Discrete Skeleton Research Articles

Approximation of multistage stochastic programming problems by smoothed quantization

We present an approximation technique for solving multistage stochastic programming problems with an underlying Markov stochastic process. This process is approximated by a discrete skeleton process, which is consequently smoothed down by means of the original unconditional distribution. Approximated in this way, the problem is solvable by means of Markov Stochastic Dual Dynamic Programming. We state an upper bound for the nested distance between the exact process and its approximation and discuss its convergence in the one-dimensional case. We further propose an adjustment of the approximation, which guarantees that the approximate problem is bounded. Finally, we apply our technique to a real-life production-emission trading problem and demonstrate the performance of its approximation given the “true” distribution of the random parameters.

Curve Skeleton Extraction from Incomplete Point Clouds of Livestock and Its Application in Posture Evaluation

As consumer-grade depth sensors provide an efficient and low-cost way to obtain point cloud data, an increasing number of applications regarding the acquisition and processing of livestock point clouds have been proposed. Curve skeletons are abstract representations of 3D data, and they have great potential for the analysis and understanding of livestock point clouds. Articulated skeleton extraction has been extensively studied on 2D and 3D data. Nevertheless, robust and accurate skeleton extraction from point set sequences captured by consumer-grade depth cameras remains challenging since such data are often corrupted by substantial noise and outliers. Additionally, few approaches have been proposed to overcome this problem. In this paper, we present a novel curve skeleton extraction method for point clouds of four-legged animals. First, the 2D top view of the livestock was constructed using the concave hull algorithm. The livestock data were divided into the left and right sides along the bilateral symmetry plane of the livestock. Then, the corresponding 2D side views were constructed. Second, discrete skeleton evolution (DSE) was utilized to extract the skeletons from those 2D views. Finally, we divided the extracted skeletons into torso branches and leg branches. We translated each leg skeleton point to the border of the nearest banded point cluster and then moved it to the approximate centre of the leg. The torso skeleton points were calculated according to their positions on the side view and top view. Extensive experiments show that quality curve skeletons can be extracted from many livestock species. Additionally, we compared our method with representative skeleton extraction approaches, and the results show that our method performs better in avoiding topological errors caused by the shape characteristics of livestock. Furthermore, we demonstrated the effectiveness of our extracted skeleton in detecting frames containing pigs with correct postures from the point cloud stream.

Three-Dimensional Diffusion Model in Sports Dance Video Human Skeleton Detection and Extraction

The research in this paper mainly includes as follows: for the principle of action recognition based on the 3D diffusion model convolutional neural network, the whole detection process is carried out from fine to coarse using a bottom-up approach; for the human skeleton detection accuracy, a multibranch multistage cascaded CNN structure is proposed, and this network structure enables the model to learn the relationship between the joints of the human body from the original image and effectively predict the occluded parts, allowing simultaneous prediction of skeleton point positions and skeleton point association information on the one hand, and refinement of the detection results in an iterative manner on the other. For the combination problem of discrete skeleton points, it is proposed to take the limb parts formed between skeleton points as information carriers, construct the skeleton point association information model using vector field, and consider it as a feature, to obtain the relationship between different skeleton points by using the detection method. It is pointed out that the reorganization problem of discrete skeleton points in multiperson scenes is an NP-Hard problem, which can be simplified by decomposing it into a set of subproblems of bipartite graph matching, thus proposing a matching algorithm for discrete skeleton points and optimizing it for the skeleton dislocation and algorithm problems of human occlusion. Compared with traditional two-dimensional images, audio, video, and other multimedia data, the 3D diffusion model data describe the 3D geometric morphological information of the target scene and are not affected by lighting changes, rotation, and scale transformation of the target and thus can describe the realistic scene more comprehensively and realistically. With the continuous updating of diffusion model acquisition equipment, the rapid development of 3D reconstruction technology, and the continuous enhancement of computing power, the research on the application of 3D diffusion model in the detection and extraction of a human skeleton in sports dance videos has become a hot direction in the field of computer vision and computer graphics. Among them, the feature detection description and model alignment of 3D nonrigid models are a fundamental problem with very important research value and significance and challenging at the same time, which has received wide attention from the academic community.

On time-discretized versions of the stochastic SIS epidemic model: a comparative analysis.

