2D and 3D shape retrieval using skeleton filling rate

As an increasing number of digital images are generated, a demand for an efficient and effective image retrieval mechanisms grows. In this work, we present a new skeleton-based algorithm for 2D and 3D shape retrieval. The algorithm starts by drawing circles (spheres for 3D) of increasing radius around skeletons. Since each skeleton corresponds to the center of a maximally inscribed circle (sphere), this process results in circles (spheres) that are partially inside the shape. Computing the ratio between pixels that lie within the shape and the total number of pixels allows us to distinguish shapes with similar skeletons. Experimental evaluation of the proposed approach including a comprehensive comparison with the previous techniques demonstrates both effectiveness and robustness of our algorithm for shape retrieval using several 2D and 3D datasets.     

3D Skeletons: A State‐of‐the‐Art Report

Given a shape, a skeleton is a thin centered structure which jointly describes the topology and the geometry of the shape. Skeletons provide an alternative to classical boundary or volumetric representations, which is especially effective for applications where one needs to reason about, and manipulate, the structure of a shape. These skeleton properties make them powerful tools for many types of shape analysis and processing tasks. For a given shape, several skeleton types can be defined, each having its own properties, advantages, and drawbacks. Similarly, a large number of methods exist to compute a given skeleton type, each having its own requirements, advantages, and limitations. While using skeletons for two‐dimensional (2D) shapes is a relatively well covered area, developments in the skeletonization of three‐dimensional (3D) shapes make these tasks challenging for both researchers and practitioners. This survey presents an overview of 3D shape skeletonization. We start by presenting the definition and properties of various types of 3D skeletons. We propose a taxonomy of 3D skeletons which allows us to further analyze and compare them with respect to their properties. We next overview methods and techniques used to compute all described 3D skeleton types, and discuss their assumptions, advantages, and limitations. Finally, we describe several applications of 3D skeletons, which illustrate their added value for different shape analysis and processing tasks.     

Skeleton-enhanced line drawings for 3D models

We present a novel line drawing approach for 3D models by introducing their skeleton information into the rendering process. Based on the silhouettes of the input 3D models, we first extract feature lines in geometric regions by utilizing their curvature, torsion and view-dependent information. Then, the skeletons of the models are extracted by our newly developed skeleton extraction algorithm. After that, we draw the skeleton-guided lines from non-geometric regions through the skeleton information. These lines are combined with the feature lines to render the final line drawing result using the line optimization. Experimental results show that our algorithm can render line drawings more effectively with enhanced skeletons. The resulting artistic effects can capture the local geometries as well as the global skeletons of the input 3D models.     

Skeleton pruning by contour partitioning with discrete curve evolution

In this paper, we introduce a new skeleton pruning method based on contour partitioning. Any contour partition can be used, but the partitions obtained by discrete curve evolution (DCE) yield excellent results. The theoretical properties and the experiments presented demonstrate that obtained skeletons are in accord with human visual perception and stable, even in the presence of significant noise and shape variations, and have the same topology as the original skeletons. In particular, we have proven that the proposed approach never produces spurious branches, which are common when using the known skeleton pruning methods. Moreover, the proposed pruning method does not displace the skeleton points. Consequently, all skeleton points are centers of maximal disks. Again, many existing methods displace skeleton points in order to produces pruned skeletons     

保持区域平滑的3维动画形状高效编辑

目的 基于控制单元的形状编辑效果受各个控制单元对应权重的影响,而计算闭合形式的控制点权重方法难以有效地处理控制骨骼权重。针对3维空间的控制骨骼提出了一种虚拟控制单元插入算法和骨骼关节点标架变换方法,以保持骨骼控制区域的形状,从而得到过渡平滑、形状保持的良好编辑效果。方法 选择C²连续的线性权值计算方法,在用户输入相应的控制单元后,根据控制单元的支持度插入满足条件的虚拟控制点,实现了对动画形状平滑高效的编辑。首先采用离散化的方式,近似求解输入形状构成的封闭域中任意两点之间的内部距离,然后进行Voronoi区域分解,初步获得每个控制单元的控制区域。如果控制点的支持度约束不符合要求,则通过插入虚拟控制点的方式进行调整,并根据邻接关系计算实控制点对虚拟控制点的权重实现实控制点对虚拟控制点的控制。由于算法计算权值和编辑更新顶点可以并行,因此引入图形处理器（graphics processing unit,GPU）实行并行化处理。结果 实验对比了算法在编辑细节以及对不同网格模型的适应性和编辑效率方面的表现,结果表明本文算法在局部细节处不发生过度形变且保持平滑,对非三角网格和多个封闭区域叠加的网格模型依然适用,且本文算法不需要迭代,又有GPU并行计算,编辑时间显著下降。结论 本文算法易于实现,编辑效果过渡平滑,保留细节特征;GPU并行计算极大提高效率,达到实时交互效果。     

A novel unsupervised 3D skeleton detection in RGB-D images for video surveillance

