Hierarchical part-type segmentation using voxel-based curve skeletons

We present an effective framework for segmenting 3D shapes into meaningful components using the curve skeleton. Our algorithm identifies a number of critical points on the efficiently computed curve skeleton, either fully automatically as the junctions of the curve skeleton, or based on user input. We use these points to construct a partitioning of the object surface using geodesics. Because the segmentation is based on the curve skeleton, it intrinsically reflects the shape symmetry and articulation, and can handle shapes with tunnels. We describe a voxel-based implementation of our method which is robust and noise resistant, able to handle shapes of complex articulation and topology, produces smooth segment borders, and delivers hierarchical level-of-detail segmentations. We demonstrate the framework on various real-world 3D shapes. Additionally, we discuss the use of both curve and surface skeletons to produce part-type and patch-type, respectively, segmentations of 3D shapes.     

Curve-skeleton extraction using iterative least squares optimization

A curve skeleton is a compact representation of 3D objects and has numerous applications. It can be used to describe an object's geometry and topology. In this paper, we introduce a novel approach for computing curve skeletons for volumetric representations of the input models. Our algorithm consists of three major steps: 1) using iterative least squares optimization to shrink models and, at the same time, preserving their geometries and topologies, 2) extracting curve skeletons through the thinning algorithm, and 3) pruning unnecessary branches based on shrinking ratios. The proposed method is less sensitive to noise on the surface of models and can generate smoother skeletons. In addition, our shrinking algorithm requires little computation, since the optimization system can be factorized and stored in the pre-computational step. We demonstrate several extracted skeletons that help evaluate our algorithm. We also experimentally compare the proposed method with other well-known methods. Experimental results show advantages when using our method over other techniques.     

A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton

We introduce a new topology-preserving 3D thinning procedure for deriving the curve voxel skeleton from 3D binary digital images. Based on a rigorously defined classification procedure, the algorithm consists of sequential thinning iterations each characterized by six parallel directional sub-iterations followed by a set of sequential sub-iterations. The algorithm is shown to produce concise and geometrically accurate 3D curve skeletons. The thinning algorithm is also insensitive to object rotation and only moderately sensitive to noise. Although this thinning procedure is valid for curve skeleton extraction of general elongated objects, in this paper, we specifically discuss its application to the orientation modeling of trabecular biological tissues.     

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.     

Variational Curve Skeletons Using Gradient Vector Flow

Representing a 3D shape by a set of 1D curves that are locally symmetric with respect to its boundary (i.e., curve skeletons) is of importance in several machine intelligence tasks. This paper presents a fast, automatic, and robust variational framework for computing continuous, subvoxel accurate curve skeletons from volumetric objects. A reference point inside the object is considered a point source that transmits two wave fronts of different energies. The first front (beta-front) converts the object into a graph, from which the object salient topological nodes are determined. Curve skeletons are tracked from these nodes along the cost field constructed by the second front (alpha-front) until the point source is reached. The accuracy and robustness of the proposed work are validated against competing techniques as well as a database of 3D objects. Unlike other state-of-the-art techniques, the proposed framework is highly robust because it avoids locating and classifying skeletal junction nodes, employs a new energy that does not form medial surfaces, and finally extracts curve skeletons that correspond to the most prominent parts of the shape and hence are less sensitive to noise.     

Isthmus based parallel and symmetric 3D thinning algorithms

We propose a 3D symmetric homotopic thinning method based on the critical kernels framework. It may produce either curvilinear or surface skeletons, depending on the criterion that is used to prevent salient features of the object from deletion. In our new method, rather than detecting curve or surface extremities, we detect isthmuses, that is, parts of an object that are “locally like a curve or a surface”. This allows us to propose a natural extension of our new method that copes with the robustness to noise issue, this extension is based on a notion of “isthmus persistence”. As far as we know, this is the first method that permits to obtain 3D symmetric and robust curvilinear/surface skeletons of objects made of voxels.     

