Mesh repair with user-friendly topology control

Limitations of current 3D acquisition technology often lead to polygonal meshes exhibiting a number of geometrical and topological defects which prevent them from widespread use. In this paper we present a new method for model repair which takes as input an arbitrary polygonal mesh and outputs a valid 2-manifold triangle mesh. Unlike previous work, our method allows users to quickly identify areas with potential topological errors and to choose how to fix them in a user-friendly manner. Key steps of our algorithm include the conversion of the input model into a set of voxels, the use of morphological operators to allow the user to modify the topology of the discrete model, and the conversion of the corrected voxel set back into a 2-manifold triangle mesh. Our experiments demonstrate that the proposed algorithm is suitable for repairing meshes of a large class of shapes.     

Correctness of belief propagation in Gaussian graphical models of arbitrary topology

Graphical models, such as Bayesian networks and Markov random fields, represent statistical dependencies of variables by a graph. Local "belief propagation" rules of the sort proposed by Pearl (1988) are guaranteed to converge to the correct posterior probabilities in singly connected graphs. Recently, good performance has been obtained by using these same rules on graphs with loops, a method we refer to as loopy belief propagation. Perhaps the most dramatic instance is the near Shannon-limit performance of "Turbo codes," whose decoding algorithm is equivalent to loopy propagation. Except for the case of graphs with a single loop, there has been little theoretical understanding of loopy propagation. Here we analyze belief propagation in networks with arbitrary topologies when the nodes in the graph describe jointly gaussian random variables. We give an analytical formula relating the true posterior probabilities with those calculated using loopy propagation. We give sufficient conditions for convergence and show that when belief propagation converges, it gives the correct posterior means for all graph topologies, not just networks with a single loop. These results motivate using the powerful belief propagation algorithm in a broader class of networks and help clarify the empirical performance results.     

n-Dimensional multiresolution representation of subdivision meshes with arbitrary topology

We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topological subdivision process that is a key issue to robustly and soundly define mesh hierarchies. It fully supports multiresolution edition what allows the implementation of most mesh processing algorithms – like filtering or compression – for n-dimensional meshes with arbitrary topologies.We illustrate this model, in dimension 3, with an new truly multiresolution representation of subdivision volumes. It allows us to extend classical subdivision schemes to arbitrary polyhedrons and to handle adaptive subdivision with an elegant solution to compliance issues. We propose an implementation of this model as an effective and relatively inexpensive data structure.     

Multiresolution free-form deformation with subdivision surface of arbitrary topology

A new free-from deformation method is presented in this paper. Object deformation is controlled by a mesh of arbitrary topology, namely a control mesh. The subdivision surface determined by the control mesh spans an intermediate deformation space. The object is embedded into the space by the nearest point rule. When the shape of the control mesh is changed, the object embedded in the intermediate deformation space will be deformed accordingly. Since the subdivision surface has a multiresolution property, the proposed deformation method naturally has a multiresolution property. A technique for generating control meshes is also introduced in the paper. Compared with previous deformation methods with arbitrary topology control tools, the proposed method has the advantages of flexible control and computational efficiency.     

Globally optimal surface mapping for surfaces with arbitrary topology

Computing smooth and optimal one-to-one maps between surfaces of same topology is a fundamental problem in computer graphics and such a method provides us a ubiquitous tool for geometric modeling and data visualization. Its vast variety of applications includes shape registration/matching, shape blending, material/data transfer, data fusion, information reuse, etc. The mapping quality is typically measured in terms of angular distortions among different shapes. This paper proposes and develops a novel quasi-conformal surface mapping framework to globally minimize the stretching energy inevitably introduced between two different shapes. The existing state-of-the-art inter-surface mapping techniques only afford local optimization either on surface patches via boundary cutting or on the simplified base domain, lacking rigorous mathematical foundation and analysis. We design and articulate an automatic variational algorithm that can reach the global distortion minimum for surface mapping between shapes of arbitrary topology, and our algorithm is sorely founded upon the intrinsic geometry structure of surfaces. To our best knowledge, this is the first attempt towards numerically computing globally optimal maps. Consequently, our mapping framework offers a powerful computational tool for graphics and visualization tasks such as data and texture transfer, shape morphing, and shape matching.     

