Topological lines in 3D tensor fields and discriminant Hessian factorization

This paper addresses several issues related to topological analysis of 3D second order symmetric tensor fields. First, we show that the degenerate features in such data sets form stable topological lines rather than points, as previously thought. Second, the paper presents two different methods for extracting these features by identifying the individual points on these lines and connecting them. Third, this paper proposes an analytical form of obtaining tangents at the degenerate points along these topological lines. The tangents are derived from a Hessian factorization technique on the tensor discriminant and leads to a fast and stable solution. Together, these three advances allow us to extract the backbone topological lines that form the basis for topological analysis of tensor fields.     

Invariant imbedding and the method of lines for parallel computers

Recursion relations have been used to allow the solution of the invariant imbedding equations with singularities. We demonstrate that these same relations can be used in an efficient implementation of invariant imbedding for massively parallel computers. The parallel implementation of invariant imbedding can be used in conjuction with the method of lines to solve partial differential equations. We consider the problem of assigning lines to processors to minimize communication delays and the effect of asynchronous relaxation. Each algorithm is implemented and run on the NCUBE/ten hypercube, and timing data, speedup and normalized speedup are given. Operation counts are also given for each algorithm.     

Analyzing topological changes for structural shape simplification

The shapes of regions tend to be simplified with the decrease of spatial scale or resolution, which further leads to topological changes. Analyzing topological changes is an important aspect of formalizing semantic relations. An important fact is observed that shape simplification can be considered as a combination of generalizing basic primitives. Based on this fact, a shape is decomposed first into a set of simple primitives including convexities and concavities. And then the topological changes between lines and regions can be derived from the relations between lines and primitives. The approaches presented in this study can help to analyze the exact types and locations of topological changes for generalizing convexities and concavities, respectively. The approaches need not to conduct the real simplification of shapes, and they instead incorporate the idea of simplification for deriving the changes. Thus, they are independent on the algorithms of geometrical simplification. A prototype is developed and tested using the real world examples. The results show that the approaches in this study are helpful to analyze topological changes for shape simplification.     

二阶对称张量场可视化的一种新模式

目前二阶对称张量场的可视化均是基于最大（次大）和最小特征向量场的,但这样定义的特征向量场存在着方向不连续的问题,而应力场的特征向量的方向却是永远连续的,鉴于此,提出了基于特征向量方向连续的一种可视化的新模式。从原理上阐述了问题产生的机理,提出了特征向量场的新定义——根据特征向量方向的连续性将特征向量场定义为第一和第二（第三）特征向量场,并对新定义的特征向量场在每一点包括退化点处的取值问题进行了研究。新定义克服了传统定义方向不连续的缺点,保持了特征向量场在每一点包括退化点处的方向上的连续性,同时,基于新定义的可视化从本质上体现了应力场及其他对称张量场本身具有的属性。     

Strategies for direct volume rendering of diffusion tensor fields

Diffusion-weighted magnetic resonance imaging is a relatively new modality capable of elucidating the fibrous structure of certain types of tissue, such as the white matter within the brain. One tool for interpreting this data is volume rendering because it permits the visualization of three dimensional structure without a prior segmentation process. In order to use volume rendering, however, we must develop methods for assigning opacity and color to the data, and create a method to shade the data to improve the legibility of the rendering. Previous work introduced three such methods: barycentric opacity maps, hue-balls (for color), and lit-tensors (for shading). The paper expands on and generalizes these methods, describing and demonstrating further means of generating opacity, color, and shading from the tensor information. We also propose anisotropic reaction-diffusion volume textures as an additional tool for visualizing the structure of diffusion data. The patterns generated by this process can be visualized on their own or they can be used to supplement the volume rendering strategies described in the rest of the paper. Finally, because interpolation between data points is a fundamental issue in volume rendering, we conclude with a discussion and evaluation of three distinct interpolation methods suitable for diffusion tensor MRI data     

Shape evolution with structural and topological changes usingblending

This paper describes a framework for the estimation of shape from sparse or incomplete range data. It uses a shape representation called blending, which allows for the geometric combination of shapes into a unified model - selected regions of the component shapes are cut-out and glued together. Estimation of shape by this representation is realized using a physics-based framework, and it also includes a process for deciding how to adapt the structure and topology of the model to improve the fit. The blending representation helps avoid abrupt changes in model geometry during fitting by allowing the smooth evolution of the shape, which improves the robustness of the technique. We demonstrate this framework with a series of experiments showing its ability to automatically extract structured representations from range data given both structurally and topologically complex objects     

