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Particle shape plays a critical role in governing the properties and behavior of granular materials. Despite advances in capturing and analyzing 3D particle shapes, these remain more demanding than 2D shape analysis due to the high computational costs and time-consuming nature of 3D imaging processes. Consequently, there is a growing interest in exploring potential correlations between 3D and 2D shapes, as this approach could potentially enable a reasonable estimation of a 3D shape from a 2D particle image, or at most, a couple of images. In response to this research interest, this study provides a thorough review of previous studies that have attempted to establish a correlation between 3D and 2D shape measures. A key finding from the extensive review is the high correlation between 2D perimeter circularity (cp) and Wadell’s true sphericity (S) defined in 3D, suggesting that a 3D shape can be estimated from the cp value in terms of S. To further substantiate the correlation between cp and S, this study analyzes approximately 400 mineral particle geometries available from an open-access data repository in both 3D and 2D. The analysis reveals a strong linear relationship between S and cp compared with other 2D shape descriptors broadly used in the research community. Furthermore, the limited variance in cp values indicates that cp is insensitive to changes in viewpoint, which indicates that fewer 2D images are needed. This finding offers a promising avenue for cost-effective and reliable 3D shape estimation using 2D particle images.

Particle shape plays a critical role in governing the properties and behavior of granular materials. Despite advances in capturing and analyzing 3D particle shapes, these remain more demanding than 2D shape analysis due to the high computational costs and time-consuming nature of 3D imaging processes. Consequently, there is a growing interest in exploring potential correlations between 3D and 2D shapes, as this approach could potentially enable a reasonable estimation of a 3D shape from a 2D particle image, or at most, a couple of images. In response to this research interest, this study provides a thorough review of previous studies that have attempted to establish a correlation between 3D and 2D shape measures. A key finding from the extensive review is the high correlation between 2D perimeter circularity (cp) and Wadell’s true sphericity (S) defined in 3D, suggesting that a 3D shape can be estimated from the cp value in terms of S. To further substantiate the correlation between cp and S, this study analyzes approximately 400 mineral particle geometries available from an open-access data repository in both 3D and 2D. The analysis reveals a strong linear relationship between S and cp compared with other 2D shape descriptors broadly used in the research community. Furthermore, the limited variance in cp values indicates that cp is insensitive to changes in viewpoint, which indicates that fewer 2D images are needed. This finding offers a promising avenue for cost-effective and reliable 3D shape estimation using 2D particle images.

Detecting replacement conditions of railway point machines is important to simultaneously satisfy the budget-limit and train-safety requirements. In this study, we consider classification of the subtle differences in the aging effect—using electric current shape analysis—for the purpose of replacement condition detection of railway point machines. After analyzing the shapes of after-replacement data and then labeling the shapes of each before-replacement data, we can derive the criteria that can handle the subtle differences between “does-not-need-to-be-replaced” and “needs-to-be-replaced” shapes. On the basis of the experimental results with in-field replacement data, we confirmed that the proposed method could detect the replacement conditions with acceptable accuracy, as well as provide visual interpretability of the criteria used for the time-series classification.

In this work, we present a novel 3D indirect shape analysis method which successfully retrieves 3D shapes based on hand–object interaction. To this end, the human hand information is first transferred to the virtual environment by the Leap Motion controller. Position-, angle- and intersection-based novel features of the hand and fingers are used for this part. In the guidance of these features that define the way humans grab objects, a support vector machine (SVM) classifier is trained. Experiments validate that SVM results are useful for retrieval of 3D shapes. We also compare the retrieval performance of our method with an interaction-based indirect method based on the Data Glove controller as well as a direct method based on 3D shape distribution histograms. These comparisons reveal different advantages of our method, which are (i) being lower-cost and more accurate compared to the Data Glove, and (ii) being more discriminative compared to a direct approach. We finally note that our algorithm is rigid-motion invariant and able to explore databases of arbitrarily represented 3D shapes.

Twenty years ago, Rohlf and Marcus proclaimed that a \"revolution in morphometrics\" was underway, where classic analyses based on sets of linear distances were being supplanted by geometric approaches making use of the coordinates of anatomical landmarks. Since that time the field of geometric morphometrics has matured into a rich and cohesive discipline for the study of shape variation and covariation. The development of the field is identified with the Procrustes paradigm, a methodological approach to shape analysis arising from the intersection of the statistical shape theory and analytical procedures for obtaining shape variables from landmark data. In this review we describe the Procrustes paradigm and the current methodological toolkit of geometric morphometrics. We highlight some of the theoretical advances that have occurred over the past ten years since our prior review (Adams et al., 2004), what types of anatomical structures are amenable to these approaches, and how they extend the reach of geometric morphometrics to more specialized applications for addressing particular biological hypotheses. We end with a discussion of some possible areas that are fertile ground for future development in the field.

