Interpolating Polyhedral Models Using Intrinsic Shape Parameters

Metamorphosis, or morphing, is the gradual transformation of one shape into another. It generally consists of two subproblems: the correspondence problem and the interpolation problem. This paper presents a solution to the interpolation problem of transforming one polyhedral model into another. It is an extension of the intrinsic shape interpolation scheme (T. W. Sederberg, P. Gao, G. Wang and H. Mu, ‘2-D shape blending: an intrinsic solution to the vertex path problem, SIGGRAPH '93, pp. 15–18.) for 2D polygons. Rather than considering a polyhedron as a set of independent points or faces, our solution treats a polyhedron as a graph representing the interrelations between faces. Intrinsic shape parameters, such as dihedral angles and edge lengths that interrelate the vertices and faces in the two graphs, are used for interpolation. This approach produces more satisfactory results than the linear or cubic curve paths would, and is translation and rotation invariant. © 1997 by John Wiley & Sons, Ltd.     

Hair Interpolation for Portrait Morphing

In this paper we study the problem of hair interpolation: given two 3D hair models, we want to generate a sequence of intermediate hair models that transform from one input to another both smoothly and aesthetically pleasing. We propose an automatic method that efficiently calculates a many‐to‐many strand correspondence between two or more given hair models, taking into account the multi‐scale clustering structure of hair. Experiments demonstrate that hair interpolation can be used for producing more vivid portrait morphing effects and enabling a novel example‐based hair styling methodology, where a user can interactively create new hairstyles by continuously exploring a “style space” spanning multiple input hair models.     

Efficient Interpolation of Articulated Shapes Using Mixed Shape Spaces

Interpolation between compatible triangle meshes that represent different poses of some object is a fundamental operation in geometry processing. A common approach is to consider the static input shapes as points in a suitable shape space and then use simple linear interpolation in this space to find an interpolated shape. In this paper, we present a new interpolation technique that is particularly tailored for meshes that represent articulated shapes. It is up to an order of magnitude faster than state‐of‐the‐art methods and gives very similar results. To achieve this, our approach introduces a novel shape space that takes advantage of the underlying structure of articulated shapes and distinguishes between rigid parts and non‐rigid joints. This allows us to use fast vertex interpolation on the rigid parts and resort to comparatively slow edge‐based interpolation only for the joints.     

Principal Geodesic Analysis in the Space of Discrete Shells

Important sources of shape variability, such as articulated motion of body models or soft tissue dynamics, are highly nonlinear and are usually superposed on top of rigid body motion which must be factored out. We propose a novel, nonlinear, rigid body motion invariant Principal Geodesic Analysis (PGA) that allows us to analyse this variability, compress large variations based on statistical shape analysis and fit a model to measurements. For given input shape data sets we show how to compute a low dimensional approximating submanifold on the space of discrete shells, making our approach a hybrid between a physical and statistical model. General discrete shells can be projected onto the submanifold and sparsely represented by a small set of coefficients. We demonstrate two specific applications: model‐constrained mesh editing and reconstruction of a dense animated mesh from sparse motion capture markers using the statistical knowledge as a prior.     

圆弧路径法，一种新的多边形变形方法

二维形状变形技术在二维角色动画、模式匹配、几何造型、虚拟现实、工业模拟、科学计算可视化等领域有着重要的应用。本文提出了一种顶点路径圆弧法的二维形状变形新方法。该算法通过控制关键帧多边形顶点按照一条特殊的圆弧曲线路径进行运动，实现二维形状变形。通过许多实例的测试表明，该算法效果良好：不仅可以保持首末关键帧形状的共同特征，而且中间插值形状变化自然平滑。同时，我们的方法易于用户交互控制；容易推广到高维情形；计算量较小、能达到系统实时的要求。     

Real-Time Volume Deformations

Real-time free-form deformation tools are primarily based on surface or particle representations to allow for interactive modification and fast rendering of complex models. The efficient handling of volumetric representations, however, is still a challenge and has not yet been addressed sufficiently. Volumetric models, on the other hand, form an important class of representation in many applications. In this paper we present a novel approach to the real-time deformation of scalar volume data sets taking advantage of hardware supported 3D texture mapping. In a prototype implementation a modeling environment has been designed that allows for interactive manipulation of arbitrary parts of volumetric objects. In this way, any desired shape can be modeled and used subsequently in various applications. The underlying algorithms have wide applicability and can be exploited effectively for volume morphing and medical data processing.     

On Shape of Plane Elastic Curves

We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments non-uniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape-preserving transformations. The elastic properties of the curves are encoded in Riemannian metrics on these spaces. Geodesics in shape spaces are used to quantify shape divergence and to develop morphing techniques. The shape spaces and metrics constructed are novel and offer an environment for the study of shape statistics. Elasticity leads to shape correspondences and deformations that are more natural and intuitive than those obtained in several existing models. Applications of shape geodesics to the definition and calculation of mean shapes and to the development of shape clustering techniques are also investigated.     

