AGRELs and BIPs: Metamorphosis as a Bezier curve in the space of polyhedra

The metamorphosis between two user-specified objects offers an intuitive metaphor for designing animations of deforming shapes. We present a new technique for interactively editing such deformations and for animating them in realtime. Besides the starting and ending shapes, our approach offers easy to use additional control over the deformations. The new Bezier Interpolating Polyhedron (BIP) provides a graphics representation of such a deforming object formulated mathematically as a point describing a Bezier curve in the space of all polyhedra. We replace, in the Bezier formulation, the traditional control points by arbitrary polyhedra and the vector addition by the Minkowski sum. BIPs are composed of Animated GRaphic ELement (AGRELs), which are faces with constant orientation, but with parametrized vertices represented by Bezier curves. AGRELs were designed to efficiently support smooth realtime animation on commercially available rendering hardware. We provide a tested algorithm for automatically computing BIPs from the sequence of control polyhedra and demonstrate its applications to animation design.     

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DC规划的鲁棒模糊核聚类算法

对以径向基核函数和欧拉核函数为代表的鲁棒模糊核聚类算法进行非凸优化,以改善聚类算法目标函数非凸导致的局部解问题.采用凸差规划(DCP)将目标函数转化为2个凸函数之差的形式,减缓局部解的不良性,提高聚类性能.采用凸差算法(DCA)优化求解DCP问题,能快速搜索到相对更优的解,并保持聚类的鲁棒性.在UCI数据集上的实验验证基于DCP的鲁棒模糊核聚类算法对大规模数据集表现出相对更优的聚类性能.     

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。     

ITD在语音情感识别中的研究

为了更好地表征语音情感状态,将固有时间尺度分解（ITD）用于语音情感特征提取。从语音信号中得到前若干阶合理旋转（PR）分量,并提取PR分量的瞬时参数特征和关联维数,以此作为新的情感特征参数,结合传统特征使用支持向量机（SVM）进行语音情感识别实验。实验结果显示,引入PR特征参数后,与传统特征的方案相比,情感识别率有了明显提高。     

一种改进的基于分解的多目标进化算法

利用基于分解的多目标进化算法框架(MOEA/D),将混合策略的进化算法用于求解分解后的若干单目标优化子问题,提出了一种带局部搜索的基于分解的多目标混合策略进化算法(LMS-MOEA/D)。算法利用均匀设计产生子问题的聚合权重向量,混合交叉策略能够充分利用不同交叉算子的优势;同时算法针对演化过程收敛的特点,结合局部搜索策略,获得逼近Pareto前沿的最优解集。最后通过实验验证算法在多样性和收敛性方面的有效性。     

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.     

基于代数视角的凸壳及其特性同构化研究

现行凸壳算法通常是基于凸壳几何特性的视角来求解凸壳顶点,主要适用于求解低维几何空间凸壳问题.因高维空间凸壳的几何关系极为复杂,故研究、设计、提高求解高维几何空间凸壳的算法效率难度较大.考虑到几何与代数有着天然的本质联系,进而基于代数视角来研究凸壳问题,并给出了凸壳顶点的代数定义,研究了凸壳顶点若干代数性质;从而,为探索从代数视度来研究和设计求解高维几何空间凸壳算法提供某些基础理论与创新思路.     

三维形体的形态学运算及应用

本文首先讨论了边界表示的物体的形态学运算问题。文中讨论了任意形状的物体，包括凸物体和非凸物体；引入了负形体的概念；并提出了２Ｄ和３Ｄ连续物体的Ｍｉｎｋｏｗｓｋｉ运算的统一算法。利用这一算法，提出了３Ｄ任意形体间的变形新算法，把边界表示的物体的形态学运算的概念扩展到任意曲线和任意曲面上，并且介绍了３Ｄ物空间中曲线的概念和３Ｄ物空间双参数曲面的概念。文中任意形体的３Ｄ变形算法能很好地解决具有不同拓扑结构的３Ｄ边界表示的物体之间的变形问题。     

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.     

基于边/面遮挡关联性的多面体凸剖分方法

提出一种多面体凸剖分的方法,与国际上已有的工作相比,在计算速度、空间需求和新增顶点等方面均降低了复杂度,有大幅的效率提高,且在处理凹边很多的多面体时具有更大的优越性.其工作步骤是根据多面体的面、边沿某些方向正投影时面与面之间、边与边之间的遮挡关系进行局部化操作,以渐进地凸剖分多面体.它对应用中的常见模型表现出的时间复杂度、空间复杂度皆近似为O(n),而新点数不超过O(r n~(0.5)),这里,n为模型的点数,r为凹边数.实验结果表明,与目前国际上常用的"切割分裂"方法相比,新方法的速度提高了14～120倍,空间下降至"切割分裂"方法的1/2.3～1/7.4,而新增加的点数则最多为"切割分裂"方法的1/28,甚至有些情况下无须增加新点就能完成凸剖分.新方法剖分出的凸多面体绝大多数是四面体,多于"切割分裂"方法所得凸多面体数量.但是,很多应用是要求多面体被剖分为四面体的.如果进一步将凸多面体四面体化,则新方法的结果个数将明显少于"切割分裂"方法,因为新方法的剖分过程中所增加的新点要少很多.新方法还能方便地处理包含空洞的多面体,甚至是包含孤立面、孤立边和孤立点的非流形多面体.     

利用信息融合技术的缺损目标识别方法

拐点不变量是局部不变量的一种,具有旋转,平移,尺度缩放不变性,可以有效地应用于目标,该文利用Ｄｅｍｐｓｔｅｒ－Ｓｈａｆｅｒ证据推理法,将用不同方法求取拐点特征所得到的决策层信息进行融合,进一步提高了识别系统的可靠性,通过仿真实验对该方法进行了验证。     

Convex ensemble learning with sparsity and diversity

Classifier ensemble has been broadly studied in two prevalent directions, i.e., to diversely generate classifier components, and to sparsely combine multiple classifiers. While most current approaches are emphasized on either sparsity or diversity only, we investigate classifier ensemble focused on both in this paper. We formulate the classifier ensemble problem with the sparsity and diversity learning in a general mathematical framework, which proves beneficial for grouping classifiers. In particular, derived from the error-ambiguity decomposition, we design a convex ensemble diversity measure. Consequently, accuracy loss, sparseness regularization, and diversity measure can be balanced and combined in a convex quadratic programming problem. We prove that the final convex optimization leads to a closed-form solution, making it very appealing for real ensemble learning problems. We compare our proposed novel method with other conventional ensemble methods such as Bagging, least squares combination, sparsity learning, and AdaBoost, extensively on a variety of UCI benchmark data sets and the Pascal Large Scale Learning Challenge 2008 webspam data. Experimental results confirm that our approach has very promising performance.     

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.     

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.     

采用奇异值分解和信息增益的树突状细胞模型

针对树突状细胞算法(Dendritic Cell Algorithm,DCA)存在的信号提取过程中受人工经验影响和对无序数据的异常检测能力不强的问题,提出了采用奇异值分解(Singular Value Decomposition,SVD)和信息增益(Information Gain,IG)的树突状细胞模型——SIDCA...