一种3维动画中间帧非线性插值算法

关键帧动画是3维动画制作的常用模式，中间帧插值又是关键帧动画中最为繁琐的环节。提出了一种针对无骨架3维网格模型的非线性插值算法，用于对网格模型的关键帧姿态进行插补，自动生成中间帧动画序列。该算法首先计算动画角色的网格模型各三角片在相邻关键帧中的仿射变换，并据此生成变形梯度向量，作为3维网格模型的形变信息，这种表示形式体现了变形过程中网格顶点之间的局部互相关关系。随后将各仿射变换分解为旋转成分与拉伸缩放成分，对拉伸缩放成分进行线性插值，而对旋转成分采用四元数插值算法进行非线性插值，合成中间帧姿态的变形梯度向量，并据此计算出中间帧网格模型。当相邻关键帧姿态存在较大差异时，该算法也能快速生成平稳而生动的中间帧动画，可有效减少关键帧的数量，提高动画制作效率。     

Spatio-temporal segmentation for the similarity measurement of deforming meshes

Although there have been a large body of works on computing the similarity of static shapes, similarity judgments on deforming meshes are not studied well. In this study, we investigate a similarity measurement method for comparing two deforming meshes. Based on the degree of deformation, we first binarily label each triangle within each frame as either ‘deformed’ or ‘rigid’, then merge the ‘deformed’ triangles in both spatial and temporal domains for the segmentation. The segmentation results are encoded in a form of evolving graph, with an aim of obtaining a compact representation of the motion of the mesh. Finally, we formulate the similarity measurement as a sequence matching problem: after clustering similar graphs and assigning each of the graphs with the cluster labels, each deforming mesh is represented with a sequence of labels. Then, we apply a sequence alignment algorithm to compute the locally optimal alignment between the two label sequences, and to compute the similarity by normalizing the alignment score. The experimental results over several datasets show that the similarities of animation data can be captured correctly using our approach. This may be significant, as it solves a problem that cannot be handled by current approaches.     

A novel framework for physically based sculpting and animation of free-form solids

This paper presents a new, physically based model for performing finite element simulation of deformable objects in which all quantities – strain, stress, displacement, etc. – are computed entirely in local frames of reference. In our framework, subdivision solids with non-homogeneous material properties, such as mass and deformation distributions, can be defined throughout continuous, volumetric domains. This capability enables an animator or virtual sculptor to exert fine-level control over deforming objects and to define a wide variety of physical behaviors. Furthermore, since all quantities pertinent to physical simulation are computed locally, our model facilitates both large-scale and small-scale deformations, as well as rigid or near-rigid transformations. We demonstrate applications of our framework in animation and interactive sculpting and show that interactive simulation of non-trivial, volumetric shapes is possible with our methodologies.     

Automatic Conversion of Mesh Animations into Skeleton-based Animations

Recently, it has become increasingly popular to represent animations not by means of a classical skeleton‐based model, but in the form of deforming mesh sequences. The reason for this new trend is that novel mesh deformation methods as well as new surface based scene capture techniques offer a great level of flexibility during animation creation. Unfortunately, the resulting scene representation is less compact than skeletal ones and there is not yet a rich toolbox available which enables easy post‐processing and modification of mesh animations. To bridge this gap between the mesh‐based and the skeletal paradigm, we propose a new method that automatically extracts a plausible kinematic skeleton, skeletal motion parameters, as well as surface skinning weights from arbitrary mesh animations. By this means, deforming mesh sequences can be fully‐automatically transformed into fullyrigged virtual subjects. The original input can then be quickly rendered based on the new compact bone and skin representation, and it can be easily modified using the full repertoire of already existing animation tools.     

A mesh-based automatic in-betweening algorithm in computer-assisted animation

The automatic in-betweening technology is one of the most important technologies in computer-assisted animation. The preprocessing of inconsistency of the topological structure between the start and the end key frames is time-consuming in the traditional in-betweening algorithm. Therefore, in order to guarantee the consistency of the topology structure between the start and the end key frames, we present in this paper a new mesh-based automatic in-betweening algorithm for the key frame animation. By meshing a three-dimensional object, all the infinite and disorderly points on the surface of an object can be converted into finite and ordinal points according to some principles of each layer and between layers, and then a series of in-betweens can be automatically generated in terms of an interpolation function. The algorithm in this paper presents a solution to the corresponding principles of the vertices on each layer and between layers after meshing the start and the end key frames. The experimental results demonstrate that the animation generated based on this method is smooth, natural, and fluent. In application, our algorithm can improve the efficiency of animation production as well as greatly reducing the cost.     