Elastic Correspondence between Triangle Meshes

We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non‐linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non‐isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non‐isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross‐field computation, and consistent quadrangular remeshing of a set of shapes.     

String‐Based Synthesis of Structured Shapes

We propose a novel method to synthesize geometric models from a given class of context‐aware structured shapes such as buildings and other man‐made objects. The central idea is to leverage powerful machine learning methods from the area of natural language processing for this task. To this end, we propose a technique that maps shapes to strings and vice versa, through an intermediate shape graph representation. We then convert procedurally generated shape repositories into text databases that, in turn, can be used to train a variational autoencoder. The autoencoder enables higher level shape manipulation and synthesis like, for example, interpolation and sampling via its continuous latent space. We provide project code and pre‐trained models.     

Shape Morphing-Based Control of Robotic Visual Servoing

We present an approach for controlling robotic interactions with objects, using synthetic images generated by morphing shapes. In particular, we attempt the problem of positioning an eye-in-hand robotic system with respect to objects in the workspace for grasping and manipulation. In our formulation, the grasp position (and consequently the approach trajectory of the manipulator), varies with each object. The proposed solution to the problem consists of two parts. First, based on a model-based object recognition framework, images of the objects taken at the desired grasp pose are stored in a database. The recognition and identification of the grasp position for an unknown input object (selected from the family of recognizable objects) occurs by morphing its contour to the templates in the database and using the virtual energy spent during the morph as a dissimilarity measure. In the second step, the images synthesized during the morph are used to guide the eye-in-hand system and execute the grasp. The proposed method requires minimal calibration of the system. Furthermore, it conjoins techniques from shape recognition, computer graphics, and vision-based robot control in a unified engineering amework. Potential applications range from recognition and positioning with respect to partially-occluded or deformable objects to planning robotic grasping based on human demonstration.     

真实感人脸的形状与表情空间

提出一种建立三维人脸扫描模型参数空间的算法,其中的模板拟和算法基于能量最小的优化机制,通过非线性优化过程求解模板模型在每个顶点上的位移矢量,使之逼近目标模型.优化目标方程由以下测度组成：距离、平滑度以及人脸特征对应,如特征曲线、边界和特征点对等.使用该算法可用于不同人脸以及不同表情模型之间的对应建立,从而获取一致参数化的人脸形状和表情空间.在文中系统中,三维面部特征曲线通过Canny边检测算法自动获取,这样自动检测获取的特征曲线可用于降低三维形状描述的维数,同时完整的面部几何形状通过径向基函数插值得到.在中性人脸和表情人脸模型上所作的一致参数化为许多应用提供了平台,如形状渐变,纹理迁移和表情迁移.考虑到自动提取的特征曲线和二维线画卡通人脸的相似性,使用迭代优化算法实现二维线画卡通人脸姿态到三维真实人脸模型的迁移.     

Interactive Regression Lens for Exploring Scatter Plots

Data analysis often involves finding models that can explain patterns in data, and reduce possibly large data sets to more compact model‐based representations. In Statistics, many methods are available to compute model information. Among others, regression models are widely used to explain data. However, regression analysis typically searches for the best model based on the global distribution of data. On the other hand, a data set may be partitioned into subsets, each requiring individual models. While automatic data subsetting methods exist, these often require parameters or domain knowledge to work with. We propose a system for visual‐interactive regression analysis for scatter plot data, supporting both global and local regression modeling. We introduce a novel regression lens concept, allowing a user to interactively select a portion of data, on which regression analysis is run in interactive time. The lens gives encompassing visual feedback on the quality of candidate models as it is interactively navigated across the input data. While our regression lens can be used for fully interactive modeling, we also provide user guidance suggesting appropriate models and data subsets, by means of regression quality scores. We show, by means of use cases, that our regression lens is an effective tool for user‐driven regression modeling and supports model understanding.     

基于Grassmann流形的仿射不变形状识别

传统的Kendall形状空间理论仅适用于相似变换, 然而成像过程中目标发生的几何变形在更多情形时应该用仿射变换来刻画. 基于Grassmann流形理论, 本文分析了仿射不变形状空间的非线性几何结构, 提出了基于Grassmann流形的仿射不变形状识别算法. 算法首先对训练集中的每类形状分别计算形状均值和方差, 进而在形状均值附近的切空间构建多变量正态分布; 最后,根据测试形状的观测和先验形状模型求解测试形状的最大似然类, 对形状进行贝叶斯分类. MPEG 7形状数据库的实验结果表明, 与传统Kendall形状分析中的基于Procrustean度量识别算法相比, 本文识别算法具有明显优势; 真实场景中的目标识别结果进一步表明, 本文算法对仿射变形有更好的适应能力, 在复杂场景下能以较高的后验概率辨识出目标类别.     

