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In human-human interaction, body language is one of the most important emotional expressions. However, each emotion category contains abundant emotional body gestures, and basic emotions used in most researches are difficult to describe complex and diverse emotional states. It is costly to collect sufficient samples of all emotional expressions, and new emotions or new body gestures that are not included in the training set may appear during testing. To address the above problems, we design a novel mechanism that treats each emotion category as a collection of multiple body gesture categories to make better use of gesture information for emotion recognition. A Generalized Zero-Shot Learning (GZSL) framework is introduced to recognize both seen and unseen body gesture categories with the help of semantic information, and emotion predictions are further provided based on the relationship between gestures and emotions. This framework consists of two branches. The first branch is a Hierarchical Prototype Network (HPN) which learns the prototypes of body gestures and uses them to calculate the emotion attentive prototypes. This branch aims to obtain predictions on samples of the seen gesture categories. The second branch is a Semantic Auto-Encoder (SAE) which utilizes semantic representations to predict samples of unseen gesture categories. Thresholds are further trained to determine which branch result will be used during testing, and the emotion labels are finally obtained from these results. Comprehensive experiments are conducted on an emotion recognition dataset which contains skeleton data of multiple body gestures, and the performance of our framework is superior to both the traditional emotion classifier and state-of-the-art zero-shot learning methods.

In this paper, we proposed a multi-view system for 3D human skeleton tracking based on multi-cue fusion. Multiple Kinect version 2 cameras are applied to build up a low-cost system. Though Kinect cameras can detect 3D skeleton from their depth sensors, some challenges of skeleton extraction still exist, such as left–right confusion and severe self-occlusion. Moreover, human skeleton tracking systems often have difficulty in dealing with lost tracking. These challenges make robust 3D skeleton tracking nontrivial. To address these challenges in a unified framework, we first correct the skeleton's left–right ambiguity by referring to the human joints extracted by OpenPose. Unlike Kinect, and OpenPose extracts target joints by learning-based image analysis to differentiate a person's front side and backside. With help from 2D images, we can correct the left–right skeleton confusion. On the other hand, we find that self-occlusion severely degrades Kinect joint detection owing to incorrect joint depth estimation. To alleviate the problem, we reconstruct a reference 3D skeleton by back-projecting the corresponding 2D OpenPose joints from multiple cameras. The reconstructed joints are less sensitive to occlusion and can be served as 3D anchors for skeleton fusion. Finally, we introduce inter-joint constraints into our probabilistic skeleton tracking framework to trace all joints simultaneously. Unlike conventional methods that treat each joint individually, neighboring joints are utilized to position each other. In this way, when joints are missing due to occlusion, the inter-joint constraints can ensure the skeleton consistency and preserve the length between neighboring joints. In the end, we evaluate our method with five challenging actions by building a real-time demo system. It shows that the system can track skeletons stably without error propagation and vibration. The experimental results also reveal that the average localization error is smaller than that of conventional methods.

Three-dimensional human body curve-skeleton is widely used in pose estimation, skeleton animation and other fields. This paper proposes an improved $$\ell _1$$ median model that can extract three-dimensional human body curve-skeleton. The model includes three-dimensional human body reconstruction from multi-view images, interpolation curve-skeleton extraction, $$\ell _1$$ median skeleton completion, and continuous frame curve-skeleton optimization. Through the completion and optimization processes, the curve-skeleton we extract is smoother and more complete compared with previous methods. We conduct experiments on multi-view human body image dataset collected from light field acquisition system. Both quantitative and qualitative results demonstrate the effectiveness of our model.

Graph convolutional networks (GCN) have received more and more attention in skeleton-based action recognition. Many existing GCN models pay more attention to spatial information and ignore temporal information, but the completion of actions must be accompanied by changes in temporal information. Besides, the channel, spatial, and temporal dimensions often contain redundant information. In this paper, we design a temporal graph convolutional network (FTGCN) module which can concentrate more temporal information and properly balance them for each action. In order to better integrate channel, spatial and temporal information, we propose a unified attention model of the channel, spatial and temporal (CSTA). A basic block containing these two novelties is called FTC-GCN. Extensive experiments on two large-scale datasets, compared with 17 methods on NTU-RGB+D and 8 methods on Kinetics-Skeleton, show that for skeleton-based human action recognition, our method achieves the best performance.

One of the most recent challenging tasks in computer vision is Human Activity Recognition (HAR), which aims to analyze and detect the human actions for the benefit of many fields such as video surveillance, behavior analysis and healthcare. Several works in the literature are based on the extraction and analysis of human skeletons in the aim of actions recognition. This paper introduces a new HAR approach based on the extraction of human skeletons from videos. Three features extraction techniques are proposed in this work. They used the extracted skeletons from the videos frames in order to construct a single image that summarizes the activity in that video. The first technique, called dynamic skeleton, is founded on the concept of dynamic images introduced in the literature, while the second one, called skeleton superposition, is based on the superposition of the extracted human skeletons in the same image. The third contribution is called body articulations and it uses only the body joints instead of the whole skeleton in order to recognize the ongoing activity. The obtained images from these three techniques are analyzed and classified using a classification system based on transfer learning principle by fine-tuning three well-known pre-trained CNNs (MobileNet, ResNet-50, VGG16). The designed system is validated and tested on two famous datasets for human activity recognition, which are RGBD-HuDact and KTH datasets. The obtained results are outstanding and proved that the implemented system outperforms the state-of-the-art approaches.