Threshold conditions for arbitrary cascade models on arbitrary networks

Given a network of who-contacts-whom or who-links-to-whom, will a contagious virus/product/meme spread and ‘take over’ (cause an epidemic) or die out quickly? What will change if nodes have partial, temporary or permanent immunity? The epidemic threshold is the minimum level of virulence to prevent a viral contagion from dying out quickly and determining it is a fundamental question in epidemiology and related areas. Most earlier work focuses either on special types of graphs or on specific epidemiological/cascade models. We are the first to show the G2-threshold (twice generalized) theorem, which nicely de-couples the effect of the topology and the virus model. Our result unifies and includes as special case older results and shows that the threshold depends on the first eigenvalue of the connectivity matrix, (a) for any graph and (b) for all propagation models in standard literature (more than 25, including H.I.V.). Our discovery has broad implications for the vulnerability of real, complex networks and numerous applications, including viral marketing, blog dynamics, influence propagation, easy answers to ‘what-if’ questions, and simplified design and evaluation of immunization policies. We also demonstrate our result using extensive simulations on real networks, including on one of the biggest available social-contact graphs containing more than 31?million interactions among more than 1?million people representing the city of Portland, Oregon, USA.     

Isogeometric analysis with trimming technique for problems of arbitrary complex topology

Trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to CAD files created by using NURBS. In the present work, it is shown that any complex multiply-connected NURBS domain can be described by using trimming curves only. Isogeometric analysis for linear elasticity problems of complex topology described in this way is presented. For fully communicative interaction between CAD and CAE, a specific searching algorithm and an integration scheme of trimmed elements are introduced to utilize the IGES files exported from CAD system for Isogeometric analysis. Schemes for imposing essential and traction boundary conditions on trimming curves are presented. It has been demonstrated that with the presented schemes trimmed cases in any complicated situations can be successfully treated. With the examples of complex topology that could be described by employing trimming curves only, effectiveness and robustness of present method are demonstrated.     

Data/voice integration for fibre optic LANs with arbitrary topology

A high-performance protocol for arbitrary point-to-point fibre optic local area networks with combined voice and data traffic is described. Simulation on a 3 Mbit/s nine-node mesh network has shown that it is capable of supporting a substantial number of data users and more than 100 active voice calls (200 active telephone users, coding rate 64 kbit/s without silence detection) with a packet delay of less than 10 ms and without any loss of information. The network performance is superior to the previous reported voice protocol which used the modified anarchy flood routing (MAFR) technique. Performance limitation due to growing network size for flood-routed networks is also discussed. A method of extending the flood-routing protocols over subnetworks which are connected via bridges is also presented. This method enables a large network to be divided into smaller subnetworks which reduces the number of links required.     

无线 Mesh网络规则拓扑结构与容量研究*

拓扑控制技术可以有效地提高无线Mesh网络的网络容量并增强网络可靠性,采用拓扑控制所构成的规则网络拓扑结构还具有良好网络路由和链路分集能力。通过对随机拓扑和规则拓扑的网络容量与拓扑特征的分析,表明规则拓扑在无线Mesh网络中具有优良网络品质。为了使规则拓扑适应密集组网的应用环境,设计一种虚拟层次化的规则拓扑结构;进一步通过拓扑分割构成微虚拟小区解决网络的可扩展性问题。仿真证明规则拓扑及其拓扑分割技术提高了无线Mesh网络容量等网络性能。     

Parameterization-free active contour models with topology control

We present a novel approach for representing and evolving deformable active contours by restricting the movement of the contour vertices to the grid lines of a uniform lattice. This restriction implicitly controls the (re)parameterization of the contour and hence makes it possible to employ parameterization-independent evolution rules. Moreover, the underlying uniform grid makes self-collision detection very efficient. Our contour model is also able to perform topology changes, but – more importantly – it can detect and handle self-collisions at subpixel precision. In applications where topology changes are not appropriate, we generate contours that touch themselves without any gaps or self-intersections.     