Mesh Sequence Morphing

Morphing is an important technique for the generation of special effects in computer animation. However, an analogous technique has not yet been applied to the increasingly prevalent animation representation, i.e. 3D mesh sequences. In this paper, a technique for morphing between two mesh sequences is proposed to simultaneously blend motions and interpolate shapes. Based on all possible combinations of the motions and geometries, a universal framework is proposed to recreate various plausible mesh sequences. To enable a universal framework, we design a skeleton‐driven cage‐based deformation transfer scheme which can account for motion blending and geometry interpolation. To establish one‐to‐one correspondence for interpolating between two mesh sequences, a hybrid cross‐parameterization scheme that fully utilizes the skeleton‐driven cage control structure and adapts user‐specified joint‐like markers, is introduced. The experimental results demonstrate that the framework, not only accomplishes mesh sequence morphing, but also is suitable for a wide range of applications such as deformation transfer, motion blending or transition and dynamic shape interpolation.     

Example‐Driven Deformations Based on Discrete Shells

Despite the huge progress made in interactive physics‐based mesh deformation, manipulating a geometrically complex mesh or posing a detailed character is still a tedious and time‐consuming task. Example‐driven methods significantly simplify the modelling process by incorporating structural or anatomical knowledge learned from example poses. However, these approaches yield counter‐intuitive, non‐physical results as soon as the shape space spanned by the example poses is left. In this paper, we propose a modelling framework that is both example‐driven and physics‐based and thereby overcomes the limitations of both approaches. Based on an extension of the discrete shell energy we derive mesh deformation and mesh interpolation techniques that can be seamlessly combined into a simple and flexible mesh‐based inverse kinematics system.     

Data‐driven detailed hair animation for game characters

We propose a data‐driven method to realize high‐quality detailed hair animations in interactive applications like games. By devising an error metric method to evaluate hair animation similarities, we take hair features into consideration as much as possible. We also propose a novel database construction algorithm based on Secondary Motion Graph. Our algorithm can improve the efficiency of such graphs to reduce redundant data and also achieves visually smooth connection of two animation clips while taking into consideration their future motions. The costs for the run‐time process using our Secondary Motion Graph are relatively low, allowing real‐time interactive operations. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Context Aware Terrain Visualization for Wayfinding and Navigation

To assist wayfinding and navigation, the display of maps and driving directions on mobile devices is nowadays commonplace. While existing system can naturally exploit GPS information to facilitate orientation, the inherently limited screen space is often perceived as a drawback compared to traditional street maps as it constrains the perception of contextual information. Moreover, occlusion issues add to this problem if the environment is shown from the popular egocentric perspective. In this paper we describe an interactive visualization system that addresses these problems by reallocating the available screen space. At the heart of our system are three novel visualization techniques: First, we propose a non‐standard perspective that allows to blend between the familiar pedestrian perspective and a standard map depiction with reduced occlusion. Second, we derive an efficient deformation technique that allows an interactive allocation of screen space to areas of interest like e.g. nearby touristic attractions. Finally, a path adaptive isometric perspective is proposed that reveals otherwise hidden facades in top‐down views. We describe efficient implementations of all techniques and exemplify our interactive system on real world urban models.     

Homotopic Morphing of Planar Curves

This paper presents an algorithm for morphing between closed, planar piecewise‐C¹ curves. The morph is guaranteed to be a regular homotopy, meaning that pinching will not occur in the intermediate curves. The algorithm is based on a novel convex characterization of the space of regular closed curves and a suitable symmetric length‐deviation energy. The intermediate curves constructed by the morphing algorithm are guaranteed to be regular due to the convexity and feasibility of the problem. We show that our method compares favorably with standard curve morphing techniques, and that these methods sometimes fail to produce a regular homotopy, and as a result produce an undesirable morph. We explore several applications and extensions of our approach, including morphing networks of curves with simple connectivity, morphing of curves with different turning numbers with minimal pinching, convex combination of several curves, and homotopic morphing of b‐spline curves via their control polygon.     

Moment invariants for the analysis of 2D flow fields

We present a novel approach for analyzing two-dimensional (2D) flow field data based on the idea of invariant moments. Moment invariants have traditionally been used in computer vision applications, and we have adapted them for the purpose of interactive exploration of flow field data. The new class of moment invariants we have developed allows us to extract and visualize 2D flow patterns, invariant under translation, scaling, and rotation. With our approach one can study arbitrary flow patterns by searching a given 2D flow data set for any type of pattern as specified by a user. Further, our approach supports the computation of moments at multiple scales, facilitating fast pattern extraction and recognition. This can be done for critical point classification, but also for patterns with greater complexity. This multi-scale moment representation is also valuable for the comparative visualization of flow field data. The specific novel contributions of the work presented are the mathematical derivation of the new class of moment invariants, their analysis regarding critical point features, the efficient computation of a novel feature space representation, and based upon this the development of a fast pattern recognition algorithm for complex flow structures.