In this paper we present a novel moment-based skeleton detection for representing human objects in RGB-D videos with animated 3D skeletons. An object often consists of several parts, where each of them can be concisely represented with a skeleton. However, it remains as a challenge to detect the skeletons of individual objects in an image since it requires an effective part detector and a part merging algorithm to group parts into objects. In this paper, we present a novel fully unsupervised learning framework to detect the skeletons of human objects in a RGB-D video. The skeleton modeling algorithm uses a pipeline architecture which consists of a series of cascaded operations, i.e., symmetry patch detection, linear time search of symmetry patch pairs, part and symmetry detection, symmetry graph partitioning, and object segmentation. The properties of geometric moment-based functions for embedding symmetry features into centers of symmetry patches are also investigated in detail. As compared with the state-of-the-art deep learning approaches for skeleton detection, the proposed approach does not require tedious human labeling work on training images to locate the skeleton pixels and their associated scale information. Although our algorithm can detect parts and objects simultaneously, a pre-learned convolution neural network (CNN) can be used to locate the human object from each frame of the input video RGB-D video in order to achieve the goal of constructing real-time applications. This much reduces the complexity to detect the skeleton structure of individual human objects with our proposed method. Using the segmented human object skeleton model, a video surveillance application is constructed to verify the effectiveness of the approach. Experimental results show that the proposed method gives good performance in terms of detection and recognition using publicly available datasets.

     

拓扑和形状特征相结合的三维模型检索

针对整体相似性检索算法在局部细节特征上的表达能力不足,提出了一种将拓扑和形状特征相结合的三维模型相似性比较方法.首先提取三维模型的骨架,获得模型的整体拓扑特征;然后根据骨架节点将模型分解为多个子部分,并利用球面谐波算法提取每一个子部分的形状特征.模型的匹配分为3步进行:整体骨架的拓扑特征相似性比较,相对应的子部分的局部形状特征相似性比较,模型总的相似性是整体骨架相似性与对应子部分局部形状相似性的加权和.实验结果表明:该方法从整体到局部、由粗到精,综合考虑了拓扑和形状特征,较传统的考虑单一拓扑或形状特征的检索算法有较高的检索精度,同时又支持基于局部特征的相似性检索.     

Skeleton-guided 3D shape distance field metamorphosis

We introduce an automatic 3D shape morphing method without the need of manually placing anchor correspondence points. Given a source and a target shape, we extract their skeletons and automatically estimate the meaningful anchor points based on their skeleton node correspondences. Based on the anchors, dense correspondences between the interior of source and target shape can be established using earth mover’s distance (EMD) optimization. Skeleton node correspondence, estimated with a voting-based method, leads to part correspondence which can be used to confine the dense correspondence within matched part pairs. This produces smooth and plausible morphing sequence based on distance field interpolation (DFI). We demonstrate the effectiveness of our algorithm over shapes with large geometric variation and structural difference.     

Distance functions and skeletal representations of rigid and non-rigid planar shapes

Shape skeletons are fundamental concepts for describing the shape of geometric objects, and have found a variety of applications in a number of areas where geometry plays an important role. Two types of skeletons commonly used in geometric computations are the straight skeleton of a (linear) polygon, and the medial axis of a bounded set of points in the k-dimensional Euclidean space. However, exact computation of these skeletons of even fairly simple planar shapes remains an open problem.In this paper we propose a novel approach to construct exact or approximate (continuous) distance functions and the associated skeletal representations (a skeleton and the corresponding radius function) for solid 2D semi-analytic sets that can be either rigid or undergoing topological deformations. Our approach relies on computing constructive representations of shapes with R-functions that operate on real-valued halfspaces as logic operations. We use our approximate distance functions to define a new type of skeleton, i.e, the C-skeleton, which is piecewise linear for polygonal domains, generalizes naturally to planar and spatial domains with curved boundaries, and has attractive properties. We also show that the exact distance functions allow us to compute the medial axis of any closed, bounded and regular planar domain. Importantly, our approach can generate the medial axis, the straight skeleton, and the C-skeleton of possibly deformable shapes within the same formulation, extends naturally to 3D, and can be used in a variety of applications such as skeleton-based shape editing and adaptive motion planning.     

Empirical mode decomposition on skeletonization pruning

This paper presents a novel skeleton pruning approach based on a 2D empirical mode like decomposition (EMD-like). The EMD algorithm can decompose any nonlinear and non-stationary data into a number of intrinsic mode functions (IMFs). When the object contour is decomposed by empirical mode like decomposition (EMD-like), the IMFs of the object provide a workspace with very good properties for obtaining the object's skeleton. The theoretical properties and the performed experiments demonstrate that the obtained skeletons match to hand-labeled skeletons provided by human subjects. Even in the presence of significant noise and shape variations, cuts and tears, the resulted skeletons have the same topology as the original skeletons. In particular, the proposed approach produces no spurious branches as many existing skeleton pruning methods and moreover, does not displace the skeleton points, which are all centers of maximal disks.     

