ProcDef: Local‐to‐global Deformation for Skeleton‐free Character Animation

Animations of characters with flexible bodies such as jellyfish, snails, and, hearts are difficult to design using traditional skeleton‐based approaches. A standard approach is keyframing, but adjusting the shape of the flexible body for each key frame is tedious. In addition, the character cannot dynamically adjust its motion to respond to the environment or user input. This paper introduces a new procedural deformation framework (ProcDef) for designing and driving animations of such flexible objects. Our approach is to synthesize global motions procedurally by integrating local deformations. ProcDef provides an efficient design scheme for local deformation patterns; the user can control the orientation and magnitude of local deformations as well as the propagation of deformation signals by specifying line charts and volumetric fields. We also present a fast and robust deformation algorithm based on shape‐matching dynamics and show some example animations to illustrate the feasibility of our framework.     

沿参数曲面的均匀变形方法

基于参数曲面控制的物体自由变形是一项实用的技术，在已有的方法中，待变形物体被直接主控制曲面的参数空间，由于映射的非线性，导致物体变形同扭曲现象，本提出了一种基于参数曲面控制的均匀变形方法，新方法中，变形控制曲面首先以等距或局部等怕方式展开为平面，然后经由平面的线性映射，将待为形物体嵌入控制曲面的参数空间中，从而产生符合控制曲面形状的局部均匀变形，实验结果表明，本方法所产生的结果是令人满意的。     

Rigidity controllable as-rigid-as-possible shape deformation

Shape deformation is one of the fundamental techniques in geometric processing. One principle of deformation is to preserve the geometric details while distributing the necessary distortions uniformly. To achieve this, state-of-the-art techniques deform shapes in a locally as-rigid-as-possible (ARAP) manner. Existing ARAP deformation methods optimize rigid transformations in the 1-ring neighborhoods and maintain the consistency between adjacent pairs of rigid transformations by single overlapping edges. In this paper, we make one step further and propose to use larger local neighborhoods to enhance the consistency of adjacent rigid transformations. This is helpful to keep the geometric details better and distribute the distortions more uniformly. Moreover, the size of the expanded local neighborhoods provides an intuitive parameter to adjust physical stiffness. The larger the neighborhood is, the more rigid the material is. Based on these, we propose a novel rigidity controllable mesh deformation method where shape rigidity can be flexibly adjusted. The size of the local neighborhoods can be learned from datasets of deforming objects automatically or specified by the user, and may vary over the surface to simulate shapes composed of mixed materials. Various examples are provided to demonstrate the effectiveness of our method.     

SR-SIHKS：一种非刚体全局形状特征

非刚体由于姿态变化会产出多样的形变,因此非刚体的形状检索比刚体更具挑战性。形状特征提取是非刚体三维模型形状检索的关键问题。为了提高非刚体形状检索的准确度,提出了一种非刚体全局形状特征提取方法。此方法的核心思想是将稀疏表示（Sparse Representation,SR）理论用于对尺度无关的热核特征（Scale Invariant Heat Kernel Signature,SIHKS）进行稀疏编码,因此被称为SR-SIHKS。改进了SIHKS局部特征的提取方法,根据所处理的模型库来自适应地确定热扩散时间参数;采用K-SVD算法来训练字典,借助Batch-OMP算法实现局部特征的稀疏编码;将非刚体三维模型的所有局部特征的稀疏编码汇聚为全局形状特征。实验结果表明,SR-SIHKS具有比SIHKS和HKS更优的检索效果。     

Free-form deformation with weighted T-spline

A new method of free-form deformation, w-TFFD, is proposed, for which an original shape is deformed using weighted T-spline volumes. We generalize T-splines to weighted T-spline volumes that also permit T-junctions. Weighted T-spline volumes are a natural generalization of NURBS volumes but permit more flexible control lattices. Thus, w-TFFD holds many virtues of traditional FFDs and is more adaptive to objects with arbitrary topology or complex shape. The lattices can be automatically generated and approximate the shape of the object arbitrarily close by octree subdivision.Besides constructing and deforming a multiresolution lattice, users can also sculpt specific local details to their required shape by modifying weights. A set of direct-acting tools that are similar to previously proposed techniques can be applied to w-TFFD.     