目标骨架的多尺度树表示

基于骨架的目标表示是计算机视觉领域的重要研究内容．虽然目前基于不同原理提出了许多骨架提取算法．但是关于利用骨架信息来有效地表示并识别目标的研究却很少．文章对骨架的结构基元自顶向下地进行分解,将基元组织成层次树表示．通过引入尺度的概念．获得了目标的节点数目小、连接关系稳定的多尺度树表示．实验表明，它可以紧致、稳健地表示目标，并可降低图匹配过程的复杂度．     

Generating skeletons and centerlines from the distance transform

We describe an algorithm for generating connected skeletons of objects in a binary image. The algorithm combines essentially all desirable properties of a skeletonization method: (1) the skeletons it produces have the same simple connectivity as the objects; it is based on a distance transform and can use any “natural” distance metric (in particular those giving a good approximation to the Euclidean distance), resulting in skeletons that are both (2) well-centered and (3) robust with respect to rotation; the skeletons allow the objects to be reconstructed either (4) exactly or (5) approximately to within a specified error; (6) for approximate reconstruction, the skeletons are insensitive to “border noise” without image prefiltering or skeleton postpruning; (7) the skeletons can be thin; (8) the algorithm is fast, taking a fixed number of passes through the image regardless of the width of the objects; and (9) the skeletons have a pleasing visual appearance. Several of these properties may conflict. For example, skeletons cannot always be both thin and allow exact reconstruction and our algorithm can be run to give priority to either property. This paper describes the skeletonization algorithm, discusses the tradeoffs involved and summarizes the formal proofs of its connectivity and reconstructability properties. Because the algorithm is fast, robust, flexible, and provably correct, it is ideally suited for many of the applications of skeletonization—data compression, OCR, shape representation and binary image analysis. The quality of the skeletons produced is demonstrated with numerous examples.     

Mean Curvature Skeletons

Inspired by recent developments in contraction‐based curve skeleton extraction, we formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take advantage of its area‐minimizing characteristic to drive the curvature flow towards the extreme so as to collapse the input mesh geometry and obtain a skeletal structure. By analyzing the differential characteristics of the flow, we reveal that MCF locally increases shape anisotropy. This justifies the use of curvature motion for skeleton computation, and leads to the generation of what we call “mean curvature skeletons”. To obtain a stable and efficient discretization, we regularize the surface mesh by performing local remeshing via edge splits and collapses. Simplifying mesh connectivity throughout the motion leads to more efficient computation and avoids numerical instability arising from degeneracies in the triangulation. In addition, the detection of collapsed geometry is facilitated by working with simplified mesh connectivity and monitoring potential non‐manifold edge collapses. With topology simplified throughout the flow, minimal post‐processing is required to convert the collapsed geometry to a curve. Formulating skeletonization via MCF allows us to incorporate external energy terms easily, resulting in a constrained flow. We define one such energy term using the Voronoi medial skeleton and obtain a medially centred curve skeleton. We call the intermediate results of our skeletonization motion meso‐skeletons; these consist of a mixture of curves and surface sheets as appropriate to the local 3D geometry they capture.     

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.     

Part‐type Segmentation of Articulated Voxel‐Shapes using the Junction Rule

We present a part‐type segmentation method for articulated voxel‐shapes based on curve skeletons. Shapes are considered to consist of several simpler, intersecting shapes. Our method is based on the junction rule: the observation that two intersecting shapes generate an additional junction in their joined curve‐skeleton near the place of intersection. For each curve‐skeleton point, we construct a piecewise‐geodesic loop on the shape surface. Starting from the junctions, we search along the curve skeleton for points whose associated loops make for suitable part cuts. The segmentations are robust to noise and discretization artifacts, because the curve skeletonization incorporates a single user‐parameter to filter spurious curve‐skeleton branches. Furthermore, segment borders are smooth and minimally twisting by construction. We demonstrate our method on several real‐world examples and compare it to existing part‐type segmentation methods.     

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.     

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.

