Convex Hodge Decomposition and Regularization of Image Flows

The total variation (TV) measure is a key concept in the field of variational image analysis. In this paper, we focus on vector-valued data and derive from the Hodge decomposition of image flows a definition of TV regularization for vector-valued data that extends the standard componentwise definition in a natural way. We show that our approach leads to a convex decomposition of arbitrary vector fields, providing a richer decomposition into piecewise harmonic fields rather than piecewise constant ones, and motion texture. Furthermore, our regularizer provides a measure for motion boundaries of piecewise harmonic image flows in the same way, as the TV measure does for contours of scalar-valued piecewise constant images.

物体变形的广义形态变换方法

将广义形态变换理论用于非刚体运动的描述和内插,通过对非刚体的凸剖分把非刚体的运动分解为非刚体的变形与子凸集的旋转,提出物体近似骨架的概念;通过近似骨架实现子凸集匹配,实现了任意非同拓扑结构(包括有孔及凹多面体)物体的变形．广义形态变换具有基于体元的变形方法和基于边界形状的变形方法的优点,同时克服了它们的缺点．实验表明,该方法变形物体边界光滑、定位精度高、计算速度快,可应用于CAD、虚拟现实和生物医学工程。     

Improved Approximation Algorithm for Convex Recoloring of Trees

A pair (T,C) of a tree T and a coloring C is called a colored tree. Given a colored tree (T,C) any coloring C′ of T is called a recoloring of T. Given a weight function on the vertices of the tree the recoloring distance of a recoloring is the total weight of recolored vertices. A coloring of a tree is convex if for any two vertices u and v that are colored by the same color c, every vertex on the path from u to v is also colored by c. In the minimum convex recoloring problem we are given a colored tree and a weight function and our goal is to find a convex recoloring of minimum recoloring distance. The minimum convex recoloring problem naturally arises in the context of phylogenetic trees. Given a set of related species the goal of phylogenetic reconstruction is to construct a tree that would best describe the evolution of this set of species. In this context a convex coloring corresponds to perfect phylogeny. Since perfect phylogeny is not always possible the next best thing is to find a tree which is as close to convex as possible, or, in other words, a tree with minimum recoloring distance. We present a (2+ε)-approximation algorithm for the minimum convex recoloring problem, whose running time is O(n ²+n(1/ε)²4^1/ε ). This result improves the previously known 3-approximation algorithm for this NP-hard problem. We also present an algorithm for computing an optimal convex recoloring whose running time is , where n ^* is the number of colors that violate convexity in the input tree, and Δ is the maximum degree of vertices in the tree. The parameterized complexity of this algorithm is O(n ²+n⋅k⋅2 ^k ).     

基于GPU的多层次并行QR分解算法研究

QR分解作为一个基本计算模块,广泛应用在图像处理、信号处理、通信工程等众多领域.传统的并行QR分解算法只能挖掘计算过程中的数据级并行.在分析快速Givens Rotation分解特征的基础上,提出了一种多层次并行算法,能够同时挖掘计算过程中的任务级并行和数据级并行,非常适合于以图形处理器(GPU)为代表的大规模并行处理器.同时,采用GPU的并行QR分解算法可以作为基本运算模块被GPU平台上的众多应用程序直接调用.实验结果显示,与CPU平台上使用OpenMP实现的算法相比,基于GPU的多层次并行算法能够获得5倍以上的性能提升,而调用QR分解模块的奇异值分解(SVD)应用可以获得3倍以上的性能提升.     

大型网络的SKT可靠性的分散计算法

提出了一种基于分解法的计算大型网络从源点到特定节点集K(即SKT)可靠性的算法。按照一定的分解规则将大型网络划分为若干较小规模的子网络,从而最终将枚举原网络的K树这一复杂问题转化为计算这些子网络的最小路。对求得的K树进行不交化运算,最终得到网络的SKT可靠性。     

Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition

The need to perform fast and accurate proximity queries arises frequently in physically-based modeling, simulation, animation, real-time interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approximate minimum distance computation, and (disjoint) contact determination. Specialized data structures and algorithms have often been designed to perform each type of query separately. We present a unified approach to perform any of these queries seamlessly for general, rigid polyhedral objects with boundary representations which are orientable 2-manifolds. The proposed method involves a hierarchical data structure built upon a surface decomposition of the models. Furthermore, the incremental query algorithm takes advantage of coherence between successive frames. It has been applied to complex benchmarks and compares very favorably with earlier algorithms and systems.     

