Shape Classification Research Articles

Cephalofacial Differences Between Males 18 Years of Age and 20-30 Years of Age

The human skull is comprised of many flat and irregular bones, divided into two groups: cranial and facial bones. The size, shape and growth of the human skull are the product of many interrelated internal and external factor interactions. The purpose of the present study was to explore the systematic differences in cephalofacial size and shape classification between two measured groups of different ages and different period of done measurements. Five cephalofacial variables and four cephalofacial indexes were measured on 795 entities of the Kosovo Albanian population in two different timelines; 401 male entities aged 20-30 years old were measured during the timeline 1997-1999, while 394 male entities aged 18 years old were measured during the timeline 2016-2018. The gained data were analyzed in terms of basic descriptive statistical parameters and the percentage of distribution of results. The most pronounced differences between the age groups of 18 year-olds and the age group of 20-30 year-olds, are mainly emphasized in the morphological height of the face, total facial index and transverse cephalic index. While in other dimensions, the distribution of results is very similar. Differences between groups can be justified by the age at which the growth of the cephalofacial bones ends and the influence of external factors such as nutritional and socio-economic factors.

THE CLASSIFICATION OF TERM STRUCTURE SHAPES IN THE TWO-FACTOR VASICEK MODEL — A TOTAL POSITIVITY APPROACH

We provide a full classification of all attainable term structure shapes in the two-factor Vasicek model of interest rates. In particular, we show that the shapes normal, inverse, humped, dipped and hump-dip are always attainable. In certain parameter regimes, up to four additional shapes can be produced. Our results apply to both forward and yield curves and show that the correlation and the difference in mean-reversion speeds of the two factor processes play a key role in determining the scope of attainable shapes. The key mathematical tool is the theory of total positivity, pioneered by Samuel Karlin and others in the 1950s.

Structure and dynamics of small-scale turbulence in vaporizing two-phase flows

Improving our fundamental understanding of multiphase turbulent flows will be beneficial for analyses of a wide range of industrial and geophysical processes. Herein, we investigate the topology of the local flow in vaporizing forced homogeneous isotropic turbulent two-phase flows. The invariants of the velocity-gradient, rate-of-strain, rate-of-rotation tensors, and scalar gradient were computed and conditioned for different distances from the liquid–gas surface. A Schur decomposition of the velocity gradient tensor into a normal and non-normal parts was undertaken to supplement the classical double decomposition into rotation and strain tensors. Using direct numerical simulations results, we show that the joint probability density functions of the second and third invariants have classical shapes in all carrier-gas regions but gradually change as they approach the carrier-liquid interface. Near the carrier-liquid interface, the distributions of the invariants are remarkably similar to those found in the viscous sublayer of turbulent wall-bounded flows. Furthermore, the alignment of both vorticity and scalar gradient with the strain-rate field changes spatially such that its universal behaviour occurs far from the liquid–gas interface. We found also that the non-normal effects of the velocity gradient tensor play a crucial role in explaining the preferred alignment.

Impact of proximal femoral shape on leg length discrepancy after total hip arthroplasty

To investigate the effect of different proximal femoral shapes on leg length discrepancy(LLD) after total hip arthroplasty(THA). Total 131 patients with osteoarthritis or osteonecrosis received unilateral biological total hip arthroplasty from June 2013 to June 2019. All patients' age, sex, side and pelvis anteroposterior digital radiography were retraspectively analyzed. There were 69 males and 62 females, 57 cases of left hip and 74 cases of right hip. The age ranges from 25 to 89 with an average age of 62 years. There were 48 cases of osteoarthritis and 83 cases of osteonecrosis. In this study, femoral cortical index (FCI) was used as the classification of proximal femoral shape, and bilateral lower limb length differences were measured by preoperative and postoperative pelvis anteroposterior digital radiography. Grouping according to FCI:> 0.6 was Dorr A group, 0.5 to 0.6 was Dorr B group, <0.5 was the Dorr C group, and the relationship between proximal femur morphology and the leg length discrepancy after total hip arthroplasty was determined. The postoperative average FCI was(0.56±0.08) mm and the median LLD was 5.10 mm (IQR -1.00 to 8.80 mm). Three groups were divided according to the level of FCI, and there were no statistically significant differences in gender, age, side, diagnosis and intraoperative fracture rate distribution among three groups. FCI>0.6, the postoperative LLD was 6.30 mm (IQR 1.00 to 10.95 mm). When FCI was 0.5 to 0.6, the postoperative LLD was 5.85 mm(IQR-0.55 to 8.90 mm). FCI<0.5, the postoperative LLD was 1.95 mm(IQR -2.50 to 6.68 mm). LLD comparison of different proximal femoral shape was statistically significant (P<0.05). High FCI increases the risk of lower extremity prolongation after surgery on the affectedside, while low FCI reduces the risk of lower extremity prolongation after surgery on the affected side. The surgeon can assess the shape of the proximal femur of the patient preoperatively and inform the patient in advance of possible changes in leg length of both lower extremities after total hip replacement.