Topological methods for 2D time-dependent vector fields based on stream lines and path lines

This paper describes approaches to topologically segmenting 2D time-dependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines. Because of this, two segmentations are possible: either concerning the behavior of stream lines or of path lines. While topological features based on stream lines are well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology, we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations as well as a method of tracking all isolated closed stream lines. To get the path line oriented topology, we segment the vector field into areas of attracting, repelling, and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of test data sets.     

Locally supported tangential vector,n-vector,and tensor fields

We introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangential fields. Important features of our construction are that it is based on a general principle, from which constructions for different types of tangential fields can be derived, and that it is scalable, making it possible to efficiently compute and store large subspace bases for large meshes. Moreover, the construction is adaptive, which allows for controlling the distribution of the degrees of freedom of the subspaces over the surface. We evaluate our construction in several experiments addressing approximation quality, scalability, adaptivity, computation times and memory requirements. Our design choices are justified by comparing our construction to possible alternatives. Finally, we discuss examples of how subspace methods can be used to build interactive tools for tangential field design and processing tasks.     

Invariant analysis of CP violation

The invariant formulation of CP violation involves the generation of sets of invariant constraints for CP conservation, the manipulation of their expressions and the identification of complete and minimal subsets of such constraints. In this paper we present a collection of subroutines to deal with these tasks in a fast, reliable and systematic way, with examples for the leptonic sector.     

Invariant kernel functions for pattern analysis and machine learning

In many learning problems prior knowledge about pattern variations can be formalized and beneficially incorporated into the analysis system. The corresponding notion of invariance is commonly used in conceptionally different ways. We propose a more distinguishing treatment in particular in the active field of kernel methods for machine learning and pattern analysis. Additionally, the fundamental relation of invariant kernels and traditional invariant pattern analysis by means of invariant representations will be clarified. After addressing these conceptional questions, we focus on practical aspects and present two generic approaches for constructing invariant kernels. The first approach is based on a technique called invariant integration. The second approach builds on invariant distances. In principle, our approaches support general transformations in particular covering discrete and non-group or even an infinite number of pattern-transformations. Additionally, both enable a smooth interpolation between invariant and non-invariant pattern analysis, i.e. they are a covering general framework. The wide applicability and various possible benefits of invariant kernels are demonstrated in different kernel methods. Editor: Phil Long.     

Interactive exploration of tensor fields in geosciences using volume rendering

Volume rendering methods enable the user to explore interactively scalar data on regularly spaced three-dimensional grids. This article discusses how to use this method to explore and analyse three-dimensional tensor fields. The proposed visualization makes use of the programmability of modern graphics hardware and of “Line Integral Convolution”, a texture-based technique for the visualization of vector fields. While an example from geomechanics is used for presentation purposes, the rendering methods introduced are generic and would suit other application areas that involve volumetric data with several attributes equally well.     

Quantization of massive second- and third-rank antisymmetric tensor fields in curved space

We consider massive second- and third-rank antisymmetric tensor fields in arbitrary four-dimensional curved space-time. We perform quantization of these models and evaluation of the effective actions. The massive theories of antisymmetric tensor fields do not possess gauge invariance, which is inherent to massless antisymmetric models. To evaluate the effective actions, we restore gauge invariance in massive theories with the help of the Stückelberg multistep procedure. The result is presented in terms of d’Alembertians acting on a scalar, vector, second- and third-rank antisymmetric tensor fields.     

Discriminative optical flow tensor for video semantic analysis

This paper presents a novel framework for effective video semantic analysis. This framework has two major components, namely, optical flow tensor (OFT) and hidden Markov models (HMMs). OFT and HMMs are employed because: (1) motion is one of the fundamental characteristics reflecting the semantic information in video, so an OFT-based feature extraction method is developed to make full use of the motion information. Thereafter, to preserve the structure and discriminative information presented by OFT, general tensor discriminant analysis (GTDA) is used for dimensionality reduction. Finally, linear discriminant analysis (LDA) is utilized to further reduce the feature dimension for discriminative motion information representation; and (2) video is a sort of information intensive sequential media characterized by its context-sensitive nature, so the video sequences can be more effectively analyzed by some temporal modeling tools. In this framework, we use HMMs to well model different levels of semantic units (SU), e.g., shot and event. Experimental results are reported to demonstrate the advantages of the proposed framework upon semantic analysis of basketball video sequences, and the cross validations illustrate its feasibility and effectiveness.     