     

Skeleton-based intrinsic symmetry detection on point clouds

We present a skeleton-based algorithm for intrinsic symmetry detection on imperfect 3D point cloud data. The data imperfections such as noise and incompleteness make it difficult to reliably compute geodesic distances, which play essential roles in existing intrinsic symmetry detection algorithms. In this paper, we leverage recent advances in curve skeleton extraction from point clouds for symmetry detection. Our method exploits the properties of curve skeletons, such as homotopy to the input shape, approximate isometry-invariance, and skeleton-to-surface mapping, for the detection task. Starting from a curve skeleton extracted from an input point cloud, we first compute symmetry electors, each of which is composed of a set of skeleton node pairs pruned with a cascade of symmetry filters. The electors are used to vote for symmetric node pairs indicating the symmetry map on the skeleton. A symmetry correspondence matrix (SCM) is constructed for the input point cloud through transferring the symmetry map from skeleton to point cloud. The final symmetry regions on the point cloud are detected via spectral analysis over the SCM. Experiments on raw point clouds, captured by a 3D scanner or the Microsoft Kinect, demonstrate the robustness of our algorithm. We also apply our method to repair incomplete scans based on the detected intrinsic symmetries.     

A Pruning Algorithm for Stable Voronoi Skeletons

We present a skeleton computation algorithm for binary image shape which is stable and efficient. The algorithm follows these steps: first the shape boundary curves are subsampled, then the Voronoi Skeleton is computed from the resulting reduced boundary set of points, and finally, a?novel two stage pruning procedure is applied to obtain a?simplified skeleton. The first stage removes skeleton edges non fully included in the shape. The second stage applies an enhanced variation of the Discrete Curve Evolution (DCE) for Voronoi skeletons. We obtain improved skeleton stability, complexity reduction and noise robustness. Pruning computing time efficiency is improved thanks to some properties of Voronoi skeletons. Entire skeleton edges can be removed or retained on the basis of conditions tested on the edge endpoints. Pattern recognition experiments and skeleton stability experiments of the algorithm outperform previous approaches in the literature.     

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.     

Consistent mesh partitioning and skeletonisation using the shape diameter function

Mesh partitioning and skeletonisation are fundamental for many computer graphics and animation techniques. Because of the close link between an object’s skeleton and its boundary, these two problems are in many cases complementary. Any partitioning of the object can assist in the creation of a skeleton and any segmentation of the skeleton can infer a partitioning of the object. In this paper, we consider these two problems on a wide variety of meshes, and strive to construct partitioning and skeletons which remain consistent across a family of objects, not a single one. Such families can consist of either a single object in multiple poses and resolutions, or multiple objects which have a general common shape. To achieve consistency, we base our algorithms on a volume-based shape-function called the shape-diameter-function (SDF), which remains largely oblivious to pose changes of the same object and maintains similar values in analogue parts of different objects. The SDF is a scalar function defined on the mesh surface; however, it expresses a measure of the diameter of the object’s volume in the neighborhood of each point on the surface. Using the SDF we are able to process and manipulate families of objects which contain similarities using a simple and consistent algorithm: consistently partitioning and creating skeletons among multiple meshes.     

Effective Piecewise Linear Skeletonization of Sparse Shapes

Conventional image skeletonization techniques implicitly assume the pixel level connectivity. However, noise inside the object regions destroys the connectivity and exhibits sparseness in the image. We present a skeletonization algorithm designed for these kinds of sparse shapes. The skeletons are produced quickly by using three operations. First, initial skeleton nodes are selected by farthest point sampling with circles containing the maximum effective information. A skeleton graph of these nodes is imposed via inheriting the neighborhood of their associated pixels, followed by an edge collapse operation. Then a skeleton tting process based on feature-preserving Laplacian smoothing is applied. Finally, a re nement step is proposed to further improve the quality of the skeleton and deal with noise or different local shape scales. Numerous experiments demonstrate that our algorithm can effectively handle several disconnected shapes in an image simultaneously, and generate more faithful skeletons for shapes with intersections or different local scales than classic methods.