Connected Coulomb columns: analysis and numerics

We consider a version of Gamow’s liquid drop model with a short range attractive perimeter-penalizing potential and a long-range Coulomb interaction of a uniformly charged mass in . Here we constrain ourselves to minimizing among the class of shapes that are columnar, i.e., constant in one spatial direction. Using the standard perimeter in the energy would lead to non-existence for any prescribed cross-sectional area due to the infinite mass in the constant spatial direction. In order to overcome this issue we use a connected perimeter instead. We prove existence of minimizers for this connected isoperimetric problem with long-range interaction and study the shapes of minimizers in the small and large cross section regimes. For an intermediate regime we use an Ohta–Kawasaki phase field model with connectedness constraint to study the shapes of minimizers numerically.

Spectral Shape Recovery and Analysis Via Data-driven Connections

We introduce a novel learning-based method to recover shapes from their Laplacian spectra, based on establishing and exploring connections in a learned latent space. The core of our approach consists in a cycle-consistent module that maps between a learned latent space and sequences of eigenvalues. This module provides an efficient and effective link between the shape geometry, encoded in a latent vector, and its Laplacian spectrum. Our proposed data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Moreover, these latent space connections enable novel applications for both analyzing and controlling the spectral properties of deformable shapes, especially in the context of a shape collection. Our learning model and the associated analysis apply without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), nature of the latent space (generated by an auto-encoder or a parametric model), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, latent space exploration and analysis, mesh super-resolution, shape exploration, style transfer, spectrum estimation for point clouds, segmentation transfer and non-rigid shape matching.

Swept volumes via spacetime numerical continuation

Given a solid 3D shape and a trajectory of it over time, we compute its swept volume - the union of all points contained within the shape at some moment in time. We consider the representation of the input and output as implicit functions, and lift the problem to 4D spacetime, where we show the problem gains a continuous structure which avoids expensive global searches. We exploit this structure via a continuation method which marches and reconstructs the zero level set of the swept volume, using the temporal dimension to avoid erroneous solutions. We show that, compared to other methods, our approach is not restricted to a limited class of shapes or trajectories, is extremely robust, and its asymptotic complexity is an order lower than standards used in the industry, enabling its use in applications such as modeling, constructive solid geometry, and path planning.

Geometric and Topological Bases of a New Classification of Wood Vascular Tissues Part 1: Shape and Arrangement Classifications of Vessels

The need to identify wood by its anatomical features requires a detailed analysis of all the elements that make it up. This is a significant problem of structural wood science, the most general and complete solution of which is yet to be sought. In recent years, increasing attention has been paid to the use of computer vision methods to automate processes such as the detection, identification, and classification of different tissues and different tree species. The more successful use of these methods in wood anatomy requires a more precise and comprehensive definition of the anatomical elements, according to their geometric and topological characteristics. In this article, we conduct a detailed analysis of the limits of variation of the location and grouping of vessels in the observed microscopic samples. The present development offers criteria and quantitative indicators for defining the terms shape, location, and group of wood tissues. It is proposed to differentiate the quantitative indicators of the vessels depending on their geometric and topological characteristics. Thus, with the help of computer vision technics, it will be possible to establish topological characteristics of wood vessels, the extraction of which would be used to develop an algorithm for the automatic classification of tree species.