基于奇异值分解的量化水印盲检算法

提出了一种基于奇异值分解的量化水印盲检算法.利用图像矩阵的奇异值稳定性好且最大奇异值远远大于其他奇异值的特点,首先时分块图像最大奇异值进行量化,再结合其奇偶性将二值水印嵌入量化后的奇异值中.实验结果表明,水印算法在满足较好的不可见性和较强的鲁棒性的同时;还可实现水印的盲提取.     

Fast and intuitive generation of geometric shape transitions

We describe a novel method for continuously transforming two triangulated models of arbitrary topology into each other. Equal global topology for both objects is assumed. However, extensions for genus changes during metamorphosis are provided. The proposed method addresses the major challenge in 3D metamorphosis, namely, specifying the morphing process intuitively with minimal user interaction and sufficient detail. Corresponding regions and point features are interactively identified. These regions are parametrized automatically and consistently, providing a basis for smooth interpolation. Suitable 3D interaction techniques offer a simple and intuitive control over the whole morphing process.     

Determining Generative Models of Objects Under Varying Illumination: Shape and Albedo from Multiple Images Using SVD and Integrability

We describe a method of learning generative models of objects from a set of images of the object under different, and unknown, illumination. Such a model allows us to approximate the objects' appearance under a range of lighting conditions. This work is closely related to photometric stereo with unknown light sources and, in particular, to the use of Singular Value Decomposition (SVD) to estimate shape and albedo from multiple images up to a linear transformation (Hayakawa, 1994). Firstly we analyze and extend the SVD approach to this problem. We demonstrate that it applies to objects for which the dominant imaging effects are Lambertian reflectance with a distant light source and a background ambient term. To determine that this is a reasonable approximation we calculate the eigenvectors of the SVD on a set of real objects, under varying lighting conditions, and demonstrate that the first few eigenvectors account for most of the data in agreement with our predictions. We then analyze the linear ambiguities in the SVD approach and demonstrate that previous methods proposed to resolve them (Hayakawa, 1994) are only valid under certain conditions. We discuss alternative possibilities and, in particular, demonstrate that knowledge of the object class is sufficient to resolve this problem. Secondly, we describe the use of surface consistency for putting constraints on the possible solutions. We prove that this constraint reduces the ambiguities to a subspace called the generalized bas relief ambiguity (GBR) which is inherent in the Lambertian reflectance function (and which can be shown to exist even if attached and cast shadows are present (Belhumeur et al., 1997)). We demonstrate the use of surface consistency to solve for the shape and albedo up to a GBR and describe, and implement, a variety of additional assumptions to resolve the GBR. Thirdly, we demonstrate an iterative algorithm that can detect and remove some attached shadows from the objects thereby increasing the accuracy of the reconstructed shape and albedo.     

Convex rear view mirrors compromise distance and time-to-contact judgements

Convex rear view mirrors increasingly replace planar mirrors in automobiles. While increasing the field of view, convex mirrors are also taken to increase distance estimates and thereby reduce safety margins. However, this study failed to replicate systematic distance estimation errors in a real world setting. Whereas distance estimates were accurate on average, convex mirrors lead to significantly more variance in distance and spacing estimations. A second experiment explored the effect of mirrors on time-to-contact estimations, which had not been previously researched. Potential effects of display size were separated from effects caused by distortion in convex mirrors. Time-to-contact estimations without a mirror were most accurate. However, not distortion, but visual angle seemed to cause estimation biases. Evaluating advantages and disadvantages of convex mirrors is far more complex than expected so far.     

基于DCT域奇异值分解的图像检索技术

提出一种在DCT域获取图像的代数特征--SV特征矢量进行图像检索的方法.在图像解压到量化的DCT域时,提取粗糙纹理矩阵Ⅰ,对Ⅰ进行奇异值分解,根据图片库的特点选取部分或全部奇异值表征图像的纹理特征,试验了该特征提取技术在图像检索中的应用.     

