Topology preserving top-down compression of 2D vector fields using bintree and triangular quadtrees

We present a hierarchical top-down refinement algorithm for compressing 2D vector fields that preserves topology. Our approach is to reconstruct the data set using adaptive refinement that considers topology. The algorithms start with little data and subdivide regions that are most likely to reconstruct the original topology of the given data set. We use two different refinement techniques. The first technique uses bintree subdivision and linear interpolation. The second algorithm is driven by triangular quadtree subdivision with Coons patch quadratic interpolation. We employ local error metrics to measure the quality of compression and as a global metric we compute Earth Mover's Distance (EMD) to measure the deviation from the original topology. Experiments with both analytic and simulated data sets are presented. Results indicate that one can obtain significant compression with low errors without losing topological information. Advantages and disadvantages of different topology preserving compression algorithms are also discussed in the paper.     

Topology Aware Stream Surfaces

We present an algorithm that allows stream surfaces to recognize and adapt to vector field topology. Standard stream surface algorithms either refine the surface uncontrolled near critical points which slows down the computation considerably and may lead to a poor surface approximation. Alternatively, the concerned region is omitted from the stream surface by severing it into two parts thus generating an incomplete stream surface. Our algorithm utilizes topological information to provide a fast, accurate, and complete triangulation of the stream surface near critical points. The required topological information is calculated in a preprocessing step. We compare our algorithm against the standard approach both visually and in performance.     

Topology of real algebraic space curves

In this paper we give a new projection-based algorithm for computing the topology of a real algebraic space curve given implicitly by a set of equations. Under some genericity conditions, which may be reached through a linear change of coordinates, we show that a plane projection of the given curve, together with a special polynomial in the ideal of the curve contains all the information needed to compute its topological shape. Our method is also designed in such a way to exploit important particular cases such as complete intersection curves or curves contained in nonsingular surfaces.     

On topological properties of the Choquet weak convergence of capacity functionals of random sets

In view of the recent interests in random sets in information technology, such as models for imprecise data in intelligent systems, morphological analysis in image processing, we present, in this paper, some contributions to the foundation of random set theory, namely, a complete study of topological properties of capacity functionals of random sets, generalizing weak convergence of probability measures. These results are useful for investigating the concept of Choquet weak convergence of capacity functionals leading to tractable criteria for convergence in distribution of random sets. The weak topology is defined on the space of all capacity functionals on R^d. We show that this topological space is separable and metrizable.     

基于等级划分的复杂点云骨架提取算法

对于复杂点云的骨架提取,由于原始点云的遮挡、缺失、分布不均、分支复杂等原因,所提取骨架会产生断裂、拓扑结构错误等问题.针对复杂结构点云的骨架提取,提出了一种基于等级划分的复杂点云骨架提取算法(multilevel divided skeleton extraction,MDSE).使用L1-medial提取初始骨架点,将初始骨架点连接成单分支骨架线,通过对单分支结构的初始骨架线进行等级划分,利用连通分支的平均分叉角确定骨架线断裂位置,由底至项修补断裂骨架线;最后采用Cardinal样条曲线改善骨架形态,形成完整且符合原始点云拓扑结构的骨架线.实验结果表明,该算法能够从复杂点云中提取出较为完整、拓扑结构正确的骨架线.     

A two-level topological model for 3D features in CityGML

CityGML, as the standard for the representation and exchange of 3D city models, contains rich information in terms of geometry, semantics, topology and appearance. With respect to topology, CityGML adopts the XLink approach to represent topological relationships between different geometric aggregates or thematic features; however, it is limited to shared objects. This paper proposes a two-level model for representing 3D topological relationships in CityGML: high-level (semantic-level) topology between semantic features and low-level (geometric-level) topology between geometric primitives. Five topological relationships are adopted in this model: touch, in, equal, overlap and disjoint. The semantic-level topology is derived from the geometric-level topology on the basis of the shared geometric primitives. To maintain the 3D topology, topological consistency rules are presented. An Application Domain Extension, called TopoADE, is proposed for the implementation of the topological model. The TopoADE consists of three modules: Topology, Feature and Geometry. Finally, 3D city models with LoD1 to LoD4 are used to test this model. Experimentation on those data sets indicates a validation of the proposed topological model in CityGML.     