A novel 3D shape classification algorithm: point-to-vector capsule network

A novel 3D shape classification algorithm: point-to-vector capsule network

Applicability of Semi-Quantitative Evaluation of the Intercondylar Notch

The intercondylar notch (IN) can differ in morphology and size, influencing the contained ligaments. For a better understanding of the influence of the IN’s anatomy on knee pathologies, a classification of different shapes was proposed. However, a detailed evaluation of the reliability of these classifications is lacking thus far. In coronal knee MRIs of 330 patients, the IN width was measured and three shapes were calculated to generate objective control results. Notch shapes were classified by two blinded investigators, first without and then with visual assistance to guide the shape classification. The distribution of the three different shapes was as follows: A-shape: n = 43, 13.0%; inverse U-shape: n = 100, 30.3%; Ω-shape: n = 183, 56.7%. The semi-quantitative evaluation distribution was as follows: A-shape: n = 44, 13.3%; inverse U-shape: n = 37, 11.2%; Ω-shape: n = 249, 75%; there was fair (κ = 0.35) agreement compared to that of the control results. The assisted semi-quantitative evaluation distribution was as follows: A-shape: n = 44, 13.3%; inverse U-shape: 103, 31.2%; Ω-shape: n = 183, 55.3%; there was very good (κ = 0.92) agreement compared to that of the control results. In the shape evaluation of the IN, rigid guidelines and visual assistance must be used to ensure reliability. The utilization of visual assistance led to higher inter- and intra-rater agreements in the semi-quantitatively evaluation of the IN shape when compared to those in the classification without visual assistance.

Isogeometric boundary element analysis based on UE-splines

UE-splines are generalizations of uniform polynomial splines, trigonometric splines, hyperbolic splines and exponential splines defined as parametric splines in non-rational form. At the same time, they can exactly represent a wide class of basic analytic shapes commonly used in engineering applications. Further, UE-splines with uniform knot intervals can be conveniently generated by subdivision methods. In this paper, we use them to model many kinds of basic analytic shapes and generate circular splines interpolating points and tangents, and then conduct isogeometric boundary element analysis (IGABEM) of models defined by UE-splines. Taking 2D elasticity problems as an example, we describe a frame and technologies of IGABEM based on UE-splines, including relevant formulation, refinement based on UE-spline subdivision method and optimal post-processing. We develop traction recovery method for computing boundary stress to avoid strong singular integral problem, and adopt a divide-and-conquer strategy to obtain distribution nephograms with clear boundary for all kinds of physical items. A set of numerical experiments demonstrates that UE-splines have many merits on both modeling and solving IGABEM problems.

Comparison of Shape Derivatives Using CutFEM for Ill-posed Bernoulli Free Boundary Problem

In this paper we study and compare three types of shape derivatives for free boundary identification problems. The problem takes the form of a severely ill-posed Bernoulli problem where only the Dirichlet condition is given on the free (unknown) boundary, whereas both Dirichlet and Neumann conditions are available on the fixed (known) boundary. Our framework resembles the classical shape optimization method in which a shape dependent cost functional is minimized among the set of admissible domains. The position of the domain is defined implicitly by the level set function. The steepest descent method, based on the shape derivative, is applied for the level set evolution. For the numerical computation of the gradient, we apply the Cut Finite Element Method (CutFEM), that circumvents meshing and re-meshing, without loss of accuracy in the approximations of the involving partial differential models. We consider three different shape derivatives. The first one is the classical shape derivative based on the cost functional with pde constraints defined on the continuous level. The second shape derivative is similar but using a discretized cost functional that allows for the embedding of CutFEM formulations directly in the formulation. Different from the first two methods, the third shape derivative is based on a discrete formulation where perturbations of the domain are built into the variational formulation on the unperturbed domain. This is realized by using the so-called boundary value correction method that was originally introduced to allow for high order approximations to be realized using low order approximation of the domain. The theoretical discussion is illustrated with a series of numerical examples showing that all three approaches produce similar result on the proposed Bernoulli problem.