In this paper, the interest is in the use of time-discretized models as approximations to the continuous-time birth-death (BD) process [Formula: see text] describing the number I(t) of infective hosts at time t in the stochastic [Formula: see text] (SIS) epidemic model under the assumption of an additional source of infection from the environment. We illustrate some simple techniques for analyzing discrete-time versions of the continuous-time BD process [Formula: see text], and we show the similarities and differences between the discrete-time BD process [Formula: see text] of Allen and Burgin (Math Biosci 163:1-33, 2000), which is inspired from the infinitesimal transition probabilities of [Formula: see text], and an alternative discrete-time Markov chain [Formula: see text], which is defined in terms of the number [Formula: see text] of infective hosts at a sequence [Formula: see text] of inspection times. Processes [Formula: see text] and [Formula: see text] can be thought of as a uniformized version and the discrete skeleton of process [Formula: see text], respectively, and are commonly used to derive, in the more general setting of Markov chains, theorems about a continuous-time Markov chain by applying known theorems for discrete-time Markov chains. We shall demonstrate here that the continuous-time BD process [Formula: see text] and its discrete-time counterparts [Formula: see text] and [Formula: see text] behave asymptotically the same in the limit of large time index, while the processes [Formula: see text] and [Formula: see text] differ from the continuous-time BD process [Formula: see text] in terms of the random length of an outbreak, or when considering their dynamics during a predetermined time interval [Formula: see text]. To compare the dynamics of process [Formula: see text] with those of the discrete-time processes [Formula: see text] and [Formula: see text] during [Formula: see text], we consider extreme values (i.e., maximum and minimum number of infectives simultaneously observed during [Formula: see text]) in these three processes. Finally, we illustrate our analytical results by means of a number of numerical examples, where we use the Hellinger distance between two probability distributions to quantify the similarity between the resulting extreme value distributions of either [Formula: see text] and [Formula: see text], or [Formula: see text] and [Formula: see text].

Adversarial Attack on Skeleton-Based Human Action Recognition

Deep learning models achieve impressive performance for skeleton-based human action recognition. Graph convolutional networks (GCNs) are particularly suitable for this task due to the graph-structured nature of skeleton data. However, the robustness of these models to adversarial attacks remains largely unexplored due to their complex spatiotemporal nature that must represent sparse and discrete skeleton joints. This work presents the first adversarial attack on skeleton-based action recognition with GCNs. The proposed targeted attack, termed constrained iterative attack for skeleton actions (CIASA), perturbs joint locations in an action sequence such that the resulting adversarial sequence preserves the temporal coherence, spatial integrity, and the anthropomorphic plausibility of the skeletons. CIASA achieves this feat by satisfying multiple physical constraints and employing spatial skeleton realignments for the perturbed skeletons along with regularization of the adversarial skeletons with generative networks. We also explore the possibility of semantically imperceptible localized attacks with CIASA and succeed in fooling the state-of-the-art skeleton action recognition models with high confidence. CIASA perturbations show high transferability in black-box settings. We also show that the perturbed skeleton sequences are able to induce adversarial behavior in the RGB videos created with computer graphics. A comprehensive evaluation with NTU and Kinetics data sets ascertains the effectiveness of CIASA for graph-based skeleton action recognition and reveals the imminent threat to the spatiotemporal deep learning tasks in general.

Adaptive Bernstein Copulas and Risk Management

We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas regarding the estimation of risk measures in risk management.

HYPERBOLIC INTERPOLATION FOR ASSESSMENT OF DAMAGES OF DISCRETIZATION

It is known that the analysis of errors arising from the numerical results of solving problems is an essential part of any approximate calculation. For example, the finite difference method for forming discrete skeletons of one-dimensional and two-dimensional geometric images, used to solve the differential equations of these images, when determining the coordinates of the point skeleton of a line or surface, requires an estimation of the sampling errors that are characteristic of the finite difference method. With an increase in the sampling step, the accuracy of studies decreases, and with a decrease, it increases. However, decreasing the step, on the one hand, leads to an increase in the number of finite difference equations, and on the other hand, with an unlimited decrease in the step, a situation arises where the rounding error of the coefficients in the finite difference equations exceeds the sampling error. Each solution with a decrease in the sampling step gives a more accurate result, which monotonically changes, approaching the exact one. It is known that the discretization error can be estimated due to the hyperbolic relationship between the results of solving the problem and the discretization step, presented as a certain length, divided into n parts. This dependence is represented in the form of an equilateral hyperbole, whose axes are parallel to the coordinate axes of the Cartesian coordinate system. But an equilateral hyperbole has three free parameters, which allows it to be drawn through three points, which are the results of three solutions to the problem at different steps. In this study, we propose a method for increasing the number of free parameters of a geometric apparatus, which allows one to take into account more than three results of solving the problem in a discrete form to estimate the sampling error.

