平行线束法的仿射研究

用 3 个仿射图的投射方向构成 1 个仿射坐标系,同时也构成 1 个三棱锥,在此仿射坐标系中用球面三角重新研究由两个仿射图求第 3 个仿射图的投影作图理论 ——平行线束法。进一步还给出了由两个仿射图得到正投影的条件、由两个正投影得到第 3 个正投影的条件、以及由 V,H 两投影得到指定方向上的正投影的条件,简化了研究过程,得到了更简单的公式。     

Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

3D Motion Estimation and Motion Fusion by Affine Region Matching

In this paper,a new method is presented for 3D motion estimation by image region correspondences using stereo cameras.Under the weak perspectivity assumption.we first employ the moment tensor theory (Cyganski and Orr^[11]) to compute the monocular affine transformations relating images taken by the same camera at different time instants and the binocular affine transformations relating images taken by different cameras at the same time instant.We then show that 3D motion can be recovered from these 2D transformations.A space-time fusion strategy is proposed to aim at robust results.No knowledge of point correspondences if requred in the above processes and the computations involved are linear.To find corresponding image regions,new affine invariants,which show stronger invariance,are derived in term of tensor contraction theory.Experiments on real motion images are conducted to verify the proposed method.     

Threshold‐Based Camera Motion Characterization of MPEG Video

We propose an efficient scheme for camera motion characterization in MPEG‐compressed video. The proposed scheme detects six types of basic camera motions through threshold‐based qualitative interpretation, in which fixed thresholds are applied to motion model parameters estimated from MPEG motion vectors (MVs). The efficiency and robustness of the scheme are validated by the experiment with real compressed video sequences.     

Uniform modeling of parameter dependent nonlinear systems

This paper addresses the problem of approximating parameter dependent nonlinear systems in a unified framework. This modeling has been presented for the first time in the form of parameter dependent piecewise affine systems. In this model, the matrices and vectors defining piecewise affine systems are affine functions of parameters. Modeling of the system is done based on distinct spaces of state and parameter, and the operating regions are partitioned into the sections that we call ’multiplied simplices’. It is proven that this method of partitioning leads to less complexity of the approximated model compared with the few existing methods for modeling of parameter dependent nonlinear systems. It is also proven that the approximation is continuous for continuous functions and can be arbitrarily close to the original one. Next, the approximation error is calculated for a special class of parameter dependent nonlinear systems. For this class of systems, by solving an optimization problem, the operating regions can be partitioned into the minimum number of hyper-rectangles such that the modeling error does not exceed a specified value. This modeling method can be the first step towards analyzing the parameter dependent nonlinear systems with a uniform method.     

The analysis of global input-to-state stability for piecewise affine systems with time-delay

In this paper, global input-to-state stability (ISS) for discrete-time piecewise affine systems with time-delay are considered. Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhin and Lyapunov-Krasovskii methods are used. The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown, respectively.     

Some efficient solutions to the affine scheduling problem. Part II. Multidimensional time

This paper extends the algorithms which were developed in Part I to cases in which there is no affine schedule, i.e. to problems whose parallel complexity is polynomial but not linear. The natural generalization is to multidimensional schedules with lexicographic ordering as temporal succession. Multidimensional affine schedules, are, in a sense, equivalent to polynomial schedules, and are much easier to handle automatically. Furthermore, there is a strong connection between multidimensional schedules and loop nests, which allows one to prove that a static control program always has a multidimensional schedule. Roughly, a larger dimension indicates less parallelism. In the algorithm which is presented here, this dimension is computed dynamically, and is just sufficient for scheduling the source program. The algorithm lends itself to a divide and conquer strategy. The paper gives some experimental evidence for the applicability, performances and limitations of the algorithm.     

基于图像仿射不变特征点的零水印算法

本文提出了一种基于图像提升小波变换和仿射不变特征点的零水印算法。首先对图像进行3级提升小波变换,然后在低频部分,利用Harris-Affine算子提取出图像的仿射不变特征点和仿射协变特征区域,利用这些特征区域来构造零水印信息。实验证明,该算法不仅对常规信号处理攻击和简单的几何攻击具有很强的鲁棒性,对于剪切、纵横比改变、行列去除,局部扭曲等较复杂的几何攻击也具有较强的抵抗能力。     

基于不可分小波分解的图像配准方法

张量积小波强调的是图像中水平和垂直方向的高频信息,而不可分小波具有各向同性,可以提取图像中各个方向的边缘,能获得比较完整的图像轮廓,将这种特点应用于图像配准时,能准确定位图像仿射不变点的位置。为此,提出一种通过求取不可分小波分解后的高频子图像配准参数来配准原图像的方法,把图像的配准问题转化为其不可分小波分解后的高频子图像配准问题。从不可分小波分解的快速算法理论出发,证明该配准方法的正确性。构造一组四通道不可分小波滤波器组,在此基础上给出配准的方法和步骤。实验结果表明,该方法具有较好的配准效果,其求取图像配准参数的运算量比直接求取原图像配准参数运算量的1/4还少,与基于张量积小波分解的图像配准方法相比,具有较高的配准精度。     

与李代数A2相关的顶点算子代数N（k,0）及不可约模

介绍了仿射李代数A2的构造,并研究和构造了A2上Z＋-分次的顶点算子代数N（k,0）。再由A（V）理论算出了顶点算子代数L（1,0）不可约模L（1,μ）的分类情况。