Evolutionary biology is multivariate, and advances in phylogenetic comparative methods for multivariate phenotypes have surged to accommodate this fact. Evolutionary trends in multivariate phenotypes are derived from distances and directions between species in a multivariate phenotype space. For these patterns to be interpretable, phenotypes should be characterized by traits in commensurate units and scale. Visualizing such trends, as is achieved with phylomorphospaces, should continue to play a prominent role in macroevolutionary analyses. Evaluating phylogenetic generalized least squares (PGLS) models (e.g., phylogenetic analysis of variance and regression) is valuable, but using parametric procedures is limited to only a few phenotypic variables. In contrast, nonparametric, permutation-based PGLS methods provide a flexible alternative and are thus preferred for high-dimensional multivariate phenotypes. Permutation-based methods for evaluating covariation within multivariate phenotypes are also well established and can test evolutionary trends in phenotypic integration. However, comparing evolutionary rates and modes in multivariate phenotypes remains an important area of future development.

Shape analysis has been widely used in digital image processing and computer vision, but they have not been utilized to compare the structural characteristics of the human association pathways. Here we used shape analysis to derive length, area, volume, and shape metrics from diffusion MRI tractography and utilized them to study the morphology of human association pathways. The reliability analysis showed that shape descriptors achieved moderate to good test-retest reliability. Further analysis on association pathways showed left dominance in the arcuate fasciculus, cingulum, uncinate fasciculus, frontal aslant tract, and right dominance in the inferior fronto-occipital fasciculus and inferior longitudinal fasciculus. The superior longitudinal fasciculus has a mixed lateralization profile with different metrics showing either left or right dominance. The analysis of between-subject variations shows that the overall layout of the association pathways does not variate a lot across subjects, as shown by low between-subject variation in length, span, diameter, and radius. In contrast, the area of the pathway innervation region has a considerable between-subject variation. A follow-up analysis is warranted to thoroughly investigate the nature of population variations and their structure-function correlation. [Display omitted]

Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. Those complex objects (e.g., different brain subcortical structures) often reside in some Banach spaces, and hence their relationship cannot be well characterized by most of the existing measures of dependence such as correlation coefficients developed in Hilbert spaces. To overcome the limitations of the existing measures, we propose Ball Covariance as a generic measure of dependence between two random objects in two possibly different Banach spaces. Our Ball Covariance possesses the following attractive properties: (i) It is nonparametric and model-free, which make the proposed measure robust to model mis-specification; (ii) It is nonnegative and equal to zero if and only if two random objects in two separable Banach spaces are independent; (iii) Empirical Ball Covariance is easy to compute and can be used as a test statistic of independence. We present both theoretical and numerical results to reveal the potential power of the Ball Covariance in detecting dependence. Also importantly, we analyze two real datasets to demonstrate the usefulness of Ball Covariance in the complex dependence detection. Supplementary materials for this article are avaiable online.

This paper develops the theory of geodesic regression and least-squares estimation on Riemannian manifolds. Geodesic regression is a method for finding the relationship between a real-valued independent variable and a manifold-valued dependent random variable, where this relationship is modeled as a geodesic curve on the manifold. Least-squares estimation is formulated intrinsically as a minimization of the sum-of-squared geodesic distances of the data to the estimated model. Geodesic regression is a direct generalization of linear regression to the manifold setting, and it provides a simple parameterization of the estimated relationship as an initial point and velocity, analogous to the intercept and slope. A nonparametric permutation test for determining the significance of the trend is also given. For the case of symmetric spaces, two main theoretical results are established. First, conditions for existence and uniqueness of the least-squares problem are provided. Second, a maximum likelihood criteria is developed for a suitable definition of Gaussian errors on the manifold. While the method can be generally applied to data on any manifold, specific examples are given for a set of synthetically generated rotation data and an application to analyzing shape changes in the corpus callosum due to age.

The Josefina Ramos de Cox museum in Lima, Peru, decided to digitize hundreds of archaeological pieces from pre-Colombian cultures to support further research and create virtual educational environments. However, the 3D scanning procedure led to imperfections in the objects’ surface, mainly due to the difficulty of manipulating the fragile objects during the acquisition. The problem was that many of the scanned artifacts do not contain the base because the contact surface during acquisition was not visible to the scanner. This paper proposes a method to repair the digital objects’ surface using a data-driven approach. We design and train a point cloud neural network that learns to synthesize the missing geometry in an end-to-end manner. Our model consists of a novel architecture and training protocol that addresses the problem of point cloud completion. We propose an end-to-end neural network architecture that focuses on calculating the missing geometry and merging the known input and the predicted point cloud. Our method is composed of two neural networks: the missing part prediction network and the merging-refinement network. The first module focuses on extracting information from the incomplete input to infer the missing geometry. The second module merges both point clouds and improves the distribution of the points. Our approach is effective in repairing pottery objects with large imperfections during the scanning. Besides, our experiments on ShapeNet and Completion3D datasets show that our method is effective in a general setting for shape completion.