Asymptotics for the systematic and idiosyncratic volatility with large dimensional high-frequency data

In this paper, we decompose the volatility of a diffusion process into systematic and idiosyncratic components, which are not identified with observations discretely sampled from univariate process. Using large dimensional high-frequency data and assuming a factor structure, we obtain consistent estimates of the Laplace transforms of the systematic and idiosyncratic volatility processes. Based on the discrepancy between realized bivariate Laplace transform of the pair of systematic and idiosyncratic volatility processes and the product of the two marginal Laplace transforms, we propose a Kolmogorov–Smirnov-type independence test statistics for the two components of the volatility process. A functional central limit theorem for the discrepancy is established under the null hypothesis that the systematic and idiosyncratic volatilities are independent. The limiting Gaussian process is realized by a simulated discrete skeleton process which can be applied to define an approximate critical region for an independence test.

Noise reinforcement for Lévy processes

Dans une marche aléatoire à pas renforcés, à chaque instant entier et avec une probabilité fixée $p\in (0,1)$, le marcheur répète un de ses précédents pas tiré uniformément au hasard, et avec probabilité $1-p$ effectue un nouveau pas indépendant de loi donnée. Comme exemples dans la littérature figurent l’elephant random walk et le shark random swim. Nous nous intéressons ici à un analogue en temps continu, c’est-à-dire lorsque la marche aléatoire est remplacée par un processus de Lévy. Pour des paramètres de mémoire sous-critiques (ou encore admissibles) $p<p_{c}$, où $p_{c}$ est lié à l’indice de Blumenthal–Getoor du processus de Lévy, nous construisons un processus de Lévy à bruit renforcé. Notre résultat principal établit la convergence en loi des marches aléatoires à pas renforcés associées aux squelettes discrets d’un processus de Lévy, vers le processus de Lévy à bruit renforcé, lorsque que le pas de la subdivision du temps tend vers $0$.

Skeleton-based cerebrovascular quantitative analysis.

BackgroundCerebrovascular disease is the most common cause of death worldwide, with millions of deaths annually. Interest is increasing toward understanding the geometric factors that influence cerebrovascular diseases, such as stroke. Cerebrovascular shape analyses are essential for the diagnosis and pathological identification of these conditions. The current study aimed to provide a stable and consistent methodology for quantitative Circle of Willis (CoW) analysis and to identify geometric changes in this structure.MethodAn entire pipeline was designed with emphasis on automating each step. The stochastic segmentation was improved and volumetric data were obtained. The L1 medial axis method was applied to vessel volumetric data, which yielded a discrete skeleton dataset. A B-spline curve was used to fit the skeleton, and geometric values were proposed for a one-dimensional skeleton and radius. The calculations used to derive these values were illustrated in detail.ResultIn one example(No. 47 in the open dataset) all values for different branches of CoW were calculated. The anterior communicating artery(ACo) was the shortest vessel, with a length of 2.6mm. The range of the curvature of all vessels was (0.3, 0.9) ± (0.1, 1.4). The range of the torsion was (−12.4,0.8) ± (0, 48.7). The mean radius value range was (3.1, 1.5) ± (0.1, 0.7) mm, and the mean angle value range was (2.2, 2.9) ± (0, 0.2) mm. In addition to the torsion variance values in a few vessels, the variance values of all vessel characteristics remained near 1. The distribution of the radii of symmetrical posterior cerebral artery(PCA) and angle values of the symmetrical posterior communicating arteries(PCo) demonstrated a certain correlation between the corresponding values of symmetrical vessels on the CoW.ConclusionThe data verified the stability of our methodology. Our method was appropriate for the analysis of large medical image datasets derived from the automated pipeline for populations. This method was applicable to other tubular organs, such as the large intestine and bile duct.Electronic supplementary materialThe online version of this article (doi:10.1186/s12880-016-0170-8) contains supplementary material, which is available to authorized users.