Recently, skeleton-based action recognition has modeled the human skeleton as a graph convolution network (GCN), and has achieved remarkable results. However, most of the methods convolute directly on the whole graph, neglecting that the human skeleton is made up of multiple body parts, which cannot accomplish the task well. We recognize that the physical property of bones (i.e., length and direction) can provide identifiable information which helps effectively to build the multi-level network structure. As the existing methods treat the channel domain and the spatial domain with equal importance, many computing resources are wasted on neglectable features. In our paper, we modify the Convolution Block Attention Module (CBAM) and apply it to the adaptive network. By capturing the implicit weighted information in the channel domain and spatial domain, the network can focus more attention on the key channels and nodes. A new two-stream adaptive-attentional subgraph convolution network (2s-AASGCN) is proposed to extract features in the spatio-temporal domain. We validate 2s-AASGCN on two skeleton datasets, i.e., NTU-RGB+D60 and NTU-RGB+D120. Our model achieves excellent results on these two datasets.

Single sensing modality is widely adopted for human activity recognition (HAR) for decades and it has made a significant stride. However, it often suffers from challenges such as noises, obstacles, or dropped signals, which might negatively impact on the recognition performance. In this paper, we propose a multi-sensing modality framework for human fine-grained activity recognition and abnormal behaviour detection by combining skeleton and acceleration data at feature level (so-called feature-level fusion). Firstly, deep temporal convolutional networks (TCN), consisting of the dilated causal convolution components, are utilized for feature learning and handling temporal properties. The feature map learnt and represented with convolutional layers in TCN is fed into two fully connected layers for the prediction. Secondly, we conduct an empirical experiment to verify our proposed method. Experimental results have shown that the proposed method could achieve 83% F1-score and surpassed several single modality models as well as early and late fusion methods on the Continuous Multimodal Multi-view Dataset of Human Fall Dataset (CMDFALL), comprised of 20 fine-grained normal and abnormal activities collected from 50 subjects. Moreover, our proposed architecture achieves 96.98% accuracy on the UTD-MHAD dataset, which has 8 subjects and 27 activities. These results indicate the effectiveness of our proposed method for the classification of human fine-grained normal and abnormal activities as well as the potential for HAR-based situated service applications.

In skeleton-based action recognition, graph convolutional networks (GCNs), which model human body skeletons using graphical components such as nodes and connections, have recently achieved remarkable performance. While the current state-of-the-art methods for skeleton-based action recognition usually assume that completely observed skeletons will be provided, it is problematic to realize this assumption in real-world scenarios since the captured skeletons may be incomplete or noisy. In this work, we propose a skeleton-based action recognition method that is robust to noise interference for the given skeleton features. The key insight of our approach is to train a model by maximizing the mutual information between normal and noisy skeletons using predictive coding in the latent space. We conducted comprehensive skeleton-based action recognition experiments with defective skeletons using the NTU-RGB+D and Kinetics-Skeleton datasets. The experimental results demonstrate that when the skeleton samples are noisy, our approach achieves outstanding performances compared with the existing state-of-the-art methods.

We study the decidability of k-provability in $$\hbox {PA}$$ PA —the relation ‘being provable in $$\hbox {PA}$$ PA with at most k steps’—and the decidability of the proof-skeleton problem—the problem of deciding if a given formula has a proof that has a given skeleton (the list of axioms and rules that were used). The decidability of k-provability for the usual Hilbert-style formalisation of $$\hbox {PA}$$ PA is still an open problem, but it is known that the proof-skeleton problem is undecidable for that theory. Using new methods, we present a characterisation of some numbers k for which k-provability is decidable, and we present a characterisation of some proof-skeletons for which one can decide whether a formula has a proof whose skeleton is the considered one. These characterisations are natural and parameterised by unification algorithms.

In this paper, we propose two effective manners of utilizing skeleton data for human action recognition (HAR). The proposed method on one hand takes advantage of the skeleton data thanks to their robustness to human appearance change as well as the real-time performance. On the other hand, it avoids inherent drawbacks of the skeleton data such as noises, incorrect human skeleton estimation due to self-occlusion of human pose. To this end, in terms of feature designing, we propose to extract covariance descriptors from joint velocity and combine them with those of joint position. In terms of 3-D skeleton-based activity representation, we propose two schemes to select the most informative joints. The proposed method is evaluated on two benchmark datasets. On the MSRAction-3D dataset, the proposed method outperformed different hand-designed features-based methods. On the challenging dataset CMDFall, the proposed method significantly improves accuracy when compared with techniques based on recent neuronal networks. Finally, we investigate the robustness of the proposed method via a cross-dataset evaluation.