Patch‐type Segmentation of Voxel Shapes using Simplified Surface Skeletons

We present a new method for decomposing a 3D voxel shape into disjoint segments using the shape's simplified surface‐skeleton. The surface skeleton of a shape consists of 2D manifolds inside its volume. Each skeleton point has a maximally inscribed ball that touches the boundary in at least two contact points. A key observation is that the boundaries of the simplified fore‐ and background skeletons map one‐to‐one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable properties. Our method segments both noisy shapes and shapes with soft edges which vanish over low‐curvature regions. Multiscale segmentations can be obtained by varying the simplification level of the skeleton. We present a voxel‐based implementation of our approach and illustrate it on several realistic examples.     

Euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform

A general algorithm for computing Euclidean skeletons of 2D and 3D data sets in linear time is presented. These skeletons are defined in terms of a new concept, called the integer medial axis (IMA) transform. We prove a number of fundamental properties of the IMA skeleton, and compare these with properties of the CMD (centers of maximal disks) skeleton. Several pruning methods for IMA skeletons are introduced (constant, linear and square-root pruning) and their properties studied. The algorithm for computing the IMA skeleton is based upon the feature transform, using a modification of a linear-time algorithm for Euclidean distance transforms. The skeletonization algorithm has a time complexity which is linear in the number of input points, and can be easily parallelized. We present experimental results for several data sets, looking at skeleton quality, memory usage and computation time, both for 2D images and 3D volumes.     

三维重建中形状插值的快速算法研究

提出一种用于三维重建的层间数据插值算法．该算法首先利用数学形态学算子提取层内图像骨架；然后利用骨架匹配算法获取层间骨架点集的平移、旋转和缩放信息，并利用此信息的线性插值获得插值层图像的骨架点集；最后根据形态骨架的重建算法获得插值层图像．文中算法只对骨架点集进行操作，具有较小的运算复杂度，较好地保留了原始图像的形状信息．实验结果证明了该算法的有效性．     

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.     

采用CT切片的三角片曲面重构算法

采用二维平行轮廓线三维重建表面是三维建模研究领域的一项重要研究课题，具有非常广泛的应用领域。重建过程中计算量非常庞大，有效地化简重建的数据可以大大提高重建效率。文中提出了一种基于分析轮廓骨架点的表曲面重构算法。首先对CT切片进行预处理及图像分割，然后对轮廓线提取骨架，再进行骨架剪裁，最后采用模拟退火法进行三维重建。该算法使三维重构的数据大大化简，同时克服了局部优化算法中需交互指定初始连接边的缺点。     

Skeletonisation of three-dimensional object using generalized potential field

In this paper, the potential-based skeletonization approach for 2D medial axis transform (MAT), which identifies object skeleton as potential valleys using a Newtonian potential model in place of the distance function, is generalized to three dimensions. The generalized potential functions given by Chung (1998), which decay faster with distance than the Newtonian potential, is used for the 3D case. The efficiency of the proposed approach results from the fact that these functions and their gradients can be obtained in closed forms for polyhedral surfaces. According to the simulation results, the skeletons obtained with the proposed approach are closely related to the corresponding MAT skeletons. While the medial axis (surface) is 2D in general for a 3D object, the potential valleys, being one-dimensional, form a more realistic skeleton. Other desirable attributes of the algorithm include stability against perturbations of the object boundary, the flexibility to obtain partial skeleton directly, and low time complexity.     

单幅植物叶片图像的3维重建

目的 植物叶片形态复杂,在虚拟场景中很难真实表现。为了从信息量有限的单幅图像中恢复植物叶片的3维形状,本文基于从明暗恢复形状（shape from shading,SFS）的方法,利用亮度统计规律和植物形态特征恢复叶片的3维形状。方法 在SFS的基础上,设计基于图像骨架的距离场偏置加强表面细节;针对SFS对恢复宏观几何形状的不足,提出根据图像亮度统计分布选取控制点控制表面宏观形状变化,并利用叶片中轴的距离场约束恢复宏观几何形状,每种方法对于表面宏观几何形状恢复的权重基于恢复的反射图和输入图像间的相似度设定;将表面细节添加到宏观几何形状上得到目标对象的3维形状。结果 选取植物叶片图像进行实验,并与其他方法进行比较,实验结果表明本文方法增强了表面细节显示,并有明显的宏观几何形状变化。同时为了验证本文方法对其他物体表面细节恢复的适用性,分别对硬币和恐龙恢复表面细节,实验结果表明提出的增强表面细节的方法同样适用于其他物体。结论 针对单幅植物叶片图像的3维重建,在SFS的基础上提出了根据骨架特征加强表面细节,根据图像亮度统计分布和叶片中轴距离场约束共同恢复表面宏观几何形状的算法,实验结果验证了本文方法的可行性。