A boundary integral method applied to plates of arbitrary plan form and arbitrary boundary conditions

An integral equation method which has been applied to thin elastic clamped plates of arbitrary plan form[1] has been extended to include arbitrary boundary conditions. Numerical difficulties which arise in the case of free boundaries have been avoided by defining an integration contour which differs from the actual plate boundary. Thus second order singularities which arise in the integrand of the equations are avoided.The method is applied to two rectangular plates with mixed boundary conditions (i.e. clamped, simply-supported and free edges). Average errors are 1.5% for displacements and 3% for bending moments.     

Combinatorial manifold mesh reconstruction and optimization from unorganized points with arbitrary topology

In this paper, a novel approach is proposed to reliably reconstruct the geometric shape of a physically existing object based on unorganized point cloud sampled from its boundary surface. The proposed approach is composed of two steps. In the first step, triangle mesh structure is reconstructed as a continuous manifold surface by imposing explicit relationship among the discrete data points. For efficient reconstruction, a growing procedure is employed to build the 2-manifold directly without intermediate 3D representation. Local and global topological operations with ensured completeness and soundness are defined to incrementally construct the 2-manifold with arbitrary topology. In addition, a novel criterion is proposed to control the growing process for ensured geometric integrity and automatic boundary detection with a non-metric threshold. The reconstructed manifold surface captures the object topology with the built-in combinatorial structure and approximates the object geometry to the first order. In the second step, new methods are proposed to efficiently obtain reliable curvature estimation for both the object surface and the reconstructed mesh surface. The combinatorial structure of the triangle mesh is then optimized by changing its local topology to minimize the curvature difference between the two surfaces. The optimized triangle mesh achieves second order approximation to the object geometry and can serve as a basis for many applications including virtual reality, computer vision, and reverse engineering.     

Texture mapping on surfaces of arbitrary topology using norm preserving-based optimization

A simple and yet highly efficient, high-quality texture mapping method for surfaces of arbitrary topology is presented. The new method projects the given surface from the 3D object space into the 2D texture space to identify the 2D texture structure that will be used to texture the surface. The object space to texture space projection is optimized to ensure minimum distortion of the texture mapping process. The optimization is achieved through a commonly used norm preserving minimization process on edges of the surface. The main difference here is, by using an initial value approach, the optimization problem can be set up as a quadratic programming problem and, consequently, solved by a linear least squares method. Three methods to choose a good initial value are presented. Test cases show that the new method works well on surfaces of arbitrary topology, with the exception of surfaces with exceptionally abnormal curvature distribution. Other advantages of the new method include uniformity and seamlessness of the texture mapping process. The new method is suitable for applications that do not require precise texture mapping results but demand highly efficient mapping process such as computer animation or video games.     

Hidden Markov models with arbitrary state dwell-time distributions

A hidden Markov model (HMM) with a special structure that captures the ‘semi’-property of hidden semi-Markov models (HSMMs) is considered. The proposed model allows arbitrary dwell-time distributions in the states of the Markov chain. For dwell-time distributions with finite support the HMM formulation is exact while for those that have infinite support, e.g. the Poisson, the distribution can be approximated with arbitrary accuracy. A benefit of using the HMM formulation is that it is easy to incorporate covariates, trend and seasonal variation particularly in the hidden component of the model. In addition, the formulae and methods for forecasting, state prediction, decoding and model checking that exist for ordinary HMMs are applicable to the proposed class of models. An HMM with explicitly modeled dwell-time distributions involving seasonality is used to model daily rainfall occurrence for sites in Bulgaria.     

Fine-grained cache deployment scheme for arbitrary topology in ICN

Neural Computing and Applications - Information-centric networking (ICN) is one of the promising candidates for the future network architecture. In-network caching deployed on the routers is the...     

基于边界跟踪的任意形状区域填充算法

针对任意形状的多边形及孔洞区域,提出基于边界跟踪的填充算法。用细化算法对图像进行单线化预处理,分别跟踪各个封闭曲线的边界,从第1个边界点坐标出发,根据跟踪方向对每个边界点进行有向直线填充,遇到边界点时停止,将各填充图与原图进行合并。实验结果表明,该算法不受图形边界状况和自身形状的影响,能适应任意类型的封闭区域;沿边界点进行处理,避免了对背景点的重复计算;对于多孔洞的封闭图形,能对各个孔洞进行独立处理,可灵活选择填充效果。