Non-iterative approach for global mesh optimization

This paper presents a global optimization operator for arbitrary meshes. The global optimization operator is composed of two main terms, one part is the global Laplacian operator of the mesh which keeps the fairness and another is the constraint condition which reserves the fidelity to the mesh. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Our global mesh optimization approach can be effectively used in at least three applications: smoothing the noisy mesh, improving the simplified mesh, and geometric modeling with subdivision-connectivity. Many experimental results are presented to show the applicability and flexibility of the approach.     

投影算法与块匹配法结合的实时数字稳像方法

为了实时地稳定摄像系统的输出视频，特别是图像序列中存在运动物体的视频，提出了一种稳像方法.首先用灰度投影算法对图像序列进行粗匹配；然后用块匹配法在粗匹配的基础上进行精确匹配；最后将两次匹配得到的运动矢量相加得到最后的运动矢量，补偿图像序列的运动.进行匹配的小块是根据参考帧的拉普拉斯变换选取的.对实时稳像实验结果的定量分析和评价表明，该方法切实可行，并具有速度快、精度高的特点.     

保持拓扑结构的低维嵌入

引入了拓扑邻域、拓扑结构和规则拓扑结构的概念.对拓扑邻域进行了理论分析,说明其是自适应的,随着维数的不断升高,趋于平凡拓扑邻域.为了寻求具有规则拓扑结构的低维数据集,构造了数据结构规则性的度量,提出了保持数据集拓扑结构不变的降维方法.该方法是节省参数的,降维结果是近似规则的.结果表明,它能更好的揭示数据集的结构.     

Algebraic criteria for consensus problems of continuous-time networked systems

This article addresses algebraic criteria for consensus problems of continuous-time networked systems with fixed and switching topology. A special eigenvector ω of the Laplacian matrix is first constructed and correlated with the connectivity of digraph. And then, some necessary and/or sufficient algebraic conditions are presented by employing the vector ω, which can directly determine whether the consensus problem can be solved. More importantly, for the switching topology case, the obtained algebraic conditions for the average consensus problem are necessary and sufficient. Furthermore, the presented results clearly show that only the agents corresponding to the positive elements of ω contribute to the group decision value and decide the collective behaviour of the system. Particularly for the fixed topology case, the role of each agent is exactly measured by the value of the corresponding element of ω. Based on these results, some extended protocols are further proposed to solve the average consensus problem, in which the interaction digraphs are not needed to be balanced. Numerical examples are included to illustrate the obtained results.     

Towards a theoretical foundation for Laplacian-based manifold methods

In recent years manifold methods have attracted a considerable amount of attention in machine learning. However most algorithms in that class may be termed “manifold-motivated” as they lack any explicit theoretical guarantees. In this paper we take a step towards closing the gap between theory and practice for a class of Laplacian-based manifold methods. These methods utilize the graph Laplacian associated to a data set for a variety of applications in semi-supervised learning, clustering, data representation.We show that under certain conditions the graph Laplacian of a point cloud of data samples converges to the Laplace-Beltrami operator on the underlying manifold. Theorem 3.1 contains the first result showing convergence of a random graph Laplacian to the manifold Laplacian in the context of machine learning.     

An edge preserved image compression technique

An image compression technique that can preserve edges of objects is proposed here. This technique is developed by looking at small local regions of the image and classifying these regions as uniform, point, line or edge patterns from statistical likelihood ratio tests. The compression ratio depends on the size of the local region considered and the quality of the image will degrade as the size of the local region increases. Experimental results show good quality preservation when the sizes of the local region are 3 × 3, 4 × 4, 5 × 5 with the corresponding compression ratios less than or equal to 7/24, 1/5, 13/100 respectively. A comparison with discrete cosine transform is given here and shows that the new technique produces better quality in most cases.     

Preserving detailed features in digital bas-relief making

This paper presents a novel algorithm for digitally making bas-reliefs. The problem requires visibly retaining fine details present in original 3D objects while greatly compressing their depths to produce an almost planar result. Our approach performs compression on the gradient domain; gradients are first estimated from a height field representing the input scene. A new compression function based on arctangent is introduced to preserve desired details of reliefs, allowing accurate height adjustment via a data-dependent threshold. We explicitly consider how to preserve fine details present in the original objects, which is crucial for producing high-quality bas-reliefs. Laplacian coordinates are used to store detailed features before depth compression and then restore them afterwards. Laplacian sharpening is also used to emphasize detailed features in the relief itself. Prior to depth compression, we process the input height field to reduce gaps in height, and detect the outer silhouette which allows to compute the output relief relative to a planar background or other surface, by solving a Poisson equation. This combination of techniques allows our method to produce bas-reliefs with well-preserved details.     

Sparse spectral hashing

A better similarity index structure for high-dimensional feature datapoints is very desirable for building scalable content-based search systems on feature-rich dataset. In this paper, we introduce sparse principal component analysis (Sparse PCA) and Boosting Similarity Sensitive Hashing (Boosting SSC) into traditional spectral hashing for both effective and data-aware binary coding for real data. We call this Sparse Spectral Hashing (SSH). SSH formulates the problem of binary coding as a thresholding a subset of eigenvectors of the Laplacian graph by constraining the number of nonzero features. The convex relaxation and eigenfunction learning are conducted in SSH to make the coding globally optimal and effective to datapoints outside the training data. The comparisons in terms of F1 score and AUC show that SSH outperforms other methods substantially over both image and text datasets.     

分形双孔介质油气藏的试井分析模型解

针对分形双孔介质储层模型，对于裂缝介质和岩块介质分别引进了反映分形体几何特征的分形维数及分形渗流网络连通状况的分形指数；建立了外边界无穷大且考虑井筒储存和表皮效应下的变流率问题的试井分析数学模型；对一类具有广泛应用的特例，求得了无因次储层压力和井底压力的Laplace空间解，归纳出了一个通用公式，并对其进一步应用进行了讨论,对油藏数值模拟具有指导意义。 