Curve skeleton extraction by coupled graph contraction and surface clustering

In this paper, we present a practical algorithm to extract a curve skeleton of a 3D shape. The core of our algorithm comprises coupled processes of graph contraction and surface clustering. Given a 3D shape represented by a triangular mesh, we first construct an initial skeleton graph by directly copying the connectivity and geometry information from the input mesh. Graph contraction and surface clustering are then performed iteratively. The former merges certain graph nodes based on computation of an approximate centroidal Voronoi diagram, seeded by subsampling the graph nodes from the previous iteration. Meanwhile, a coupled surface clustering process serves to regularize the graph contraction. Constraints are used to ensure that extremities of the graph are not shortened undesirably, to ensure that skeleton has the correct topological structure, and that surface clustering leads to an approximately-centered skeleton of the input shape. These properties lead to a stable and reliable skeleton graph construction algorithm.Experiments demonstrate that our skeleton extraction algorithm satisfies various desirable criteria. Firstly, it produces a skeleton homotopic with the input (the genus of both shapes agree) which is both robust (results are stable with respect to noise and remeshing of the input shape) and reliable (every boundary point is visible from at least one curve-skeleton location). It can also handle point cloud data if we first build an initial skeleton graph based on k-nearest neighbors. In addition, a secondary output of our algorithm is a skeleton-to-surface mapping, which can e.g. be used directly for skinning animation.Highlights(1) An algorithm for curve skeleton extraction from 3D shapes based on coupled graph contraction and surface clustering. (2) The algorithm meets various desirable criteria and can be extended to work for incomplete point clouds.     

Reeb graph path dissimilarity for 3D object matching and retrieval

We introduce a skeletal graph for topological 3D shape representation using Morse theory. The proposed skeletonization algorithm encodes a 3D shape into a topological Reeb graph using a normalized mixture distance function. We also propose a novel graph matching algorithm by comparing the relative shortest paths between the skeleton endpoints. Experimental results demonstrate the feasibility of the proposed topological Reeb graph as a shape signature for 3D object matching and retrieval.     

From 3D magnetic resonance images to structural representations of the cortex topography using topology preserving deformations

We propose an algorithm allowing the construction of a structural representation of the cortical topography from a T1-weighted 3D MR image. This representation is an attributed relational graph (ARG) inferred from the 3D skeleton of the object made up of the union of gray matter and cerebro-spinal fluid enclosed in the brain hull. In order to increase the robustness of the skeletonization, topological and regularization constraints are included in the segmentation process using an original method: the homotopically deformable regions. This method is halfway between deformable contour and Markovian segmentation approaches. The 3D skeleton is segmented in simple surfaces (SSs) constituting the ARG nodes (mainly cortical folds). The ARG relations are of two types: first, theSS pairs connected in the skeleton; second, theSS pairs delimiting a gyrus. The described algorithm has been developed in the frame of a project aiming at the automatic detection and recognition of the main cortical sulci. Indeed, the ARG is a synthetic representation of all the information required by the sulcus identification. This project will contribute to the development of new methodologies for human brain functional mapping and neurosurgery operation planning.     

Computing hierarchical curve-skeletons of 3D objects

A curve-skeleton of a 3D object is a stick-like figure or centerline representation of that object. It is used for diverse applications, including virtual colonoscopy and animation. In this paper, we introduce the concept of hierarchical curve-skeletons and describe a general and robust methodology that computes a family of increasingly detailed curve-skeletons. The algorithm is based upon computing a repulsive force field over a discretization of the 3D object and using topological characteristics of the resulting vector field, such as critical points and critical curves, to extract the curve-skeleton. We demonstrate this method on many different types of 3D objects (volumetric, polygonal and scattered point sets) and discuss various extensions of this approach.     

Symmetry-seeking models and 3D object reconstruction

We propose models of 3D shape which may be viewed as deformable bodies composed of simulated elastic material. In contrast to traditional, purely geometric models of shape, deformable models are active—their shapes change in response to externally applied forces. We develop a deformable model for 3D shape which has a preference for axial symmetry. Symmetry is represented even though the model does not belong to a parametric shape family such as (generalized) cylinders. Rather, a symmetry-seeking property is designed into internal forces that constrain the deformations of the model. We develop a framework for 3D object reconstruction based on symmetry-seeking models. Instances of these models are formed from monocular image data through the action of external forces derived from the data. The forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2D silhouette of an object of interest. The effectiveness of our approach is demonstrated using natural images.     