A Smoothed GFEM Based on Taylor Expansion and Constrained MLS for Analysis of Reissner–Mindlin Plate

Based on the Taylor Expansion and constrained moving least square function, a smoothed GFEM (SGFEM) is proposed in this paper for static, free vibration and buckling analysis of Reissner–Mindlin plate. The displacement function based on SGFEM is composed of classical linear finite element shape function and nodal displacement function, which are obtained by introducing the gradient smoothed meshfree approximation in Taylor expansion of nodal displacement function. A constrained moving least square function is proposed for constituting meshfree nodal displacement function. The merits of the proposed SGFEM, including high accuracy, rapid error convergence, insensitive to mesh distortion, free of shear-locking problem, no extra DOFs and temporal stability, etc., are demonstrated by several typical examples and comparisons with other numerical methods.

An unsymmetric 8‐node plane element immune to mesh distortion for linear isotropic hardening material

AbstractAn 8‐node quadrilateral plane element US‐QUAD8 is developed for linear isotropic hardening material in the framework of updated Lagrangian unsymmetric finite formulation where matrix is constructed by classical shape function, and matrix by the higher‐order Lagrangian basis function in global coordinate system. The present element eliminates the influence of Jacobian in the elemental stiffness matrix and guarantees the quadratic completeness of displacement field even under severe distorted mesh. Two typical problems meshed with angular/curved‐edge/mid‐side distorted elements demonstrate excellent performance of distortion resistance of the present element and good computational efficiency in severe mesh distortion.

Learning Polynomial-Based Separable Convolution for 3D Point Cloud Analysis.

Shape classification and segmentation of point cloud data are two of the most demanding tasks in photogrammetry and remote sensing applications, which aim to recognize object categories or point labels. Point convolution is an essential operation when designing a network on point clouds for these tasks, which helps to explore 3D local points for feature learning. In this paper, we propose a novel point convolution (PSConv) using separable weights learned with polynomials for 3D point cloud analysis. Specifically, we generalize the traditional convolution defined on the regular data to a 3D point cloud by learning the point convolution kernels based on the polynomials of transformed local point coordinates. We further propose a separable assumption on the convolution kernels to reduce the parameter size and computational cost for our point convolution. Using this novel point convolution, a hierarchical network (PSNet) defined on the point cloud is proposed for 3D shape analysis tasks such as 3D shape classification and segmentation. Experiments are conducted on standard datasets, including synthetic and real scanned ones, and our PSNet achieves state-of-the-art accuracies for shape classification, as well as competitive results for shape segmentation compared with previous methods.

Identifying Handsaw Tooth Shape Based on the Micro- and Macroscopic Analysis of the Kerf Floor Contour

Skeletal trauma analysis is a major facet of forensic anthropology casework and can entail interpretation of sharp force saw trauma. Hand-powered saws are commonly used in cases of dismemberment and analysis requires differentiating class characteristics. Features of the kerf walls and floor provide information utilized in identifying set, shape, size, power, and direction of sawing motion of the tool. The focus of this study is to examine validity and reliability of determining tooth shape class characteristic (rip versus crosscut) from features of the kerf floor. Two crosscut and three rip handsaws, ranging from 6 to 16 teeth per inch, were used to make 30 incomplete cuts per saw for a total of 150 cuts. Each kerf floor was analyzed macroscopically and microscopically using a digital microscope at 30 × magnification by three observers of different experience levels (expert, experienced, and novice). Profile shapes were classified as U-shaped/concave (rip) or W-shaped/convex (crosscut) by each observer for all 150 cuts. Reliability tests using Cohen’s kappa ranged from substantial in the two less experienced observers to almost perfect in pairwise comparisons with the expert. Microscopic classification accuracy was 94.0% (423/450) for all three observers and macroscopic examination increased accuracy to 99.8% (449/450). Saw wear and tooth size were not a significant determiner in correct identification of saw tooth type. Overall, tooth shape can be reliably and accurately determined from incomplete cuts.