Decomposition and intersection of simple splinegons

A splinegon is a polygon whose edges have been replaced by well-behaved curves. We show how to decompose a simple splinegon into a union of monotone pieces and into a union of differences of unions of convex pieces. We also show how to use a fast triangulation algorithm to test whether two given simple splinegons intersect. We conclude with examples of splinegons that make the extension of algorithms from polygons to splinegons difficult.Work on this paper by David A. Dobkin and Diane L. Souvaine was partially supported by National Science Foundation Grants MCS 83-03926 and DCR 85-05517. Diane L. Souvaine was also partially supported by an Exxon Foundation Fellowship.     

R~m凸域包含与相交性判定的一个线性规划算法

该文提出了凸域包含与相交性判定的一个新的基于线性规划的分析型算法。该算法具有通用性,适用于任意维欧氏空间凸域的包含与相交性判定;且由于利用了成熟的线性规划方法,效率亦较高,文中研究了凸域包含与相交问题的两种线性规划表述形式,并考察了它们之间的关系,给出了算法的实现策略。     

基于小波分解和互信息的图像配准方法

根据小波分解和互信息测度的原理,提出一种快速的图像配准方法。首先,对原图像进行小波分解,在保证配准精度下对分解图像进行灰度压缩,以减少配准参数的计算量,并利用最大互信息准则和下降单纯形的搜索策略找到最优配准参数实现图像配准。实验结果表明,这种图像配准方法能在保证配准精度条件下,提高配准的速度。     

Decomposition of vegetation cover into woody and herbaceous components using AVHRR NDVI time series

A method is developed to separate Normalised Difference Vegetation Index (NDVI) time series data into contributions from woody (perennial) and herbaceous (annual) vegetation, and thereby to infer their separate leaf area indices and cover fractions. The method is formally consistent with fundamental linearity requirements for such a decomposition, and is capable of rejecting contaminated NDVI data. In this study, estimates of annual averaged woody cover and monthly averaged herbaceous cover over Australia are determined using Pathfinder AVHRR Land series (PAL) Global Area Coverage (GAC) Advanced Very High Resolution Radiometer (AVHRR) NDVI data from 1981 to 1994, together with ground-based measurements of leaf area index (LAI) and foliage projective cover (FPC).     

几何约束有向图的规划分解研究

在基于有向图表达的几何约束系统中,几何约束的匹配方向、分布状态以及有向图中强连通分量的规模直接影响到整个约束系统的求解;如何对几何约束系统进行合理规划,得到正确有效的求解序列,是目前约束分解研究的重要内容。该文提出了一个规划分解算法,它针对欠约束几何系统的特点,能够优化约束的初始匹配方向,对于约束匹配过程中生成的强连通子图,通过调整约束匹配方向,自适应地改善约束分布,从而减小强连通子图的规模,以求得到几何约束系统正确而高效的求解序列。同时,基于规划分解算法,完成了约束的奇异性分析,提供了面向分解的奇异性分析算法。     

前馈神经网络凸优化算法及其仿真应用

该文利用凸函数共轭性质中的Young不等式构造前馈神经网络优化目标函数。这个优化目标函数若固定权值,对隐层输出来说为凸函数;若固定隐层输出,对权值来说为凸函数。因此,此目标函数不存在局部最小。此目标函数的优化速度快,大大提高了前馈神经网络的学习效率。仿真试验表明,与传统算法如误差反向传播算法或BP算法和含势态因子(Momentum factor)的BP算法及现有的分层优化算法相比,新算法能加快收敛速度,并降低学习误差。利用这种快速算法对矿体进行仿真预测,取得了良好效果。     

图像目标外接多边形及凸壳的一种构造方法

对二值图像进行Hough变换后,在(ρ,θ)空间中选取了一组边界对应点,通过计算与这些边界对应点对应的图像空间中直线的交点,构造了图像目标的外接多边形;通过比较相距π/2 rad的投影区间长度是否相等,或区间长度的乘积是否为最小,得到了形状外接正方形和外接最小面积矩形;利用构造形状外接多边形的方法并通过增加边的数目,构造了形状的近似凸壳.实验和理论分析表明,文中算法具有好的抗噪性能和广泛的适用范围.     

Sweeping体的拓扑结构与精确B—Rep反算策略

本文根据五种造型法则:平行扫法则、回转扫法则、箱体法则、异形体法则和曲面立体法则的离散化原理,提出了Sweeping体的拓扑结构的生成方法。讨论了离散化多面体边界的几何属性码和CSG-索引方法,以及基于这种几何属性码和CSG-索引的精确B-Rep反算策略。