Snake terrestrial locomotion synthesis in 3D virtual environments

We present a method for a 3D snake model construction and terrestrial snake locomotion synthesis in 3D virtual environments using image sequences. The snake skeleton is extracted and partitioned into equal segments using a new iterative algorithm for solving the equipartition problem. This method is applied to 3D model construction and at the motion analysis stage. Concerning the snake motion, the snake orientation is controlled by a path planning method. An animation synthesis algorithm, based on a physical motion model and tracking data from image sequences, describes the snake’s velocity and skeleton shape transitions. Moreover, the proposed motion planning algorithm allows a large number of skeleton shapes, providing a general method for aperiodic motion sequences synthesis in any motion graph. Finally, the snake locomotion is adapted to the 3D local ground, while its behavior can be easily controlled by the model parameters yielding the appropriate realistic animations.     

基于粒子系统和形状匹配的实时无网格变形仿真

介绍了一种基于粒子系统和形状匹配的无网格变形算法。该算法将模型的每个顶点当成一个粒子,一个模型对应一个粒子系统,通过粒子系统控制物体外形。同时,每个粒子都对应一个目标位置,粒子与其目标位置之间存在弹力,能将粒子拉向目标位置,使得变形后的物体能够恢复原来的形状。目标位置可以通过粒子系统未变形时的静止状态与当前变形状态之间的形状匹配来计算。该算法简单,易于实现,且不需要复杂的数据结构。实验结果表明该算法稳定,具有实时性,可以有效地应用于三维游戏中。     

Skeleton‐Intrinsic Symmetrization of Shapes

Enhancing the self‐symmetry of a shape is of fundamental aesthetic virtue. In this paper, we are interested in recovering the aesthetics of intrinsic reflection symmetries, where an asymmetric shape is symmetrized while keeping its general pose and perceived dynamics. The key challenge to intrinsic symmetrization is that the input shape has only approximate reflection symmetries, possibly far from perfect. The main premise of our work is that curve skeletons provide a concise and effective shape abstraction for analyzing approximate intrinsic symmetries as well as symmetrization. By measuring intrinsic distances over a curve skeleton for symmetry analysis, symmetrizing the skeleton, and then propagating the symmetrization from skeleton to shape, our approach to shape symmetrization is skeleton‐intrinsic. Specifically, given an input shape and an extracted curve skeleton, we introduce the notion of a backbone as the path in the skeleton graph about which a self‐matching of the input shape is optimal. We define an objective function for the reflective self‐matching and develop an algorithm based on genetic programming to solve the global search problem for the backbone. The extracted backbone then guides the symmetrization of the skeleton, which in turn, guides the symmetrization of the whole shape. We show numerous intrinsic symmetrization results of hand drawn sketches and artist‐modeled or reconstructed 3D shapes, as well as several applications of skeleton‐intrinsic symmetrization of shapes.     

Motion estimation of elastic articulated objects from points and contours with volume invariable constraint

This paper presents a model of elastic articulated objects based on revolving conic surface and a method of model-based motion estimation. The model includes 3D object skeleton and deformable surfaces that can represent the deformation of human body surfaces. In each limb, surface deformation is represented by adjusting one or two deformation parameters. Then, the 3D deformation parameters are determined by corresponding 2D image points and contours with volume invariable constraint from a sequence of stereo images. The 3D motion parameters are estimated based on the 3D model. The algorithm presented in this paper includes model-based parameter estimation of motion and parameter determination of deformable surfaces.     

基于形变模型由立体序列图象恢复物体的3D形状

结合立体视觉和形变模型提出了一种新的物体3D形状的恢复方法。采用立体视觉方法导出物体表面的3D坐标;利用光流模型估计物体的3D运动,根据此运动移动形变模型,使其对准物体的表面块;由形变模型将由各幅图象得到的离散的3D点融为一起,得到物体的表面形状。实验结果表明该方法能用于形状复杂的物体恢复。     

Salient and non-salient fiducial detection using a probabilistic graphical model

Deformable shape detection is an important problem in computer vision and pattern recognition. However, standard detectors are typically limited to locating only a few salient landmarks such as landmarks near edges or areas of high contrast, often conveying insufficient shape information. This paper presents a novel statistical pattern recognition approach to locate a dense set of salient and non-salient landmarks in images of a deformable object. We explore the fact that several object classes exhibit a homogeneous structure such that each landmark position provides some information about the position of the other landmarks. In our model, the relationship between all pairs of landmarks is naturally encoded as a probabilistic graph. Dense landmark detections are then obtained with a new sampling algorithm that, given a set of candidate detections, selects the most likely positions as to maximize the probability of the graph. Our experimental results demonstrate accurate, dense landmark detections within and across different databases.     