For partially hyperbolic diffeomorphisms with mostly expanding and mostly contracting centers, we establish a topological structure, called skeleton—a set consisting of finitely many hyperbolic periodic points with maximal cardinality for which there exist no heteroclinic intersections. We build the one-to-one corresponding between periodic points in any skeleton and physical measures. By making perturbations on skeletons, we study the continuity of physical measures with respect to dynamics under $$C^1$$ -topology.

Humans regularly interact with their surrounding objects. Such interactions often result in strongly correlated motions between humans and the interacting objects. We thus ask: “Is it possible to infer object properties from skeletal motion alone, even without seeing the interacting object itself?” In this paper, we present a fine-grained action recognition method that learns toinfersuch latent object properties from human interaction motion alone. This inference allows us todisentanglethe motion from the object property andtransferobject properties to a given motion. We collected a large number of videos and 3D skeletal motions of performing actors using an inertial motion capture device. We analyzed similar actions and learned subtle differences between them to reveal latent properties of the interacting objects. In particular, we learned to identify the interacting object, by estimating its weight, or its spillability. Our results clearly demonstrate that motions and interacting objects are highly correlated and that related object latent properties can be inferred from 3D skeleton sequences alone, leading to new synthesis possibilities for motions involving human interaction. Our dataset is available athttp://vcc.szu.edu.cn/research/2020/IT.html.

With the development of motion capture technologies, 3D action recognition has become a popular task that finds great applicability in many areas, such as augmented reality, human–computer interaction, sports, or healthcare. On the other hand, the acquisition of 3D human skeleton data is an expensive and time-consuming process, mainly due to the high costs of capturing technologies and the absence of suitable actors. We overcome these issues by focusing on the 2D skeleton modality that can be easily extracted from ordinary videos. The objective of this work is to demonstrate a high descriptive power of such a 2D skeleton modality by achieving accuracy on the task of daily action recognition competitive to 3D skeleton data. More importantly, we thoroughly analyze the factors that significantly influence the 2D recognition accuracy, such as the sensitivity towards data normalization, scaling, quantization, and 3D-to-2D distortions in skeleton orientations and sizes, which are caused by the loss of depth dimension and fixed-angle camera view. We also provide valuable insights on how to mitigate these problems to increase recognition accuracy significantly. The experimental evaluation is conducted on three datasets different in nature. The ability to learn different types of actions better using either 2D or 3D skeletons is also reported. Throughout experiments, a generic light-weight LSTM network is used, whose architecture can be easily tuned to achieve the desired trade-off between its accuracy and efficiency. We show that the proposed approach achieves not only the state-of-the-art results in 2D skeleton action recognition but is also highly competitive to the best-performing methods classifying 3D skeleton sequences or the visual content extracted from ordinary videos.

We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of what we call `spider moves'. We then create a category by modding out by the 2-cells of our 2-category, and use the spider moves to show that for finite graphs, this category is a homotopy category in the sense that it satisfies the universal property for localizing homotopy equivalences. We then show that finite stiff graphs form a skeleton of this homotopy category.

To facilitate the input and improve the practicality of the existing virtual fitting systems, we propose a fully automatic 3D virtual fitting system to fit garment onto human models with various shapes and poses using a 2D full-body image and a 3D garment model. The proposed method constructs the 3D human model from the input 2D full-body image of the user by adopting the SMPLify method. To automatically position garment models onto human models with arbitrary postures, we present a 3D mesh segmentation method based on the discrete Reeb graph to accurately segment the different parts of a garment model, and a skeleton driving method based on mean curvature flow, which automatically adjusts the posture of the garment model according to the skeleton structural difference between the human model and the garment model. In addition, for the purpose of obtaining a more natural dress effect, we further adopt interpenetration removal and physical simulation for the deformed garment model. Compared to existing automatic 3D virtual fitting systems, the experimental results, we obtained based on the Leeds Sports Pose dataset, reveal that the proposed virtual fitting system is stable and effective.

Combined-permutation representations (CPRs) for characterizing $${\varvec{I}}_{h}$$ -skeletons (a dodecahedral skeleton 1 having 20 vertices, an icosahedral skeleton 2 having 12 vertices, and a $$\hbox {C}_{{60}}$$ -fullerene skeleton 3 having 60 vertices) are constructed by starting from respective sets of generators, where the permutation of each generator is combined with a mirror-permutation of 2-cycle to give the CPR of degree 22 (= 20 + 2) for 1, the CPR of degree 14 (= 12 + 2) for 2, and the CPR of degree 62 (= 60 + 2) for 3. Mark tables (tables of marks) of these CPRs are different in the sequence of subgroups from each other when they are produced as primary mark tables by the GAP system. On the other hand, the GAP functions MarkTableforUSCI and constructUSCITable, which have been previously developed to systematize the concordant construction of a standard mark table and a standard USCI-CF (unit-subduced-cycle-index-with-chirality-fittingness) table, are capable of constructing the standard mark table and the standard USCI-CF table even if we start from any of these CPRs. After a set of PCI-CFs (partial cycle indices with chirality fittingness) is calculated for each skeleton, symmetry-itemized combinatorial enumeration is conducted by means of the PCI method of Fujita’s USCI approach (Fujita in Symmetry and combinatorial enumeration in chemistry, Springer, Berlin, 1991). Construction of the CPR of degree 7 (= 5 + 2) for characterizing the $${\varvec{I}}_{h}$$ group is also discussed by starting from the alternating group $$\hbox {A}_{{5}}$$ isomorphic to the point group $${\varvec{I}}$$ .