COMPUTER HYBRID SYSTEM OF HEMORRHAGE (HES) DETECTION USED FOR AIDED DIAGNOSIS OF DIABETIC RETINOPATHY

Diabetes cause’s metabolic and physiological abnormalities in the retina and the changes suggest a role for inflammation in the development of diabetic retinopathy. Abnormal blood vessels can form in the back of the eye of a person with diabetes. These new blood vessels are weaker and prone to breaking and causing hemorrhage (HEs). Diabetic retinopathy (DR) accounts for 31.5–54% of all cases of vitreous hemorrhage in adults in the world. Therefore, detection of HEs is still a challenging factor task for computer-aided diagnostics of DR. Many researchers have developed advanced algorithms of hemorrhages detection using fundus images. In this paper, a robust and computationally efficient approach for HEs with different shape and size detection and classification is presented. First, brightness correction and contrast enhancement are applied to fundus images. Second, candidate hemorrhages are extracted by using an unsupervised classification algorithm. Third, an approach based on mathematical morphology is carried out for vascular network and macula segmentation. Finally, a total of 13 HEs features are considered in this study and selected for classification. The proposed method is evaluated on 419 fundus images of DIARETDB0, DIARETDB1 and MESSIDOR databases. Experimental results show that overall average sensitivity, specificity, predictive value and accuracy for hemorrhage in lesion level are 98.90%, 99.66%, 97.63% and 99.56%, respectively. The results show that the proposed method outperforms other state-of-the-art methods in detection of hemorrhages. These results indicate that this new method may improve the performance of diagnosis of DR system.

Consistent Two-Flow Network for Tele-Registration of Point Clouds.

Rigid registration of partial observations is a fundamental problem in various applied fields. In computer graphics, special attention has been given to the registration between two partial point clouds generated by scanning devices. State-of-the-art registration techniques still struggle when the overlap region between the two point clouds is small, and completely fail if there is no overlap between the scan pairs. In this article, we present a learning-based technique that alleviates this problem, and allows registration between point clouds, presented in arbitrary poses, and having little or even no overlap, a setting that has been referred to as tele-registration. Our technique is based on a novel neural network design that learns a prior of a class of shapes and can complete a partial shape. The key idea is combining the registration and completion tasks in a way that reinforces each other. In particular, we simultaneously train the registration network and completion network using two coupled flows, one that register-and-complete, and one that complete-and-register, and encourage the two flows to produce a consistent result. We show that, compared with each separate flow, this two-flow training leads to robust and reliable tele-registration, and hence to a better point cloud prediction that completes the registered scans. It is also worth mentioning that each of the components in our neural network outperforms state-of-the-art methods in both completion and registration. We further analyze our network with several ablation studies and demonstrate its performance on a large number of partial point clouds, both synthetic and real-world, that have only small or no overlap.

Aggregated pairwise classification of elastic planar shapes

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to early formulations of the problem with an object to be classified described as a vector in a relatively low-dimensional Euclidean space. Statistical shape data have two main properties that suggest a need for a novel approach: (i) shapes are inherently infinite-dimensional with strong dependence among the positions of nearby points, and (ii) shape space is not Euclidean but is fundamentally curved. To accommodate these features of the data, we work with the square-root velocity function of the curves to provide a useful formal description of the shape, pass to tangent spaces of the manifold of shapes at projection points (which effectively separate shapes for pairwise classification in the training data) and use principal components within these tangent spaces to reduce dimensionality. We illustrate the impact of the projection point and choice of subspace on the misclassification rate with a novel method of combining pairwise classifiers.

A statistical pipeline for identifying physical features that differentiate classes of 3D shapes

The recent curation of large-scale databases with 3D surface scans of shapes has motivated the development of tools that better detect global patterns in morphological variation. Studies, which focus on identifying differences between shapes, have been limited to simple pairwise comparisons and rely on prespecified landmarks (that are often known). We present SINATRA, the first statistical pipeline for analyzing collections of shapes without requiring any correspondences. Our novel algorithm takes in two classes of shapes and highlights the physical features that best describe the variation between them. We use a rigorous simulation framework to assess our approach. Lastly, as a case study we use SINATRA to analyze mandibular molars from four different suborders of primates and demonstrate its ability recover known morphometric variation across phylogenies.