二维流形上一组等距与尺度不变的形状描述子

在流形上构造了一组具有等距不变与尺度不变的形状描述子.该方法首先利用Biharmonic距离构造核函数,然后利用勒贝格积分构造具有等距不变的描述子,再利用曲面的勒贝格测度对形状描述子进行标准化,得到了一组新的描述子.这种新的形状描述子既具有等距不变性,又具有尺度不变性,反映了几何形状的内蕴性质.在非刚体模型上进行了大量实验,通过实验结果可以看出,该方法对于发生等距变形的物体具有很好的识别和区分效果.     

On the Repeatability and Quality of Keypoints for Local Feature-based 3D Object Retrieval from Cluttered Scenes

3D object recognition from local features is robust to occlusions and clutter. However, local features must be extracted from a small set of feature rich keypoints to avoid computational complexity and ambiguous features. We present an algorithm for the detection of such keypoints on 3D models and partial views of objects. The keypoints are highly repeatable between partial views of an object and its complete 3D model. We also propose a quality measure to rank the keypoints and select the best ones for extracting local features. Keypoints are identified at locations where a unique local 3D coordinate basis can be derived from the underlying surface in order to extract invariant features. We also propose an automatic scale selection technique for extracting multi-scale and scale invariant features to match objects at different unknown scales. Features are projected to a PCA subspace and matched to find correspondences between a database and query object. Each pair of matching features gives a transformation that aligns the query and database object. These transformations are clustered and the biggest cluster is used to identify the query object. Experiments on a public database revealed that the proposed quality measure relates correctly to the repeatability of keypoints and the multi-scale features have a recognition rate of over 95% for up to 80% occluded objects.     

Complete Tensor Field Topology on 2D Triangulated Manifolds embedded in 3D

This paper is concerned with the extraction of the surface topology of tensor fields on 2D triangulated manifolds embedded in 3D. In scientific visualization topology is a meaningful instrument to get a hold on the structure of a given dataset. Due to the discontinuity of tensor fields on a piecewise planar domain, standard topology extraction methods result in an incomplete topological skeleton. In particular with regard to the high computational costs of the extraction this is not satisfactory. This paper provides a method for topology extraction of tensor fields that leads to complete results. The core idea is to include the locations of discontinuity into the topological analysis. For this purpose the model of continuous transition bridges is introduced, which allows to capture the entire topology on the discontinuous field. The proposed method is applied to piecewise linear three‐dimensional tensor fields defined on the vertices of the triangulation and for piecewise constant two or three‐dimensional tensor fields given per triangle, e.g. rate of strain tensors of piecewise linear flow fields.     

Mandatory Critical Points of 2D Uncertain Scalar Fields

This paper introduces a novel, non‐local characterization of critical points and their global relation in 2D uncertain scalar fields. The characterization is based on the analysis of the support of the probability density functions (PDF) of the input data. Given two scalar fields representing reliable estimations of the bounds of this support, our strategy identifies mandatory critical points: spatial regions and function ranges where critical points have to occur in any realization of the input. The algorithm provides a global pairing scheme for mandatory critical points which is used to construct mandatory join and split trees. These trees enable a visual exploration of the common topological structure of all possible realizations of the uncertain data. To allow multi‐scale visualization, we introduce a simplification scheme for mandatory critical point pairs revealing the most dominant features. Our technique is purely combinatorial and handles parametric distribution models and ensemble data. It does not depend on any computational parameter and does not suffer from numerical inaccuracy or global inconsistency. The algorithm exploits ideas of the established join/split tree computation. It is therefore simple to implement, and its complexity is output‐sensitive. We illustrate, evaluate, and verify our method on synthetic and real‐world data.     

Hierarchical Correlation Clustering in Multiple 2D Scalar Fields

Sets of multiple scalar fields can be used to model many types of variation in data, such as uncertainty in measurements and simulations or time‐dependent behavior of scalar quantities. Many structural properties of such fields can be explained by dependencies between different points in the scalar field. Although these dependencies can be of arbitrary complexity, correlation, i.e., the linear dependency, already provides significant structural information. Existing methods for correlation analysis are usually limited to positive correlation, handle only local dependencies, or use combinatorial approximations to this continuous problem. We present a new approach for computing and visualizing correlated regions in sets of 2‐dimensional scalar fields. This paper describes the following three main contributions: (i) An algorithm for hierarchical correlation clustering resulting in a dendrogram, (ii) a generalization of topological landscapes for dendrogram visualization, and (iii) a new method for incorporating negative correlation values in the clustering and visualization. All steps are designed to preserve the special properties of correlation coefficients. The results are visualized in two linked views, one showing the cluster hierarchy as 2D landscape and the other providing a spatial context in the scalar field's domain. Different coloring and texturing schemes coupled with interactive selection support an exploratory data analysis.     

Injectivity Conditions of 2D and 3D Uniform Cubic B-Spline Functions

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is crucial to obtaining desirable results in these areas. This paper considers the injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric interpretation of the injectivity of a uniform cubic B-spline function, with which 2D and 3D cases can be handled in a similar way. Based on our geometric interpretation, we present sufficient conditions for injectivity which are represented in terms of control point displacements. These sufficient conditions can be easily tested and will be useful in guaranteeing the injectivity of mapping functions in application areas.     