Fragments of death. A taphonomic study of human remains from Neolithic Orkney

Recognition of tremendous variation in the treatment of the dead, both temporally and geographically, has done little to curtail the pursuit of homogenous mortuary rites for monuments which appear, by virtue of their architecture, to be similar. This is aptly demonstrated in considering the Neolithic tombs of Orkney, Scotland. The Orcadian human bone assemblages represent the largest volume for this time period from Britain – a significant resource. However, discrete skeletons are lacking, the researcher being presented with formidable volumes of disarticulated and commingled remains. Themes of transformation, fragmentation and manipulation of the body permeate the literature, conferring significance on the tombs as places of transition. Previously, the inherent complexity of the remains has made them an unattractive proposition for detailed study. New interpretations are derived from examination of excavation reports, rather than the material itself. However, advances in taphonomic analysis means techniques now exist for approaching such complex assemblages. A study has now been successfully carried out on the Orcadian remains, uncovering a wealth of new data. This data draws attention to subtle variations in practice between and within tombs, and advocates for a dramatic reconsideration of the current understanding of the practices and cosmologies associated with these enigmatic structures.

Extracting hurricane eye morphology from spaceborne SAR images using morphological analysis

Hurricanes are among the most destructive global natural disasters. Thus recognizing and extracting their morphology is important for understanding their dynamics. Conventional optical sensors, due to cloud cover associated with hurricanes, cannot reveal the intense air–sea interaction occurring at the sea surface. In contrast, the unique capabilities of spaceborne synthetic aperture radar (SAR) data for cloud penetration, and its backscattering signal characteristics enable the extraction of the sea surface roughness. Therefore, SAR images enable the measurement of the size and shape of hurricane eyes, which reveal their evolution and strength. In this study, using six SAR hurricane images, we have developed a mathematical morphology method for automatically extracting the hurricane eyes from C-band SAR data. Skeleton pruning based on discrete skeleton evolution (DSE) was used to ensure global and local preservation of the hurricane eye shape. This distance weighted algorithm applied in a hierarchical structure for extraction of the edges of the hurricane eyes, can effectively avoid segmentation errors by reducing redundant skeletons attributed to speckle noise along the edges of the hurricane eye. As a consequence, the skeleton pruning has been accomplished without deficiencies in the key hurricane eye skeletons. A morphology-based analyses of the subsequent reconstructions of the hurricane eyes shows a high degree of agreement with the hurricane eye areas derived from reference data based on NOAA manual work.

Circadian rhythms and photic entrainment of swimming activity in cave-dwelling fish Astyanax mexicanus (Actinopterygii: Characidae), from El Sotano La Tinaja, San Luis Potosi, Mexico

Circadian regulation has a profound adaptive meaning in timing the best performance of biological functions in a cyclic niche. However, in cave-dwelling animals (troglobitic), a lack of photic cyclic environment may represent a disadvantage for persistence of circadian rhythms. There are different populations of cave-dwelling fish Astyanax mexicanus in caves of the Sierra El Abra, Mexico, with different evolutive history. In the present work, we report that fish collected from El Sótano la Tinaja show circadian rhythms of swimming activity in laboratory conditions. Rhythms observed in some of the organisms entrain to either continuous light–dark cycles or discrete skeleton photoperiods tested. Our results indicate that circadian rhythm of swimming activity and their ability to entrain in discrete and continuous photoperiods persist in some organisms that might represent one of the oldest populations of cave-dwelling A. mexicanus in the Sierra El Abra.

Randomly trapped random walks on [formula omitted

We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on Zd, d≥2. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has a slowly varying return probability, we show that the scaling limit of its clock process is either deterministic linearly growing or a stable subordinator. In the case when the discrete skeleton is a simple random walk on Zd, this implies that the scaling limit of the randomly trapped random walk is either Brownian motion or the Fractional Kinetics process, as conjectured in Ben Arous et al. (2014).

AUTOMATIC SURFACE GENERATION WITH A VOXEL-BASED SKELETON DEFINING TOPOLOGICAL CONSTRAINTS

Shape design is often performed by starting from a basic surface and by refining it afterward by adding details. In order to construct this first approximation surface, we present in this article a method to generate a basic polyhedron from a volumic voxel-based skeleton. This approach preserves the topology described by the discrete skeleton in a 3D grid considering the 26-adjacency: if a cycle is sketched, then there is a hole in the resulting surface, and if a closed hull is designed, then the output has a cavity. We verify the same properties for connected components. This surrounding basic polyhedron is computed with simple geometrical rules, and it is a good starting point for 3D shape design from a discrete voxel skeleton. In order to add multiresolution features to our approach, we use this rough mesh as the control polyhedron of a subdivision surface, according to the Loop scheme dedicated to triangulated surfaces. We show that the resulting set of smooth refined meshes is well suited for further modifications in the frame of a 3D modeling software.