Mesh Parametrization Driven by Unit Normal Flow

Based on mesh deformation, we present a unified mesh parametrization algorithm for both planar and spherical domains. Our approach can produce intermediate frames from the original meshes to the targets. We derive and define a novel geometric flow: ‘unit normal flow (UNF)’ and prove that if UNF converges, it will deform a surface to a constant mean curvature (CMC) surface, such as planes and spheres. Our method works by deforming meshes of disk topology to planes, and spherical meshes to spheres. Our algorithm is robust, efficient, simple to implement. To demonstrate the robustness and effectiveness of our method, we apply it to hundreds of models of varying complexities. Our experiments show that our algorithm can be a competing alternative approach to other state-of-the-art mesh parametrization methods. The unit normal flow also suggests a potential direction for creating CMC surfaces.     

一种基于约束特征的网格编辑技术

为了改进自由变形技术在用户交互和编辑灵活性的不足,提出了一种直观的交互式网格模型编辑技术,该技术可以根据不同的约束变形特征、封闭的变形边界以及编辑参考曲线来完成网格模型的编辑,并且为了模型的平滑和自然,采用了自适应细分策略。实验证明,该方法简便直观,有良好的交互性,并能得到很好的编辑结果。此技术可以方便地应用于CAD/CAM和计算机动画系统中。     

Hyperspectral Inverse Skinning

In example-based inverse linear blend skinning (LBS), a collection of poses (e.g. animation frames) are given, and the goal is finding skinning weights and transformation matrices that closely reproduce the input. These poses may come from physical simulation, direct mesh editing, motion capture or another deformation rig. We provide a re-formulation of inverse skinning as a problem in high-dimensional Euclidean space. The transformation matrices applied to a vertex across all poses can be thought of as a point in high dimensions. We cast the inverse LBS problem as one of finding a tight-fitting simplex around these points (a well-studied problem in hyperspectral imaging). Although we do not observe transformation matrices directly, the 3D position of a vertex across all of its poses defines an affine subspace, or flat. We solve a ‘closest flat’ optimization problem to find points on these flats, and then compute a minimum-volume enclosing simplex whose vertices are the transformation matrices and whose barycentric coordinates are the skinning weights. We are able to create LBS rigs with state-of-the-art reconstruction error and state-of-the-art compression ratios for mesh animation sequences. Our solution does not consider weight sparsity or the rigidity of recovered transformations. We include observations and insights into the closest flat problem. Its ideal solution and optimal LBS reconstruction error remain an open problem.     

Using surface variability characteristics for segmentation of deformable 3D objects with application to piecewise statistical deformable model

To cope with the small sample size problem in the construction of Statistical Deformable Models (SDM), this paper proposes two novel measures that quantify the similarity of the variability characteristics among deforming 3D meshes. These measures are used as the basis of our proposed technique for partitioning a 3D mesh for the construction of piecewise SDM in a divide-and-conquer strategy. Specifically, the surface variability information is extracted by performing a global principal component analysis on the set of sample meshes. An iterative face clustering algorithm is developed for segmenting a mesh that favors grouping triangular faces having similar variability characteristics into a same mesh component. We apply the proposed mesh segmentation algorithm to the construction of piecewise SDM and evaluate the representational ability of the resulting piecewise SDM through the reconstruction of unseen meshes. Experimental results show that our approach outperforms several state-of-the-art methods in terms of the representational ability of the resulting piecewise SDM as evaluated by the reconstruction accuracy.     

Segmenting animated objects into near-rigid components

We present a novel approach to solve the problem of segmenting a sequence of animated objects into near-rigid components based on k given poses of the same non-rigid object. We model the segmentation problem as a clustering problem in dual space and find near-rigid segments with the property that segment boundaries are located at regions of large deformation. The presented approach is asymptotically faster than previous approaches that achieve the same property and does not require any user-specified parameters. However, if desired, the user may interactively change the number of segments. We demonstrate the practical value of our approach using experiments.     

CAD mesh model segmentation by clustering

CAD mesh models have been widely employed in current CAD/CAM systems, where it is quite useful to recognize the features of the CAD mesh models. The first step of feature recognition is to segment the CAD mesh model into meaningful parts. Although there are lots of mesh segmentation methods in literature, the majority of them are not suitable to CAD mesh models. In this paper, we design a mesh segmentation method based on clustering, dedicated to the CAD mesh model. Specifically, by the agglomerative clustering method, the given CAD mesh model is first clustered into the sparse and dense triangle regions. Furthermore, the sparse triangle region is separated into planar regions, cylindrical regions, and conical regions by the Gauss map of the triangular faces and Hough transformation; the dense triangle region is also segmented by the mean shift operation performed on the mean curvature field defined on the mesh faces. Lots of empirical results demonstrate the effectiveness and efficiency of the CAD mesh segmentation method in this paper.     

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.     

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.     