Current approaches of human body skeleton extraction mainly suffer from following problems: insufficient temporal and spatial continuity, unrobust to background, ambient noise, etc. This paper proposes a three-dimensional human body skeleton extraction method from consecutive meshes. We extract the consistent skeletons from consecutive surfaces based on shape segmentation and skeleton sequences; then, we present a spatiotemporal skeleton optimization model to adjust the skeleton sequences. Experiments on multiview images captured from a light field device demonstrate that our method captures more complete and accurate skeletons compared to state-of-the-art methods.

In this paper, an automatic method is proposed to generate a symmetry-aware kinematic skeleton for a human body model with an arbitrary pose and orientation. First, a template kinematic skeleton with semantics is embedded into the input human body model. Then, the joints of the embedded kinematic skeleton are refined according to the geometry of the human body model and some prior knowledge. Finally, a specific local coordinate system is defined on the kinematic skeleton and is used to distinguish the symmetry of the kinematic skeleton. In this way, the symmetric joints of the kinematic skeleton, e.g., the left knee joint and the right knee joint, can be distinguished. Quantitative and qualitative analysis and comparison show that the proposed method can generate a symmetry-aware kinematic skeleton with accurate joints and has no restrictions on the pose and orientation of the input human body model. Moreover, this paper presents validation of the proposed method in many applications, such as shape alignment, shape deformation, shape co-segmentation and shape correspondence.

Recently, skeleton-based action recognition approaches achieve great improvement by providing various features from skeleton sequences as the inputs of deep neural networks for classification. Compared with other works which directly utilize the locations of joints as the representation of each action for recognition, our paper describes the relative relations embedded in skeletons to alleviate the impact of viewpoint diversity. Specifically, we propose a novel feature descriptor based on the rotation relations in skeletons to represent a certain action. Geometric algebra (GA) is introduced to calculate and derive the rotation relations according to the particular operator, namely the rotor in GA. In order to exploit the spatial and temporal characteristics in one skeleton sequence, we design two different rotor-based feature descriptors, respectively, from one frame of skeleton and two skeletons of consecutive frames. Then an efficient feature encoding strategy is proposed to transform each kind of feature descriptor into a RGB image. Afterward, we propose a two-stream convolutional neural network(CNN) based framework to learn the RGB images generated by each skeleton sequence and then fuse the scores of two networks to provide final recognition accuracy. Extensive experimental results on NTU RGB+D, Northwestern-UCLA, Gaming 3D, SYSU and UTD-MHAD datasets have demonstrated the superiority of our method.

In recent years, skeleton-based human action recognition has attracted substantial attentions. However, owing to the complexity and nonlinearity of human action data, it is still a challenging task to precisely represent skeleton features. Motivated by the effectiveness of Lie Group skeletal representations in extracting human action features and the powerful capability of deep neural networks in feature learning and high-dimensional data processing, we proposed to combine Lie Group features and deep learning for human action recognition. Human skeleton information was firstly used to overcome the interference of external factors such as changes of lighting conditions and body shape. And then, Lie Group was applied to naturally represent the complex and diverse action data. Finally, we took use of convolutional neural networks to learn and classify the Lie Group features. Experiments were performed on three public datasets, and the experimental results show that our methods can achieve higher average recognition accuracy of 93.00% on Florence3D-Action, 93.68% on MSR Action Pairs, and 97.96% on UT Kinect-Action, which outperforms many of the state-of-the-art methods.

The collection of hereditary classes of modules over an arbitrary ring R is a pseudocomplemented complete big lattice. The elements of its skeleton are precisely the natural classes of R-modules. In this paper we extend some results about hereditary classes in R-Mod to the category $$\mathcal {L}_\mathcal {M}$$ of linear modular lattices, which has as objects all modular complete lattices and as morphisms all linear morphisms. We also define natural classes in the full subcategory $$\mathcal {L}_{{\mathcal {M}}_{c}}$$ of upper semicontinuous modular complete lattices and show that the collection of these classes is the skeleton of the big lattice of hereditary classes in $$\mathcal {L}_{{\mathcal {M}}_{c}}$$ and is a boolean big lattice.