基于集成深度学习的玻璃缺陷识别方法

针对玻璃缺陷形态复杂多变,难以准确识别其所属类型的特点,文章提出了一种集成深度学习模型对玻璃缺陷进行识别,该模型本质上是一种稀疏编码分类器与深度卷积神经网络的结合。该模型在自编码器的基础上引进了KL距离和L1范数作为稀疏项,构成新的稀疏自编码器。并在次通过稀疏自编码器学习输入样本特征,将训练好的权值作为卷积神经网络的卷积核从而提高了识别速度。在稀疏编码阶段用L<sub>1</sub>-L<sub>2</sub>范数代替L<sub>0</sub>范数,并在KSVD上添加了判别分类能力使其更好的进行分类运算,以此提高识别准确率。实验结果表明,该方法识别准确率达到了95%,满足了工程上的应用,并有很好的鲁棒性。     

An efficient large deformation method using domain decomposition

Efficiently simulating large deformations of flexible objects is a challenging problem in computer graphics. In this paper, we present a physically based approach to this problem, using the linear elasticity model and a finite elements method. To handle large deformations in the linear elasticity model, we exploit the domain decomposition method, based on the observation that each sub-domain undergoes a relatively small local deformation, involving a global rigid transformation. In order to efficiently solve the deformation at each simulation time step, we pre-compute the object responses in terms of displacement accelerations to the forces acting on each node, yielding a force–displacement matrix. However, the force–displacement matrix could be too large to handle for densely tessellated objects. To address this problem, we present two methods. The first method exploits spatial coherence to compress the force-displacement matrix using the clustered principal component analysis method; and the second method pre-computes only the force–displacement vectors for the boundary vertices of the sub-domains and resorts to the Cholesky factorization to solve the acceleration for the internal vertices of the sub-domains. Finally, we present some experimental results to show the large deformation effects and fast performance on complex large scale objects under interactive user manipulations.     

Spectral Affine‐Kernel Embeddings

In this paper, we propose a controllable embedding method for high‐ and low‐dimensional geometry processing through sparse matrix eigenanalysis. Our approach is equally suitable to perform non‐linear dimensionality reduction on big data, or to offer non‐linear shape editing of 3D meshes and pointsets. At the core of our approach is the construction of a multi‐Laplacian quadratic form that is assembled from local operators whose kernels only contain locally‐affine functions. Minimizing this quadratic form provides an embedding that best preserves all relative coordinates of points within their local neighborhoods. We demonstrate the improvements that our approach brings over existing nonlinear dimensionality reduction methods on a number of datasets, and formulate the first eigen‐based as‐rigid‐as‐possible shape deformation technique by applying our affine‐kernel embedding approach to 3D data augmented with user‐imposed constraints on select vertices.     

An Affine-Invariant Tool for Retrieving Images from Homogeneous Databases

In this paper, we examine the complexities involved in retrieving images from a database comprised of objects of very similar appearance. Such an operation requires a process that can discriminate among images at a very fine level, such as distinguishing among various species of fish. Furthermore, incidental environmental factors such as change in viewpoints and slight, nonessential shape deformation must be excluded from the similarity criteria. To this end, we propose a new method for content-based image retrieval and indexing, one that is well suited for discriminating among objects within the same class in a way that is insensitive to incidental environmental changes. The scheme comprises a global alignment and a local matching process. Affine transform is used to model the different viewpoints associated with positioning the camera, while multi-dimensional indexing techniques are used to make the global alignment scheme efficient. A local matching process based on dynamic programming allows the optimal matching of local structures using cost metrics that may ignore nonessential local shape deformation. Results show the method's ability to cancel out visual distortions caused by a changing viewpoint, and its tolerance to noise, occlusion, and slight deformations of the object.     

Polyhedral Surface Modeling with a Diffusion System

This paper presents a method of generating polyhedral surfaces by using a diffusion system that calculates the positional and normal vectors on their vertices. The system generates smooth shapes that satisfy the minimum norm property, and can be extended to imitate the shape controls of curvature continuous surfaces with bias and tension parameters. The shape of a surface is determined by the stable state of nonlinear and local calculations between vertices, and is easily controlled by adding constraints on arbitrary vertices. Such bottom-up calculation of surfaces enhances flexibility in the interactive design of complicated free-form shapes.     

基于Lp范数的2DPCA的人脸识别方法

主成分分析（PCA）是降维的一种经典方法。二维主成分分析（2DPCA）在特征抽取之前不需要将图像矩阵转化为向量形式,所以能快速地提取特征。但是基于L2范数的PCA和2DPCA在遇到异常值时的表现不稳定而且得到的向量通常不是稀疏的。提出了一种基于L1范数的且受Lp范数约束的2DPCA方法（2DPCA-Lp）。当参数p接近1时,它可以得到稀疏的解。该方法既具有2DPCA的快速方便性,又是泛化的并且对异常值较不敏感。同时也证明该方法可以取得一个局部最大化的解。通过在ORL和UMIST人脸库上的实验表明了该方法的有效性。     

Deformation by examples: a density flow approach

In this article, a shape transformation technique is introduced for deforming objects based on a given deformation example. The example consists of two reference shapes representing two different states of an object. The reference shapes are assumed to morph from one state to the other. The evolution between the two reference shapes determines the shape transformation function. Any given objects can then be deformed by the same transformation. A continuous 4D Radial Basis Function is used to construct a density flow field (an extension of the optical flow in computer vision) representing the shape transformation of the example in 3‐space. Objects embedded in the density flow field are deformed by moving vertices of the objects along the density flow vectors. Additional parameters are introduced to control the process of the deformation. This provides explicit control on the shape of the object obtained in the deformation process. Copyright © 2007 John Wiley & Sons, Ltd.     