Morphing active contours

A method for deforming curves in a given image to a desired position in a second image is introduced. The algorithm is based on deforming the first image toward the second one via a partial differential equation (PDE), while tracking the deformation of the curves of interest in the first image with an additional, coupled PDE; both the images and the curves on the frame/slices of interest are used for tracking. The technique can be applied to object tracking and sequential segmentation. The topology of the deforming curve can change without any special topology handling procedures added to the scheme. This permits, for example, the automatic tracking of scenes where, due to occlusions, the topology of the objects of interest changes from frame to frame. In addition, this work introduces the concept of projecting velocities to obtain systems of coupled PDEs for image analysis applications. We show examples for object tracking and segmentation of electronic microscopy     

基于线型草图的多源3维动画传输

为了对3维动画进行鲁棒地传输,提出了一种基于线型草图的3维动画传输方法,该方法可以把多个源网格的动画传输到一个目标网格。该方法由以下几个步骤组成:(1)使用线型草图在源网格和目标网格间建立映射;(2)使用差分均值坐标(differential mean value coordinates),根据源动画来变形目标网格;(3)对齐各部分变形后的目标网格,通过求解最小化约束函数,以获取光滑的目标网格,从而生成目标动画的关键帧;(4)对由步骤(3)产生的结果进行插值,即可产生完整的目标对象的3维动画。通过对上述几个方面的深入研究,以及将这些成果集成在原型系统中的结果表明,该方法具有以下特点:①既不需要源网格和目标网格有相同的顶点数和三角面片数,也不需要有类似的拓扑信息;②源动画既可以是3维的,也可以是2维视频或Flash;③目标对象可以是无结构化的点云数据。实践表明,该方法直观易用,可以生成逼真的3维动画。最后通过从狗、猫、蛇、人体的3维动画与2维车轮视频的合成来产生复杂的马车动画,对该方法进行了验证。另外,原型系统还通过产生其他几个例子来进一步验证其通用性和鲁棒性。     

Segmentation of temporal mesh sequences into rigidly moving components

In this paper is considered the segmentation of meshes into rigid components given temporal sequences of deforming meshes. We propose a fully automatic approach that identifies model parts that consistently move rigidly over time. This approach can handle meshes independently reconstructed at each time instant. It allows therefore for sequences of meshes with varying connectivities as well as varying topology. It incrementally adapts, merges and splits segments along a sequence based on the coherence of motion information within each segment. In order to provide tools for the evaluation of the approach, we also introduce new criteria to quantify a mesh segmentation. Results on both synthetic and real data as well as comparisons are provided in the paper.     

A mobile environment for sketching-based skeleton generation

Articulated character animation is typically performed by manually creating and rigging a skeleton into an unfolded 3D object. However, such tasks are not trivial, as they require a substantial amount of training and practices. Although automatic skeleton extraction methods have been proposed, they generally may not guarantee that the resulting skeleton can help produce desired animations according to user intention. In this paper, we present a sketching-based skeleton generation method suitable for use in the mobile environment. This method takes user sketching as an input, and based on the mesh segmentation result of a 3D object, it estimates a skeleton for articulated character animation. In addition, we are currently developing a Web-based mobile platform to support mesh editing by a group of collaborative users and we depict the system architecture of such a platform. Results show that our method can produce better skeletons in terms of joint positions and topological structure.     

从运动捕获数据中提取关键帧

在四元数表示下导出了两个旋转之间差异的一种简单形式，将人体各关节上总的旋转变化作为帧间距，设计了一种从运动捕获数据中提取关键帧的高效算法，通过向量的线性插值和四元数的球面线性插值重建了原始动画。实验表明，该算法具有很好的数据压缩效果，而且提取出的关键帧在视觉上对原始动画具有概括力。     

Dynamic highlight line generation for locally deforming NURBS surfaces

The highlight line model is a powerful tool in assessing the quality of a surface. Efficient highlight line generation is especially important for an interactive design environment. In this paper, a method for dynamic generation of highlight lines on a locally deforming NURBS surface is presented. The method generates frames of the deforming surface and the corresponding highlight lines by directly modifying the current highlight lines using a Taylor expansion technique, instead of going through a tracing process. The highlight lines computation process adopted here enables a unified distance surface to generate all highlight lines in the highlight line family. The computation process is facilitated by looking up pre-calculated information of the tessellation mesh and an indexing technique for the distance surface. The indexing technique is presented to determine when the highlight line model should be re-generated and, to facilitate the highlight line re-generation process. The new technique is suitable for interactive design environments and animation applications as the updating process takes only one subtraction and one vector inner product to get the new parameters for each new node.     

基于形变模型的真实感三维人脸动画研究

论文提出了一种新的基于三维人脸形变模型,并兼容于MPEG-4的三维人脸动画模型。采用基于均匀网格重采样的方法建立原型三维人脸之间的对齐,应用MPEG-4中定义的三维人脸动画规则,驱动三维模型自动生成真实感人脸动画。给定一幅人脸图像,三维人脸动画模型可自动重建其真实感的三维人脸,并根据FAP参数驱动模型自动生成人脸动画。