运载火箭控制系统的BIT设计与实现

根据拓扑性质知觉原理,视觉原语是从整体到局部,拓扑感知优先。根据此仿生原理,建立感知目标物的形状拓扑信息的数学模型。首先提取物体三维轮廓信息;将空间图形轮廓降维映射到二维投影平面中进行处理;建立提取空间图形拓扑特征的数学模型。将轮廓拓扑空间同胚映射到(Hausdorf或度量空间或)二维投影平面,保持了拓扑不变性,因此便于分析出拓扑特征,可继续应用拓扑映射原理,分析点集拓扑。最终,拓扑特征与知识库模型相匹配,识别出物体。     

Implicit simplicial models for adaptive curve reconstruction

Parametric deformable models have been extensively and very successfully used for reconstructing free-form curves and surfaces, and for tracking nonrigid deformations, but they require previous knowledge of the topological type of the data, and good initial curve or surface estimates. With deformable models, it is also computationally expensive to check for and to prevent self-intersections while tracking deformations. The implicit simplicial models that we introduce in this paper are implicit curves and surfaces defined by piecewise linear functions. This representation allows for local deformations, control of the topological type, and prevention of self-intersections during deformations. As a first application, we also describe an algorithm for 2D curve reconstruction from unorganized sets of data points. The topology, the number of connected components, and the geometry of the data are all estimated using an adaptive space subdivision approach. The main four components of the algorithm are topology estimation, curve fitting, adaptive space subdivision, and mesh relaxation     

Authenticating topological integrity of process plant models through digital watermarking

Process plant models, which feature their intrinsical complex topological relation, are important industrial art works in the field of Computer-Aided Design (CAD). This paper investigates the topology authentication problem for process plant models. Compared with the widely studied watermarking based geometrical information protection and authentication techniques for traditional mechanical CAD drawings, topology authentication is still in its infancy and offers very interesting potentials for improvements. A semi-fragile watermarking based algorithm is proposed to address this interesting issue in this paper. We encode the topological relation among joint plant components into the watermark bits based on the hamming code. A subset of the model’s connection points are selected as mark points for watermark embedding. Then those topology sensitive watermark bits are embedded into selected mark points via bit substitution. Theoretical analysis and experimental results demonstrate that our approach yields a strong ability in detecting and locating malicious topology attacks while achieves robustness against various non-malicious attacks.     

Sub-Voxel Topology Control for Level-Set Surfaces

Active contour models are an efficient, accurate, and robust tool for the segmentation of 2D and 3D image data.In particular, geometric deformable models (GDM) that represent an active contour as the level set of an implicitfunction have proven to be very effective. GDMs, however, do not provide any topology control, i.e. contours maymerge or split arbitrarily and hence change the genus of the reconstructed surface. This behavior is inadequate insettings like the segmentation of organic tissue or other objects whose genus is known beforehand. In this paperwe describe a novel method to overcome this limitation while still preserving the favorable properties of the GDMsetup. We achieve this by adding (sparse) topological information to the volume representation at locations whereit is necessary to locally resolve topological ambiguities. Since the sparse topology information is attached to theedges of the voxel grid, we can reconstruct the interfaces where the deformable surface touches itself at sub-voxelaccuracy. We also demonstrate the efficiency and robustness of our method.     

多面体线框模型的表面识别技术

提出一种综合利用线框模型几何信息和拓扑信息的表面识别算法。首先利用平行投影法将3维线框模型投影到2维平面上,隐藏被遮挡边和悬边悬链;然后在可见投影边线图中,根据各个顶点的关联边序列,按照顺时针最小转角原则搜索最小回路;最后根据Moebius规则和二流形体的性质,及时删除不是表面投影的非法回路和图中的完备边,并调整回路的方向,使其均指向体外。通过各类典型立体的表面识别实验表明,算法具有广泛的立体适应能力和较高的效率。     

一种适合多域WDM光网络的拓扑聚合算法

根据多域波分复用光网络的特点提出一种以波长为压缩参数的拓扑聚合算法。该算法根据原拓扑资源图构造边界节点的全连通拓扑,在其基础上进一步压缩为非对称星型图。用随机产生的网络拓扑仿真表明,算法能在很小的精度损失情况下有效地压缩信息。相对于全连通拓扑,其压缩后的复杂度可降低到O（N）。     

Topological properties of generalized approximation spaces

Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper concerns generalized approximation spaces via topological methods and studies topological properties of rough sets. Classical separation axioms, compactness and connectedness for topological spaces are extended to generalized approximation spaces. Relationships among separation axioms for generalized approximation spaces and relationships between topological spaces and their induced generalized approximation spaces are investigated. An example is given to illustrate a new approach to recover missing values for incomplete information systems by regularity of generalized approximation spaces.     