基于四边形网格均值坐标的K-2环网格曲面构造

为在曲面造型中避免产生扭曲、褶皱等现象,将四边形网格中内点的 K-2 环网格作为控制网格, 提出一种简单、灵活的曲面构造方法。给定一个 K-2 环控制网格,构造一个与其具有同样拓扑结构的平面网格。 再将平面网格拓展成空间四边形网格,同时在平面网格内进行采样。然后计算采样点关于空间四边形网格顶点 的四边形网格均值坐标,最后利用四边形网格均值坐标生成曲面,保证曲面上的每一点都满足 C∞ 。在这个过 程中设置了一个全局形状因子 h,用于控制曲面与初始控制网格的逼近程度,通过实例证明,h 越小,曲面越 逼近初始控制网格。     

As‐Rigid‐AsPossible Distance Field Metamorphosis

Widely used for morphing between objects with arbitrary topology, distance field interpolation (DFI) handles topological transition naturally without the need for correspondence or remeshing, unlike surface‐based interpolation approaches. However, lack of correspondence in DFI also leads to ineffective control over the morphing process. In particular, unless the user specifies a dense set of landmarks, it is not even possible to measure the distortion of intermediate shapes during interpolation, let alone control it. To remedy such issues, we introduce an approach for establishing correspondence between the interior of two arbitrary objects, formulated as an optimal mass transport problem with a sparse set of landmarks. This correspondence enables us to compute non‐rigid warping functions that better align the source and target objects as well as to incorporate local rigidity constraints to perform as‐rigid‐aspossible DFI. We demonstrate how our approach helps achieve flexible morphing results with a small number of landmarks.     

Interpretive Tools for 3-D Structural Geological Modeling Part I: Bézier-Based Curves, Ribbons and Grip Frames

Interpreting the geometry of geological objects is a standard activity of field-based geologists. We present new graphics tools that will aid in extending this activity from 2-D geological mapping into a 3-D environment. Much of the existing 3-D geological modeling software supports the construction of objects with the input of dense control data. However, for regional mapping and near mine exploration work, sparse data is the norm. Tools are required therefore, which give the expert interpreter full control of the graphics objects, while at the same time constraining interpretations to specific control data from field observations. We present the initial results of a software design and programming project for the visualization of complex regional scale geologic objects using Bézier-based graphics tools that are optimized for sparse data interpretation. We also introduce the concept of a structural ribbon, which is a 3-D extended map trace, along with methods for the optimization of surface construction using graphical grip frames.     

Shape deformation with tunable stiffness

The paper presents a 2D or 3D shape deformation method which incorporates global and local stiffness controls. First, a geometric object is embedded into a regular lattice and then the deformation is conducted on the lattice; thus, the method is independent of the underlying object representation. The lattice cells are organized as overlapping local rigid regions, and the region width could be regarded as a means of the global lattice stiffness control. For each region, there is a local stiffness coefficient to control the lattice deformation locally. During the deformation a nonlinear objective function is optimized to achieve the natural lattice deformation with the prescribed global and local stiffnesses. Then, the lattice deformation is passed to the embedded object through bilinear or trilinear interpolation. In this way we can deform the object in a more physically plausible way with tunable stiffness. Experimental results show that the method is intuitive and flexible.     

基于L0稀疏约束的近似稀疏解人耳识别*

传统的人耳识别算法在人耳图像遮挡、噪声和人耳多姿态变化中表现出低识别率,近年来稀疏表示在模式识别领域中取得很好的成果。决定稀疏分类器识别精确度的因素主要是稀疏解的稀疏度。而稀疏度的估计就是稀疏向量中非0元素的估计,即向量L0范数。因此在人耳稀疏分类算法的研究中引入L0范数稀疏约束。综上所述,采取基于SRC（Sparse Representation-based Classification）稀疏模型,选取对人耳姿态变化具有强鲁棒性的特征逼近过完备字典,然后使用OMP(Orthogonal Matching Pursuit)算法直接解L0问题,并加入稀疏约束,从优化稀疏解的角度对人耳稀疏分类算法进行改进,提高人耳识别效率。