Real-time 3D face tracking based on active appearance model constrained by depth data

Active Appearance Model (AAM) is an algorithm for fitting a generative model of object shape and appearance to an input image. AAM allows accurate, real-time tracking of human faces in 2D and can be extended to track faces in 3D by constraining its fitting with a linear 3D morphable model. Unfortunately, this AAM-based 3D tracking does not provide adequate accuracy and robustness, as we show in this paper. We introduce a new constraint into AAM fitting that uses depth data from a commodity RGBD camera (Kinect). This addition significantly reduces 3D tracking errors. We also describe how to initialize the 3D morphable face model used in our tracking algorithm by computing its face shape parameters of the user from a batch of tracked frames. The described face tracking algorithm is used in Microsoft's Kinect system.     

一种提取物体线形骨架的新方法

提出了一种提取物体线形骨架的新方法. 该方法首先计算物体距离变换的梯度, 从而得到一个矢量场. 距离变换的梯度对提取物体线形骨架具有重要意义, 可据此获得物体内部的关键点, 其中每一个关键点代表了物体的一个凸部分. 之后, 用搜索梯度最短路径的方法连接关键点, 得到物体的线形骨架. 本文方法得到的线形骨架能很好地反映物体拓扑和形状特征, 并不易受边界噪声干扰. 此外, 本文方法克服了基于距离变换的骨架提取算法的固有缺点, 获得了具有良好连通性的骨架. 因此, 基于本文方法得到的骨架能用于物体识别和匹配等领域. 对大量二维、三维物体的实验取得了令人满意的效果.     

基于骨架层次分解的目标的图表示

基于骨架的目标表示技术是模式识别和计算机视觉的重要研究内容,近年来人们提出了许多骨架化算法,但是有关利用骨架信息表示并识别目标的研究还非常有限。Ablameyko等1996年提出了通过分解由距离标号的骨架为有意义的结构基元从而获得目标的层次结构图的方法。该图可以准确地刻画基元之间的拓扑关系,但是它对于骨架中的噪声比较敏感。主要表现为噪声基元破坏其它基元的完整性和图的稳定性。该文采用将分支编组为分支链以及构造多尺度结构图的改进策略来克服这些缺点,最终获得了目标的节点数更小、节点显著度更高、节点间连接关系更稳定的多尺度图,从而显著地提高后续利用不精确图匹配技术进行目标识别的效率。这项技术已经被应用于一个基于形状特征的图像数据库检索系统中。     

基于形变模型的3D表面自适应重建

结合形变模型和ＡＣＤ方法提出了基于变形模型的３Ｄ表面自适应重建方法。同时引入了与图象统计特性有关的外力,使得表面重建结果与模型的初始位置无关,利用ＡＣＤ方法使模型自适应地改变其拓扑结构;为了提高表面重建的程度和鲁棒性,提出了多尺度重建算法,该方法适用于形状、结构复杂的物体重建,实验结果证明了该方法的有效性。     

融合形状特征的MRG骨架树三维检索方法

提出一种基于MRG骨架树的三维模型检索方法。根据多分辨率Reeb图(MRG)的原理,提取反映模型拓扑特征的Reeb图骨架并且映射成树形结构,分析了节点的拓扑属性。针对拓扑属性在形状特征上的表达能力不足,在节点相应区域提取离散曲率和面积比例描绘局部的形状特征。有效地结合了模型的拓扑特征和形状特征计算模型的相似度。该方法突出了模型的整体拓扑特征和形状特征,实验结果表明了该方法的高效性和鲁棒性。     

d-Dimensional parametric models for dynamic animation of deformable objects

This paper introduces an accurate, efficient, and unified engine dedicated to dynamic animation of d-dimensional deformable objects. The objects are modelled as d-dimensional manifolds defined as functional combinations of a mesh of 3D control points, weighted by parametric blending functions. This model ensures that, at each time step, the object shape conforms to its manifold definitions. The object motion is deduced from the control points dynamic animation. In fact, control points should be viewed as the degrees of freedom of the continuous object. The chosen dynamic equations (Lagrangian formalism) reflect this generic modelling scheme and yield an exact and computationally efficient linear system.     

Skeleton growing: an algorithm to extract a curve skeleton from a pseudonormal vector field

A curve skeleton is used to represent a 3D object in many different applications. It is a 1D curve that captures topology of the 3D object. The proposed method extracts a curve skeleton from the vector field inside the 3D object. A vector at each voxel of the 3D object is calculated using a pseudonormal vector. By using such a calculation, the computation time is significantly reduced compared with using a typical potential field. A curve skeleton is then extracted from the pseudonormal vector field by using a skeleton-growing algorithm. The proposed algorithm uses high-curvature boundary voxels to search for a set of critical points and skeleton branches near high-curvature areas. The set of detected critical points is then used to grow a curve skeleton in the next step. All parameters of our algorithms are calculated from the 3D object itself, without user intervention. The effectiveness of our method is demonstrated in our experiments.