symmetric thinning schemes which have the following qualities:

They are effective and sound, in the sense that they are guaranteed to preserve topology. This guarantee is obtained thanks to a theorem on critical kernels;

They are powerful, in the sense that they remove more points, in one iteration, than any other symmetric parallel thinning scheme;

They are versatile, as conditions for the preservation of geometrical features (e.g., curve extremities or surface borders) are independent of those accounting for topology preservation;

They are efficient: we provide in this article a small set of masks, acting in the grid ?³, that is sufficient, in addition to the classical simple point test, to straightforwardly implement them.

     

Topology optimization of periodic 3D heat transfer problems with 2D design

Structural and Multidisciplinary Optimization - We consider a model for density-based topology optimization (TO) of stationary heat transfer problems with design-dependent internal convection in 3D...