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.     

Optimized Topological Surgery for Unfolding 3D Meshes

Constructing a 3D papercraft model from its unfolding has been fun for both children and adults since we can reproduce virtual 3D models in the real world. However, facilitating the papercraft construction process is still a challenging problem, especially when the shape of the input model is complex in the sense that it has large variation in its surface curvature. This paper presents a new heuristic approach to unfolding 3D triangular meshes without any shape distortions, so that we can construct the 3D papercraft models through simple atomic operations for gluing boundary edges around the 2D unfoldings. Our approach is inspired by the concept of topological surgery, where the appearance of boundary edges of the unfolded closed surface can be encoded using a symbolic representation. To fully simplify the papercraft construction process, we developed a genetic‐based algorithm for unfolding the 3D mesh into a single connected patch in general, while optimizing the usage of the paper sheet and balance in the shape of that patch. Several examples together with user studies are included to demonstrate that the proposed approach works well for a broad range of 3D triangular meshes.     

Preserving Topology by a Digitization Process

The main task of digital image processing is to recognize properties of real objects based on their digital images. These images are obtained by some sampling device, like a CCD camera, and represented as finite sets of points that are assigned some value in a gray-level or color scale. Based on technical properties of sampling devices, these points are usually assumed to form a square grid and are modeled as finite subsets of Z². Therefore, a fundamental question in digital image processing is which features in the digital image correspond, under certain conditions, to properties of the underlying objects. In practical applications this question is mostly answered by visually judging the obtained digital images. In this paper we present a comprehensive answer to this question with respect to topological properties. In particular, we derive conditions relating properties of real objects to the grid size of the sampling device which guarantee that a real object and its digital image are topologically equivalent. These conditions also imply that two digital images of a given object are topologically equivalent. This means, for example, that shifting or rotating an object or the camera cannot lead to topologically different images, i.e., topological properties of obtained digital images are invariant under shifting and rotation.     

面向跨语言词云可视化的拓扑布局算法研究

针对大范围替换词云中单词后出现的词云拓扑结构不稳定的现象,提出一种词云可视化的拓扑保持布局算法。首先,该算法通过对替换后的词云中单词进行分散处理,使之前或重叠远离的单词按原拓扑相应分离;再利用Delaunay三角剖分算法对离词云风格化,形成控制风格;最后在控制风格的基础上采用紧凑布局的方法将分散词云紧凑为与替换前原词云拓扑一致的词云布局。针对替换的一种具体情况,即跨语言翻译词云的情况做详细介绍。该算法在提高词云而已稳定性,保持原词云拓扑结构方面是一个新的突破。     

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.     

脑皮层的立体脑回图展成平面的新方法

用核磁共振 (MRI)大脑断层图 ,分析患者的脑皮层解剖特征是一项困难的工作 .一个可能的途径是将分割后的脑皮层进行三维重建 .但是重建后的三维立体脑皮层图 ,如不经过 36 0°旋转仅能看到脑皮层上脑回的一部分 .因此还需要展开成平面脑回图以看到脑回的完整走向 .文中提出的投影方法能够在变形尽量小的前提下将立体脑回图展开在平面上 ,直观地看到脑回走向的全貌 ,便于临床诊断或治疗中应用     

Partial 3D Shape Retrieval by Reeb Pattern Unfolding

This paper presents a novel approach for fast and efficient partial shape retrieval on a collection of 3D shapes. Each shape is represented by a Reeb graph associated with geometrical signatures. Partial similarity between two shapes is evaluated by computing a variant of their maximum common sub-graph.
By investigating Reeb graph theory, we take advantage of its intrinsic properties at two levels. First, we show that the segmentation of a shape by a Reeb graph provides charts with disk or annulus topology only. This topology control enables the computation of concise and efficient sub-part geometrical signatures based on parameterisation techniques. Secondly, we introduce the notion of Reeb pattern on a Reeb graph along with its structural signature. We show this information discards Reeb graph structural distortion and still depicts the topology of the related sub-parts. The number of combinations to evaluate in the matching process is then dramatically reduced by only considering the combinations of topology equivalent Reeb patterns.
The proposed framework is invariant against rigid transformations and robust against non-rigid transformations and surface noise. It queries the collection in interactive time (from 4 to 30 seconds for the largest queries). It outperforms the competing methods of the SHREC 2007 contest in term of NDCG vector and provides, respectively, a gain of 14.1% and 40.9% on the approaches by Biasotti et al. [ BMSF06 ] and Cornea et al. [ CDS*05 ].
As an application, we present an intelligent modelling-by-example system which enables a novice user to rapidly create new 3D shapes by composing shapes of a collection having similar sub-parts.     

Connectivity Preserving Multivalued Functions in Digital Topology

We study connectivity preserving multivalued functions (Kovalevsky in A new concept for digital geometry, shape in picture, 1994) between digital images. This notion generalizes that of continuous multivalued functions (Escribano et al. in Discrete geometry for computer imagery, lecture notes in computer science, 2008; Escribano et al. in J Math Imaging Vis 42:76–91, 2012) studied mostly in the setting of the digital plane \({\mathbb {Z}}^2\). We show that connectivity preserving multivalued functions, like continuous multivalued functions, are appropriate models for digital morphological operations. Connectivity preservation, unlike continuity, is preserved by compositions, and generalizes easily to higher dimensions and arbitrary adjacency relations.     