The surface of a 3-dimensional cube can be continuously flattened onto any of its faces, by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. Let $$C_n$$ be an n-dimensional cube with $$n \ge 4$$, and S be the set of its 2-dimensional faces, i.e., the 2-dimensional skeleton of the square faces in $$C_n$$. We show that S can be continuously flattened onto any face F of S, such that the faces of S that are parallel to F, do not have any crease, that is, they are rigid during the motion.

Person re-identification is to search for a correct match for a person of interest across different camera views among a large number of impostors. While the approaches based on RGB modality have been widely studied to re-identify people, other modalities could be exploited as additional information sources, like depth and skeleton modalities. In this paper, we perform multi- and single-modal person re-identification using RGB, depth and skeleton modalities obtained by RGB-D sensors. First of all, the depth and RGB images are divided into three regions of head, torso and legs. Then, each region is explained by the histograms of local vector patterns (LVP). In depth and RGB modalities, the depth values of pixels and the gray levels of pixels are used for extracting LVPs, respectively. The skeleton features are extracted by computing the various Euclidean distances for the joint points of skeleton images. Then, features extracted by different modalities are combined as double and triple combinations using score-level fusion. The experiments are evaluated on two RGBD-ID and KinectREID databases, and results illustrate the acceptable performance of the proposed method.

The main goal of this work is to design an automated solution based on RGB-D data for quantitative analysis, perceptible evaluation and comparison of handball player’s performance. To that end, we introduced a new RGB-D dataset that can be used for an objective comparison and evaluation of handball player’s performance during throws. We filmed 62 handball players (44 beginners and 18 experts), who performed the same type of action, using a Kinect V2 sensor that provides RGB data, depth data and skeletons. Moreover, using skeleton data simulating 3D joint connections, we examined the main angles responsible for throwing performance in order to analyze individual skills of handball players (beginners against model and experts) relatively to throw actions. The comparison was performed statically (using only one frame) as well as dynamically during the entire throwing action. In particular, given the temporal sequence of 25 joints of each handball player, we adopted the dynamic time warping technique to compare the throwing motion between two athletes. The obtained results were found to be promising. Thus, the suggested markless solution would help handball coaches to optimize beginners’ movements during throwing actions.

We obtain the sufficient conditions of boundedness of L-index in joint variables for analytic functions in the unit ball, where $$ L:{\mathbb{C}}^n\to {\mathbb{R}}_{+}^n $$ is a continuous positive vector-function. They give an stimate of the maximum modulus of an analytic function by its minimum modulus on a skeleton in a polydisc and describe the behavior of all partial logarithmic derivatives outside some exceptional set and the distribution of zeros. The deduced results are also new for analytic functions in the unit disc of bounded index and l-index. They generalize known results by G. H. Fricke, M. M. Sheremeta, A. D. Kuzyk, and V. O. Kushnir.

Parallel programming can be difficult and error prone, in particular if low-level optimizations are required in order to reach high performance in complex environments such as multi-core clusters using MPI and OpenMP. One approach to overcome these issues is based on algorithmic skeletons. These are predefined patterns which are implemented in parallel and can be composed by application programmers without taking care of low-level programming aspects. Support for algorithmic skeletons is typically provided as a library. However, optimizations are hard to implement in this setting and programming might still be tedious because of required boiler plate code. Thus, we propose a domain-specific language for algorithmic skeletons that performs optimizations and generates low-level C++ code. Our experimental results on four benchmarks show that the models are significantly shorter and that the execution time and speedup of the generated code often outperform equivalent library implementations using the Muenster Skeleton Library.

We study the complexity of approximating complex zero sets of certain $n$-variate exponential sums. We show that the real part, $R$, of such a zero set can be approximated by the $(n-1)$-dimensional skeleton, $T$, of a polyhedral subdivision of $\mathbb{R}^n$. In particular, we give an explicit upper bound on the Hausdorff distance: $\Delta(R,T) =O\left(t^{3.5}/\delta\right)$, where $t$ and $\delta$ are respectively the number of terms and the minimal spacing of the frequencies of $g$. On the side of computational complexity, we show that even the $n=2$ case of the membership problem for $R$ is undecidable in the Blum-Shub-Smale model over $\mathbb{R}$, whereas membership and distance queries for our polyhedral approximation $T$ can be decided in polynomial-time for any fixed $n$., Comment: 18 pages, 3 figures. This version corrects an erroneous proof of Theorem 1.1, and a small typo in Assertion (3) of Theorem 1.5, in the published version

The paper established a double filtering method (DFM) to visualize the skeleton industrial structure (SIS) of one economy and find its evolution rule. Different with the previous researches, this method is from a new view of industrial conjunctions combined by leading sectors to depict the industrial structure. It was proved that the leading sector selected by DFM must be key sector selected by Hirschman-Rasmussen method. Applied DFM to input-output tables of China, Japan and USA and MFA to Japan and USA, the results analysis showed that DFM could overtake the two main shortcomings of minimum flow analysis (MFA), scratch SIS of each economy with its own characteristics, visualize the general evolution rules of the industrial structure with crisscrossed conjunctions among leading sectors.