基于二维局部鉴别高斯的特征提取方法

特征提取是人脸识别的关键。特征提取方法一般需要预先把二维图像转化成一维图像向量。然而高维的图像向量会导致不能快速、精确地计算所需的协方差矩阵及其特征向量。针对该问题,提出了一种基于二维局部鉴别高斯的特征提取方法(2D-LDG)。该方法继承一维局部鉴别高斯降维方法的优点,其目标函数是留一交叉验证误差的光滑逼近,并且只考虑训练样本的局部分布,对训练样本的全局分布不做任何假设。同时,2D-LDG直接对二维图像做特征提取,不需要事先把图像转化为维数巨大的图像向量,能快速、精确地计算协方差矩阵及其特征向量。在ORL、YaleB人脸数据库上的实验结果表明,2D-LDG特征提取方法有良好的识别效果。     

三维标量场并行等值面提取与绘制技术

通过研究并行等值面提取与绘制的各项关键技术要点,面向三维标量场的特点,在sort-last并行绘制模式的基础上提出一个三维标量场并行等值面提取与绘制框架.该框架在任务分配时采用静态分配的模式,在等值面提取时采用Marching Tetrahedra等值面提取算法,在并行绘制与场景合成时采用预先构建绘制节点控制模型的混合场景并行绘制合成算法.实验结果表明,该框架能够有效地提高大规模时变三维标量场的等值面提取与绘制效率,满足实际应用的需要.     

非刚性三维形状匹配中基于谱分析的形状描述符综述

基于谱分析的形状描述符在非刚性三维形状匹配中取得了较好的匹配效果，引起了研究者的广泛关注.谱分析是基于流形上拉普拉斯贝尔特拉米算子谱分解的一种内蕴形状分析方法.谱形状描述符和谱距离分布函数是最主要的两类谱分析形状描述符，它们具有不同的数学性质和物理意义.基于两类不同的形状描述符，给出了详细的方法分析及其在形状匹配中的应用.首先，给出了应用基于谱分析的形状描述符的非刚性三维形状匹配框架，介绍了几种常用的谱形状描述符及谱距离分布函数的基本思想和计算方法；然后，分析比较了这些形状描述符的优缺点及应用场景，为研究者选择基于谱分析的形状描述符提供参考；最后，通过实验对比了不同基于谱分析的形状描述符的算法鲁棒性、时间耗费及非刚性匹配性能，以此推动谱分析形状描述符的应用进程.     

Computing Contour Trees for 2D Piecewise Polynomial Functions

Contour trees are extensively used in scalar field analysis. The contour tree is a data structure that tracks the evolution of level set topology in a scalar field. Scalar fields are typically available as samples at vertices of a mesh and are linearly interpolated within each cell of the mesh. A more suitable way of representing scalar fields, especially when a smoother function needs to be modeled, is via higher order interpolants. We propose an algorithm to compute the contour tree for such functions. The algorithm computes a local structure by connecting critical points using a numerically stable monotone path tracing procedure. Such structures are computed for each cell and are stitched together to obtain the contour tree of the function. The algorithm is scalable to higher degree interpolants whereas previous methods were restricted to quadratic or linear interpolants. The algorithm is intrinsically parallelizable and has potential applications to isosurface extraction.     

Cryptographic Hardness of Random Local Functions

Constant parallel-time cryptography allows to perform complex cryptographic tasks at an ultimate level of parallelism, namely by local functions that each of their output bits depend on a constant number of input bits. A natural way to obtain local cryptographic constructions is to use random local functions in which each output bit is computed by applying some fixed d-ary predicate P to a randomly chosen d-size subset of the input bits.In this work, we will study the cryptographic hardness of random local functions. In particular, we will survey known attacks and hardness results, discuss different flavors of hardness (one-wayness, pseudorandomness, collision resistance, public-key encryption), and mention applications to other problems in cryptography and computational complexity. We also present some open questions with the hope to develop a systematic study of the cryptographic hardness of local functions.     

3D Face Recognition Using a Fusion of PCA and ICA Convolution Descriptors

Neural Processing Letters - This paper introduces a hybrid filter bank-based convolutional network to develop a 3D face recognition system in different orientations. The filter banks approach has...     

Precision,Local Search and Unimodal Functions

We investigate the effects of precision on the efficiency of various local search algorithms on 1-D unimodal functions. We present a (1+1)-EA with adaptive step size which finds the optimum in O(log n) steps, where n is the number of points used. We then consider binary (base-2) and reflected Gray code representations with single bit mutations. The standard binary method does not guarantee locating the optimum, whereas using the reflected Gray code does so in Θ((log n)²) steps. A(1+1)-EA with a fixed mutation probability distribution is then presented which also runs in O((log n)²). Moreover, a recent result shows that this is optimal (up to some constant scaling factor), in that there exist unimodal functions for which a lower bound of Ω((log n)²) holds regardless of the choice of mutation distribution. For continuous multimodal functions, the algorithm also locates the global optimum in O((log n)²). Finally, we show that it is not possible for a black box algorithm to efficiently optimise unimodal functions for two or more dimensions (in terms of the precision used).