Time-varying contour topology

The contour tree has been used to compute the topology of isosurfaces, generate a minimal seed set for accelerated isosurface extraction, and provide a user interface to segment individual contour components in a scalar field. In this paper, we extend the benefits of the contour tree to time-varying data visualization. We define temporal correspondence of contour components and describe an algorithm to compute the correspondence information in time-dependent contour trees. A graph representing the topology changes of time-varying isosurfaces is constructed in real-time for any selected isovalue using the precomputed correspondence information. Quantitative properties, such as surface area and volume of contour components, are computed and labeled on the graph. This topology change graph helps users to detect significant topological and geometric changes in time-varying isosurfaces. The graph is also used as an interactive user interface to segment, track, and visualize the evolution of any selected contour components over time.     

Three-dimensional topology preserving reduction on the 4-subfields

This paper discusses thinning on 3D binary images with the 4-subfield approach. Although a thinning algorithm concerns binary images, the algorithm itself can be represented as a set of three-color reduction templates. A thinning algorithm is topology preserving if the set of all three-color templates is topology preserving. Sufficient and necessary conditions of time complexity O(n) were proposed for verifying the topological soundness of a 3D 4-subfield thinning algorithm of n three-color templates. Theories and techniques for computerizing such conditions were discussed. Two 4-subfield thinning algorithms on 3D images, one for generating medial curves, and the other one for generating medial surfaces, are proposed and proved to preserve topology by our sufficient and necessary conditions.     

Generating protein three-dimensional fold signatures using inductive logic programming

Inductive logic programming (ILP) has been applied to automatically discover protein fold signatures. This paper investigates the use of topological information to circumvent problems encountered during previous experiments, namely (1) matching of non-structurally related secondary structures and (2) scaling problems. Cross-validation tests were carried out for 20 folds. The overall estimated accuracy is 73.37±0.35%. The new representation allows us to process the complete set of examples, while previously it was necessary to sample the negative examples. Topological information is used in approximately 90% of the rules presented here. Information about the topology of a sheet is present in 63% of the rules. This set of rules presents characteristics of the overall architecture of the fold. In contrast, 26% of the rules contain topological information which is limited to the packing of a restricted number of secondary structures, as such, the later set resembles those found in our previous studies.     

Infinite arrays and infinite computations

A complete metric topology is introduced on the set of all finite and infinite arrays and the topological properties of the space are studied. In this complete metric topology, infinite arrays are the limits of increasing sequences of finite arrays. The notion of successful infinite derivations in Generalized Context-free Kolam Array Grammars, yielding infinite arrays, is a subclass of Generalized context-free kolam array grammars. For this class, the finite array language generated by a reduced grammar in Greibach normal form and the set of infinite arrays generated by it are related through the notion of adherence.     

Generating protein three-dimensional fold signatures using inductive logic programming.

Inductive logic programming (ILP) has been applied to automatically discover protein fold signatures. This paper investigates the use of topological information to circumvent problems encountered during previous experiments, namely (1) matching of non-structurally related secondary structures and (2) scaling problems. Cross-validation tests were carried out for 20 folds. The overall estimated accuracy is 73.37+/-0.35%. The new representation allows us to process the complete set of examples, while previously it was necessary to sample the negative examples. Topological information is used in approximately 90% of the rules presented here. Information about the topology of a sheet is present in 63% of the rules. This set of rules presents characteristics of the overall architecture of the fold. In contrast, 26% of the rules contain topological information which is limited to the packing of a restricted number of secondary structures, as such, the later set resembles those found in our previous studies.     

Local topological beautification of reverse engineered models

Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and by numerical errors in the model building software. The quality of such models can be improved in a beautification step, where geometric regularities need to be detected and imposed on the model, and defects requiring topological change need to be corrected. This paper considers changes to the topology such as the removal of short edges, small faces and sliver faces, filling of holes in the surface of the model (arising due to missing data), adjusting pinched faces, etc. A practical algorithm for detecting and correcting such problems is presented. Analysis of the algorithm and experimental results show that the algorithm is able to quickly provide the desired changes. Most of the time required for topological beautification is spent on adjusting the geometry to agree with the new topology.     

基于IP网络的物理拓扑自动发现算法

网络管理已成为网络系统运行好坏的关键，而网络拓扑构造的自动发现是进行网络管理、性能分析、故障定位的前提条件．随着网络规模的不断扩大，网络层拓扑结构已经不能准确反映网络设备之间的连接关系．因此，本文依据标准的SNMP和ICMP等协议和相关的MIB信息，提出并证明了以太网设备连接判定定理，并以此为基础提出了一种物理拓扑自动发现算法．与已有的物理拓扑发现算法相比，该算法不要求所有网络设备都支持SNMP协议，具有高效、实用的优点．试验结果显示，该算法能快速、准确地生成IP网络的物理拓扑图．