System of vectorization of binary images

In the paper, a system of vectorization of discrete binary images is proposed, which is based on approximation of the image by a polygonal figure. On the basis of this figure, we construct continuous models of the discrete binary image, namely, boundary, skeleton, and circular models. This approach results in efficient complex analysis of the image boundary and skeleton. The system includes data structures and an XML-based language for description and storage of continuous models, as well as software for constructing representations of binary raster images and image processing and visualization.

Spatial symmetry groups as sensorimotor guidelines

While some aspects of neuroanatomical organization are related to packing and access rather than to function, other aspects of anatomical/physiological organization are directly related to function. The mathematics of symmetry groups can be used to determine logical structure in projections and to relate it to function. This paper reviews two studies of the symmetry groups of vestibular projections that are related to the spatial functions of the vestibular complex, including gaze, posture, and movement. These logical structures have been determined by finding symmetry groups of two vestibular projections directly from physiological and anatomical data. Logical structures in vestibular projections are distinct from mapping properties such as the ability to maintain two- and three-dimensional coordinate systems; rather, they provide anatomical/physiological foundations for these mapping properties. The symmetry group of the direct projection from the semicircular canal primary afferents to neck motor neurons is that of the cube (O, the octahedral group), which can serve as a discrete skeleton for coordinate systems in three-dimensional space. The symmetry group of the canal projection from the secondary vestibular afferents to the inferior olive and thence to the cerebellar uvula-nodulus is that of the square (D8), which can support coordinates for the horizontal plane. While the mathematical relationship between these symmetry groups and functions of the vestibular complex are clear, these studies open a larger question: what is the causal logic by which neural centers and their intrinsic organization affect each other and behavior? The relationship of vestibular projection symmetry groups to spatial function make them ideal projections for investigating this causal logic. The symmetry group results are discussed in relationship to possible ways they communicate spatial structure to other neural centers and format spatial functions such as body movements. These two projection symmetry groups suggest that all vestibular projections may have symmetry groups significantly related to function, perhaps all to spatial function.

On the detection of simple points in higher dimensions using cubical homology

Simple point detection is an important task for several problems in discrete geometry, such as topology preserving thinning in image processing to compute discrete skeletons. In this paper, the approach to simple point detection is based on techniques from cubical homology, a framework ideally suited for problems in image processing. A (d-dimensional) unitary cube (for a d-dimensional digital image) is associated with every discrete picture element, instead of a point in epsilon(d) (the d-dimensional Euclidean space) as has been done previously. A simple point in this setting then refers to the removal of a unitary cube without changing the topology of the cubical complex induced by the digital image. The main result is a characterization of a simple point p (i.e., simple unitary cube) in terms of the homology groups of the (3d - 1) neighborhood of p for arbitrary, finite dimensions

Fragmentation energy

Motivated by a problem arising in the mining industry, we estimate the energy ε(η) that is needed to reduce a unit mass to fragments of size at most η in a fragmentation process, when η→0. We assume that the energy used in the instantaneous dislocation of a block of size s into a set of fragments (s 1,s 2,…) is s βφ(s 1/s,s 2/s,…), where φ is some cost function and β a positive parameter. Roughly, our main result shows that if α&amp;gt;0 is the Malthusian parameter of an underlying Crump-Mode-Jagers branching process (with α = 1 when the fragmentation is mass-conservative), then there exists a c∈(0,∞) such that ε(η)∼cηβ-α when β&amp;lt;α. We also obtain a limit theorem for the empirical distribution of fragments of size less than η that result from the process. In the discrete setting, the approach relies on results of Nerman for general branching processes; the continuous approach follows by considering discrete skeletons. In the continuous setting, we also provide a direct approach that circumvents restrictions induced by the discretization.

Fragmentation energy

Motivated by a problem arising in the mining industry, we estimate the energy ε(η) that is needed to reduce a unit mass to fragments of size at most η in a fragmentation process, when η→0. We assume that the energy used in the instantaneous dislocation of a block of size s into a set of fragments (s1,s2,…) is sβφ(s1/s,s2/s,…), where φ is some cost function and β a positive parameter. Roughly, our main result shows that if α&gt;0 is the Malthusian parameter of an underlying Crump-Mode-Jagers branching process (with α = 1 when the fragmentation is mass-conservative), then there exists a c∈(0,∞) such that ε(η)∼cηβ-α when β&lt;α. We also obtain a limit theorem for the empirical distribution of fragments of size less than η that result from the process. In the discrete setting, the approach relies on results of Nerman for general branching processes; the continuous approach follows by considering discrete skeletons. In the continuous setting, we also provide a direct approach that circumvents restrictions induced by the discretization.