基于拓扑法的与时间相关二维矢量场的可视化

分析与时间相关二维矢量场可视化的拓扑法,并针对其在检测封闭流线时依赖网格以及不能对封闭流线精确定位的问题,进行改进。通过运用特征流场对临界点跟踪以及鞍状连接符对流面积分,提出一种检测封闭流线的方法。该方法不依赖于网格,解决了封闭流线精确定位的问题。实验结果表明本文提出的算法为与参数相关二维矢量场可视化提供一个基本框架。     

基于XGBoost与拓扑结构信息的蛋白质复合物识别算法

蛋白质相互作用(PPI)网络中存在大量不确定性及已知蛋白质复合物数据的不完整性,单独地根据结构信息进行搜索或对已知复合物进行监督学习的方法在识别蛋白质复合物的准确性上存在不足。对此,提出一种XGBoost模型与复合物拓扑结构信息相结合的搜索方法(XGBP)。首先,根据复合物拓扑结构信息进行特征提取;然后,把所提取的特征用XGBoost模型进行训练;最后,将拓扑结构信息与监督学习方法相结合,建立特征与复合物之间的映射关系以提高蛋白质复合物预测的准确性。该算法分别与目前流行的马尔可夫聚类算法(MCL)、极大团聚类方法(CMC)、基于核心-附属结构算法(COACH)、快速层级聚类算法(HC-PIN)、基于重叠邻居的扩展聚类(ClusterONE)、分子复合物检测算法(MCODE)、基于不确定图模型的蛋白质复合物检测方法(DCU)和加权核心-附属算法(WCOACH)这八种非监督学习算法和三种监督学习方法贝叶斯网络(BN)、支持向量机(SVM)、回归模型(RM)进行比较,所提方法在精准度、敏感度、F-measure方面显示出良好的性能。     

高选择性拓扑指数和网络上化学结构的检索系统

描述以高选择性拓扑指数EAID为基础构建的结构检索系统。此系统以EAID指数来表征化合物的结构,即每一化合物,运用EAID计算方案得到一个数学的量,以此为基础,来进行化合物结构的检索。由于是一简单数据的比较,所以检索准确快捷,适合于网络传输和交流。现已成功地应用于检索本实验室的结构数据库。另外,文中还介绍了EAID的算法和验证。     

General tensor discriminant analysis and gabor features for gait recognition

The traditional image representations are not suited to conventional classification methods, such as the linear discriminant analysis (LDA), because of the under sample problem (USP): the dimensionality of the feature space is much higher than the number of training samples. Motivated by the successes of the two dimensional LDA (2DLDA) for face recognition, we develop a general tensor discriminant analysis (GTDA) as a preprocessing step for LDA. The benefits of GTDA compared with existing preprocessing methods, e.g., principal component analysis (PCA) and 2DLDA, include 1) the USP is reduced in subsequent classification by, for example, LDA; 2) the discriminative information in the training tensors is preserved; and 3) GTDA provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of GTDA converges, while that of 2DLDA does not.We use human gait recognition to validate the proposed GTDA. The averaged gait images are utilized for gait representation. Given the popularity of Gabor function based image decompositions for image understanding and object recognition, we develop three different Gabor function based image representations: 1) the GaborD representation is the sum of Gabor filter responses over directions, 2) GaborS is the sum of Gabor filter responses over scales, and 3) GaborSD is the sum of Gabor filter responses over scales and directions. The GaborD, GaborS and GaborSD representations are applied to the problem of recognizing people from their averaged gait images.A large number of experiments were carried out to evaluate the effectiveness (recognition rate) of gait recognition based on first obtaining a Gabor, GaborD, GaborS or GaborSD image representation, then using GDTA to extract features and finally using LDA for classification. The proposed methods achieved good performance for gait recognition based on image sequences from the USF HumanID Database. Experimental comparisons are made with nine state of the art classification methods in gait recognition.