In this article we use techniques from tropical and logarithmic geometry to construct a non-Archimedean analogue ofTeichmüller space$$\overline{{{\mathcal {T}}}}_g$$T¯gwhose points are pairs consisting of a stable projective curve over a non-Archimedean field and a Teichmüller marking of the topological fundamental group of its Berkovich analytification. This construction is closely related to and inspired by the classical construction of a non-Archimedean Schottky space for Mumford curves by Gerritzen and Herrlich. We argue that the skeleton of non-Archimedean Teichmüller space is precisely the tropical Teichmüller space introduced by Chan–Melo–Viviani as a simplicial completion of Culler–Vogtmann Outer space. As a consequence, Outer space turns out to be a strong deformation retract of the locus of smooth Mumford curves in$$\overline{{\mathcal {T}}}_g$$T¯g.

Bellow theorem says that any polyhedron with rigid faces cannot change its volume even if it is flexible. The problem on continuous flattenig of polyhedra with non-rigid faces proposed by Demaine et al. was solved for all convex polyhedra by using the notion of moving creases to change some of the faces. This problem was extended to a problem on continuous flattening of the 2-dimensional skeleton of higher dimensional polytopes. This problem was solved for all regular polytopes except three types, the 24-cell, the 120-cell, and the 600-cell. This article addresses the 24-cell and gives a continuous flattening motion for its 2-skeleton, which is related to the Jitterbug by Buckminster Fuller.

Devices with variable stiffness are drawing more and more attention with the growing interests of human-robot interaction, wearable robotics, rehabilitation robotics, etc. In this paper, the authors report on the design, analysis and experiments of a stiffness variable passive compliant device whose structure is a combination of a reconfigurable elastic inner skeleton and an origami shell. The main concept of the reconfigurable skeleton is to have two elastic trapezoid four-bar linkages arranged in orthogonal. The stiffness variation generates from the passive deflection of the elastic limbs and is realized by actively switching the arrangement of the leaf springs and the passive joints in a fast, simple and straightforward manner. The kinetostatics and the compliance of the device are analyzed based on an efficient approach to the large deflection problem of the elastic links. A prototype is fabricated to conduct experiments for the assessment of the proposed concept. The results show that the prototype possesses relatively low stiffness under the compliant status and high stiffness under the stiff status with a status switching speed around 80 ms.

A key step in processing natural trees from point cloud data is to reconstruct the trees’ skeleton, which plays an important role in forest investigation and monitoring. Although the techniques for general objects skeletonizing based on point clouds have made a large stride, there are few efficient and simple studies on the natural trees, which have complex topologies. In this paper, we propose a novel method to reconstruct tree skeletons based on the point cloud data, named as the force field driven tree skeleton extracting method, which consists of the following steps. Specifically, to make the point cloud tree a little bit cleaner, the hierarchical subdivision to the original point cloud space is firstly proposed. Then the split-level of the trees’ applied space is considered in each layers, and a simplified representation of the feature points for the tree model is then established under the neighbor relationships. After that, the feature points in the peripheral are connected by the geodesic distance. To get the initial skeleton, the surface geodesic lines are compressed into the tree model by applying a visible repulsive force field. Finally, the final skeleton is acquired by polishing the initial skeleton according to a threshold setting. The experimental results on two kinds of representative naturally growing trees, which are the Cherry and Michelia, indicate that this method can provide a satisfactory performance.

Novel methods based on depth and skeleton information of RGB-D sensors are proposed for person re-identification. Firstly, the depth images of the body are divided into three parts, i.e., head, torso and legs. Then, each part is described using histograms of local binary pattern and local derivative pattern. Also, the local pattern descriptors are combined with Gabor features for robustness against illumination. In the next step, these features are combined with skeleton features using the score-level fusion with sum rule. The results are evaluated on the KinectREID database, and experimental results show the good performance of the proposed methods.

In the traditional gait skeleton model, the fixed length proportions among different bones cause the loss of model personality, and the shoulder and hip points that are blocked by the body are difficult to be extracted. For those problems, a method based on the spatial and temporal fusion between vision and tactility is proposed, by which a equal proportion 3D gait skeleton model can be restructured in the camera coordinate system accurately through a single-frame image. In the geometric analysis process, some logical assumptions are proposed according to human anatomy and the laws of human movement, and an effective method is proposed for the extraction of thigh slope. The experimental result shows that the consistent equal proportion models, in which single bone length error is eventually controlled within $$\pm \,5\,{\text {mm}}$$, can be extracted in different position under the premise of rapidity with the aid of this method. The extracted shoulder and hip points also meet the real human body skeleton structure, which lays the foundation for the integrity and rationality of the entire skeletal model.