保持特征的三维网格模型尺寸调整

提出了一种三维模型尺寸调整的新方法.新方法通过对每条边的缩放来驱动模型尺寸的调整,然后以缩放前后三角形法向的叉乘为目标函数项进行优化,几何意义上,该法向叉乘项表示极小化每个三角形的法向变化;换Willmore能量意义上,该项可以近似地极小化缩放带来的能量变化.对需要精确保持某些特征区域的模型,采用带约束的尺寸凋整方法,通过引入拉格朗日乘数来求解满足约束条件的优化问题,从而能够精确保持模型的重要特征,目前已有的三维模型尺寸调整方法还不能做到这一点.最后,实例表明文中方法在调整模型尺寸的同时,既能很好地保持模型的敏感特征,也能精确保持某些重要的模型特征.     

Saliency‐Preserving Slicing Optimization for Effective 3D Printing

We present an adaptive slicing scheme for reducing the manufacturing time for 3D printing systems. Based on a new saliency‐based metric, our method optimizes the thicknesses of slicing layers to save printing time and preserve the visual quality of the printing results. We formulate the problem as a constrained ?₀ optimization and compute the slicing result via a two‐step optimization scheme. To further reduce printing time, we develop a saliency‐based segmentation scheme to partition an object into subparts and then optimize the slicing of each subpart separately. We validate our method with a large set of 3D shapes ranging from CAD models to scanned objects. Results show that our method saves printing time by 30–40% and generates 3D objects that are visually similar to the ones printed with the finest resolution possible.     

On Topology Preservation in 3D Thinning

Topology preservation is a major concern of parallel thinning algorithms for 2D and 3D binary images. To prove that a parallel thinning algorithm preserves topology, one must show that it preserves topology for all possible images. But it would be difficult to check all images, since there are too many possible images. Efficient sufficient conditions which can simplify such proofs for the 2D case were proposed by Ronse [Discrete Appl. Math. 21, 1988, 69-79]. By Ronse′s results, a 2D parallel thinning algorithm can be proved to be topology preserving by checking a rather small number of configurations. This paper establishes sufficient conditions for 3D parallel thinning algorithms to preserve topology.     

Mean Shift迭代构造拓扑保持图像变换

在图像弹性配准中,基于径向基函数的小形变变换模型存在拓扑关系不能保持的问题.为此针对小形变模型提出一种基于Mean Shift迭代的拓扑保持图像变换方法.首先在拓扑不能保持的区域确定新增控制点对,通过Mean Shift迭代算法调整新增目标控制点的位置,再根据形变曲面的拓扑保持情况和配准度量的改善情况筛选新增控制点对,...     

三维局部空化流数值计算分析

依据R-P方程,给出了与蒸汽相输运方程量纲一致的自然空化源项模型。依据该空化模型,数值计算了半球头、平头和45度锥角头部的圆柱在不同空化数条件下的平面稳态空化流动,并将数值计算的结果与试验数据进行对比分析。通过比较数值计算与试验的结果,验证该空化流数值计算方法的有效性。在验证算法有效性之后,数值计算了有无攻角的半球头圆柱在不同空化数条件下的三维自然空化流。计算表明,在同样攻角状态下,空化数越小,空泡流的三维非对称效应越明显。     

Feature Preserving Mesh Generation from 3D Point Clouds

We address the problem of generating quality surface triangle meshes from 3D point clouds sampled on piecewise smooth surfaces. Using a feature detection process based on the covariance matrices of Voronoi cells, we first extract from the point cloud a set of sharp features. Our algorithm also runs on the input point cloud a reconstruction process, such as Poisson reconstruction, providing an implicit surface. A feature preserving variant of a Delaunay refinement process is then used to generate a mesh approximating the implicit surface and containing a faithful representation of the extracted sharp edges. Such a mesh provides an enhanced trade‐off between accuracy and mesh complexity. The whole process is robust to noise and made versatile through a small set of parameters which govern the mesh sizing, approximation error and shape of the elements. We demonstrate the effectiveness of our method on a variety of models including laser scanned datasets ranging from indoor to outdoor scenes.     

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.     

Topology based 2D engineering drawing and 3D model matching for process plant

Process plant models mainly include 3D models and 2D engineering drawings. Matching calculation between these CAD models has wide applicability in model consistency check and retrieval. In process plant, engineering design standards make 2D engineering drawing and 3D model differ in geometry, proportion and structure, leading to the inapplicability of current shape-feature based matching approaches. Since connection relationships between components are the core of a process plant, a topology based algorithm is proposed. Firstly, by exploiting components as vertices and relationships as edges, both 2D engineering drawing and 3D model are preprocessed into graph structures. Then each model’s relationship types are extracted from the graph. Finally, regarding the extracted relationship types as primary feature, feature similarity is calculated to measure the matching degree between their corresponding models. The proposed algorithm is geometric deformation invariant. Experiments with industrial applications are presented, which demonstrates the effectiveness and feasibility of the proposed algorithm.     

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．     

保持拓扑和尖角特征的网格简化算法

提出了一种有效的保持拓扑和尖角特征的网格简化算法。由于曲率刻画了模型的尖角特征，该文利用顶点曲率的高斯加权函数对经典边折叠算法的二次误差测度矩阵进行了修正，增强了尖角点对新点位置的影响。鉴于网格的拓扑保持具有重要的工程应用，论述了网格简化中各种可能的拓扑错误，并给出了相应的解决措施。平衡二叉树和半边匹配数据结构的引入，提高了拓扑信息重建的速度。最后，几个网格简化实例显示了该文算法的有效性。     

Depth-Guided Vision Transformer With Normalizing Flows for Monocular 3D Object Detection

Monocular 3D object detection is challenging due to the lack of accurate depth information. Some methods estimate the pixel-wise depth maps from off-the-shelf depth estimators and then use them as an additional input to augment the RGB images.Depth-based methods attempt to convert estimated depth maps to pseudo-LiDAR and then use LiDAR-based object detectors or focus on the perspective of image and depth fusion learning.However, they demonstrate limited performance and efficiency as a result of ...     

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.