The purpose of this paper is to investigate restriction $$\omega $$ -semigroups. Here a restriction $$\omega $$ -semigroup is a generalisation of an inverse $$\omega $$ -semigroup. We give a description of a class of restriction $$\omega $$ -semigroups, namely, restriction $$\omega $$ -semigroups with an inverse skeleton. We show that a restriction $$\omega $$ -semigroup with an inverse skeleton is an ideal extension of a $$\widetilde{\mathcal {J}}$$ -simple restriction $$\omega $$ -semigroup by a restriction semigroup with a finite chain of projections with a zero adjoined. This result is analogous to Munn’s result for inverse $$\omega $$ -semigroups. In addition, we show that the Bruck–Reilly semigroup of a strong semilattice of monoids indexed by a finite chain is a $$\widetilde{\mathcal {J}}$$ -simple restriction $$\omega $$ -semigroup with an inverse skeleton, conversely, every $$\widetilde{\mathcal {J}}$$ -simple restriction $$\omega $$ -semigroup with an inverse skeleton arises in this way.

This paper aims to address the very challenging problem of efficient and accurate hand tracking from depth sequences, meanwhile to deform a high-resolution 3D hand model with geometric details. We propose an integrated regression framework to infer articulated hand pose, and regress high-frequency details from sparse high-resolution 3D hand model examples. Specifically, our proposed method mainly consists of four components: skeleton embedding, hand joint regression, skeleton alignment, and high-resolution details integration. Skeleton embedding is optimized via a wrinkle-based skeleton refinement method for faithful hand models with fine geometric details. Hand joint regression is based on a deep convolutional network, from which 3D hand joint locations are predicted from a single depth map, then a skeleton alignment stage is performed to recover fully articulated hand poses. Deformable fine-scale details are estimated from a nonlinear mapping between the hand joints and per-vertex displacements. Experiments on two challenging datasets show that our proposed approach can achieve accurate, robust, and real-time hand tracking, while preserve most high-frequency details when deforming a virtual hand.

This paper introduces a new method for human action recognition based on human body skeleton. The proposed method is composed of two phases: an off-line phase which selects the most discriminant human body regions and an online phase to classify the request action. In both phases, we applied the cumulative skeletonized images matrix to extract the action features. The experimental study shows that the proposed method, thanks to salient regions selection and the two-level classification strategy, provides good results comparable in terms of recognition accuracy to the most known and recent state-of-the-art methods.

Currently RNN-based methods achieve excellent performance on action recognition using skeletons. But the inputs of these approaches are limited to coordinates of joints, and they improve the performance mainly by extending RNN models in different ways and exploring relations of body parts directly from joint coordinates. Our method utilizes a universal spatial model perpendicular to the RNN model enhancement. Specifically, we propose two simple geometric features, inspired by previous work. With experiments on a 3-layer LSTM (Long Short-Term Memory) framework, we find that the geometric relational features based on vectors and normal vectors outperform other methods and achieve state-of-art results on two datasets. Moreover, we show that utilizing our features as input requires less data for training.

Facing the task of model-based retrieval, this paper proposes an L 1-medial skeleton-based 3D point cloud model retrieval method. First, L 1-medial skeleton is extracted to represent the spatial structural characteristic of individual 3D point cloud model. Second, the graph matching method is leveraged to handle pairwise 3D models matching problem. To quantitatively evaluate the proposed method, we construct a new 3D point cloud model dataset and implement extensive experiments on it. The experimental results demonstrate the superiority of the proposed method.

Dimethyl 3-(2-bromophenyl)dibenzo[b,f]pyrrolo[1,2-d][1, 4]oxazepine-1,2-dicarboxylate and its 3,13b-dihydro and 1,2,3,13b-tetrahydro analogs undergo intramolecular cyclization under free radical conditions with the formation of dimethyl 7-oxa-2a1-azabenzo[b]-cyclopenta[pq]pleiadene-1,2-dicarboxylate, the unique representative of pyrrole-fused dibenzo[b,f][1, 4]oxazepines, consisting of six fused rings. This nonplanar oxazapolyheterocycle shows a strong blue emission in dichloromethane.

This paper presents a faster RRT-based path planning approach for regular 2-dimensional (2D) building environments. To minimize the planning time, we adopt the idea of biasing the RRT tree-growth in more focused ways. We propose to calculate the skeleton of the 2D environment first, then connect a geometrical path on the skeleton, and grow the RRT tree via the seeds generated locally along this path. We conduct batched simulations to find the universal parameters in manipulating the seeds generation. We show that the proposed skeleton-biased locally-seeded RRT (skilled-RRT) is faster than the other baseline planners (RRT, RRT*, A*-RRT, Theta*-RRT, and MARRT) through experimental tests using different vehicles in different 2D building environments. Given mild assumptions of the 2D environments, we prove that the proposed approach is probabilistically complete. We also present an application of the skilled-RRT for unmanned ground vehicle. Compared to the other baseline algorithms (Theta*-RRT and MARRT), we show the applicability and fast planning of the skilled-RRT in real environment.

It is a challenge to suggest a constitutive model for describing the stress-strain behavior of sand-fines mixtures due to that these granular mixtures exhibited very complex behaviors at different densities, pressures and fines contents. In this study, an elastoplastic constitutive model within the framework of the bounding surface plasticity and critical state theories was proposed for sand-nonplastic-fines mixtures by using the concept of the equivalent-skeleton void ratio and equivalent-skeleton void-ratio state index. The proposed model with a set of material constants calibrated from a few tests could be used to model the fines-dependent and state-dependent behaviors of the sand-nonplastic-fines mixture including the strain-softening and volumetric-expansion behaviors in the drained triaxial compression tests, and also the effects of fines content on the critical state lines in both the deviatoric stress versus mean effective stress and the void ratio versus mean effective stress planes.

Skeletons provide landmark points that preserve implicit strokes or medial structure within a shape for compact representation. Though, hand posture shapes are usually recognized by region or contour representations, some applications may only be interested in the recognition of medial structures within the postures rather than their exact outlines and regions. Proposed work identifies several unique medial structures formed by a set of both one and two-handed postures and demonstrates their pure skeletal recognition in real-time. Existing skeleton-based recognition schemes apply the complex segmental processing on underlying skeleton and rely on contour information which is not suitable for fast recognition of medial structures. Presented work applies intuitive Eigen-space based Principal Components of Symbolic Structure (PCSS) and geometric Equi-Polar Signature (EPS) features to accomplish the recognition task. Both PCV and EPS process the skeleton globally without sections without associating contour information. Recognition accuracy up to 94% is obtained on a 22 posture dataset comprising of 10,560 depth frames with 480 samples for each posture. Depth sensor based acquisition is employed to meet the real-time requirements.

We introduce a distance field guided $$L_1$$ -median method to extract topologically clean 1D curve skeleton from the point cloud model. We first voxelize the input point cloud, and compute the distance field for the point cloud. Then with the distance field, we extract the initial skeleton of the model using a multi-scale parameter controlled thinning method. Finally, we incorporate the initial skeleton into the $$L_1$$ -median optimization, and develop a distance field guided $$L_1$$ -median to effectively extract the complete skeleton from the point cloud. Our method exhibits the advantages of both the distance field based skeleton extraction methods and the $$L_1$$ -median skeleton extraction methods. Our skeleton extraction system is robust and effective, and can be applied to the raw scanned point cloud data.

3D printing has become popular and has been widely used in various applications in recent years. More and more home users have motivation to design their own models and then fabricate them using 3D printers. However, the printed objects may have some structural or stress defects as the users may be lack of knowledge on stress analysis on 3D models. In this paper, we present an approach to help users analyze a model’s structural strength while designing its shape. We adopt sectional structural analysis instead of conventional FEM (Finite Element Method) analysis which is computationally expensive. Based on sectional structural analysis, our approach imports skeletons to assist in integrating mesh designing, strength computing and mesh correction well. Skeletons can also guide sections building and load calculation for analysis. For weak regions with high stress over a threshold value in the model from analysis result, our system corrects them by scaling the corresponding bones of skeleton so as to make these regions stiff enough. A number of experiments have demonstrated the applicability and practicability of our approach.

We consider the problem of minimising an inhomogeneous anisotropic elliptic functional in a class of closed $m$ dimensional subsets of $\mathbf{R}^n$ which is stable under taking smooth deformations homotopic to the identity and under local Hausdorff limits. We prove that the minimiser exists inside the class and is an $(\mathscr{H}^m,m)$~rectifiable set in the sense of Federer. The class of competitors encodes a notion of spanning a boundary. We admit unrectifiable and non-compact competitors and boundaries, and we make no restrictions on the dimension $m$ and the co-dimension $n-m$ other than $1 \le m < n$. An important tool for the proof is a novel smooth deformation theorem. The skeleton of the proof and the main ideas follow Almgren's 1968 paper. In the end we show that classes of sets spanning some closed set $B$ in homological and cohomological sense satisfy our axioms., This is a pre-print of an article accepted for publication in Calc. Var. PDE

Jan Zalasiewicz enjoys Brian Switek’s exploration of how the human scaffold — and our ideas about it — evolved. Jan Zalasiewicz enjoys Brian Switek’s exploration of how the human scaffold — and our ideas about it — evolved.

In the present paper, we investigate the question if the skeleton of a Mumford curve of genus two can be tropicalized faithfully in dimension three, i.e. if there exists an embedding of the curve in projective three space such that the tropicalization maps the skeleton of the curve isometrically to its image. Baker, Payne and Rabinoff showed that the skeleton of every analytic curve can be tropicalized faithfully. However the dimension of the ambient space in their proof can be quite large. We will define a map from the skeleton to the tropicalization of the Jacobian, which is an isometry on the cycles. It allows us to find principal divisors and simultanously to determine the retractions of their support on the skeleton which is necessary to calculate their tropicalization. It turns out that a Mumford curve of genus two whose cycles of its skeleton are either disjoint or share an edge of length at most half of the length of the cycles, can be tropicalized faithfully in dimension three., 17 pages