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Robotic manipulation of deformable linear objects has potential application in aircraft cable assembly. However, it is difficult to be implemented in real tasks due to requiring prediction of the object’s deformation and obstacle-free manipulation planning with high efficiency. Aiming at exploring automatic assembly planning for aircraft cables assembly in narrow cabins with obstacles, this paper proposes a novel planning algorithm named RRT-BwC (Bi-direction with Constrain). Firstly, formulation of the question and the manipulation objects are presented with geometric definitions. Then a bi-RRT-tree searching method is developed to design the planner for overcoming obstacles in the high dimensional planning space. The numerical distance between configurations in the cable shape space are defined to measure the demands for their transition in consideration of the manipulation logics. And the sampling zone constrains to the shape configuration nodes are also discussed. Finally, the algorithm presents a valid manipulation sequence for robotic manipulation. The functionality and performance of the improved RRT approach are demonstrated with a simulated real-world problem of aircraft cable assembly, exhibiting computation efficiency promotion.

Subjective similarity holds a prominent place in many psychological theories, influencing diverse cognitive processes ranging from attention and categorization to memory and problem solving. Despite the known importance of subjective similarity, there are few resources available to experimenters interested in manipulating the visual similarity of shape, one common type of subjective similarity. Here, across seven validation iterations, we incrementally developed a stimulus space consisting of 360 shapes using a novel image-processing method in conjunction with collected similarity judgments. The result is the Validated Circular Shape space, the first Validated Circular Shape space comparable to the commonly used "color wheel", whereby angular distance along a 2D circle is a proxy for visual similarity. This extensively validated resource is freely available to experimenters wishing to precisely manipulate the visual similarity of shape. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Shape analysis is of great importance in many fields, such as computer vision, medical imaging, and computational biology. This analysis can be performed considering shapes as closed planar curves in the shape space. This approach has been used for the first time to obtain the morphological classification of erythrocytes in digital images of sickle cell disease considering the shape space S1, which has the property of being isometric to an infinite-dimensional Grassmann manifold of two-dimensional subspaces (Younes et al., 2008), without taking advantage of all the features offered by the elastic metric related to the possibility of stretching and bending of the curves. In this paper, we study this deformation in the shape space, S2, which is based on the representation of closed planar curves by means of the square-root velocity function (SRVF) (Srivastava et al., 2011), using the elastic metric of this space to obtain more efficient geodesics and geodesic lengths between planar curves. Supervised classification with this approach achieved an accuracy of 94.3%, classification using templates achieved 94.2% and unsupervised clustering in three groups achieved 94.7%, considering three classes of erythrocytes: normal, sickle, and with other deformations. These results are better than those previously achieved in the morphological analysis of erythrocytes and the method can be used in different applications related to the treatment of sickle cell disease, even in cases where it is necessary to study the process of evolution of the deformation, something that can not be done in a natural way in the feature space.

Knowledge of human ethnicity constitutes important biometric information. An automated ethnicity classification is a good first step in facial analysis. However, most ethnicity classification methods require a complex feature extraction and model training process. We propose a novel ethnicity classification method based on the analysis of facial landmarks in Kendall shape space. Facial features with different relative positions have a close relationship with ethnicity. Facial landmarks can represent positions of facial features. We build a Discrete Landmarks Model (DLM) based on facial landmarks and construct an ethnicity classification model based on the DLM analysis. The clear advantages of our method are that it is fully automated; requires no complex data preprocessing, feature extraction or a complex training process; results in a fast and accurate classification process. We estimate the effectiveness of our method experimentally, using public databases such as Texas3D, FRGC2.0, BU-3DFE and BU-4DFE. On average, our method can achieve a 95% ethnicity classification rate with each classification attempt in 2.0 s.

Misalignment of teeth or jaws can impact the ability to chew or speak, increase the risk of gum disease or tooth decay, and potentially influence a person’s (psychological) well-being. Orthodontic treatments of misaligned teeth are complex procedures that employ dental braces to apply forces in order to move the teeth or jaws to their correct position. Photographs are typically used to document the treatment. An automatic analysis of those photographs could support the decision making and monitoring process. In this paper, we propose an automatic model-based end-to-end 3-D reconstruction approach of the teeth from five photographs with predefined viewing directions (i.e. the photographs used in orthodontic treatment documentation). It uses photo- or view-specific 2-D coupled shape models to extract the teeth contours from the images. The shape reconstruction is then carried out by a deformation-based reconstruction approach that utilizes 3-D coupled shape models and minimizes a silhouette-based loss. The optimal model parameters are determined by an optimization which maximizes the overlaps between the projected 2-D outlines of individual teeth of the 3-D model and the contours extracted from the corresponding photograph. After that the point displacements between the projected outline and segmented contour are used to iteratively deform the 3-D shape model of each tooth for all five views. Back-projection into shape space ensures that the 3-D coupled shape model consists of (statistically) valid teeth. Evaluation on 22 data sets shows promising results with an average symmetric surface distance of 0.848mm and an average DICE coefficient of 0.659.

There has been increasing interest in statistical analysis of data lying in manifolds. This paper generalizes a smoothing spline fitting method to Riemannian manifold data based on the technique of unrolling and unwrapping originally proposed in Jupp and Kent (1987) for spherical data. In particular we develop such a fitting procedure for shapes of configurations in general $m$-dimensional Euclidean space, extending our previous work for two dimensional shapes. We show that parallel transport along a geodesic on Kendall shape space is linked to the solution of a homogeneous first-order differential equation, some of whose coefficients are implicitly defined functions. This finding enables us to approximate the procedure of unrolling and unwrapping by simultaneously solving such equations numerically, and so to find numerical solutions for smoothing splines fitted to higher dimensional shape data. This fitting method is applied to the analysis of some dynamic 3D peptide data., 35 pages, 12 figures. Revised version

Cancer develops resistance to treatments through many mechanisms. Single-cell analyses reveal the intratumor heterogeneity and dynamic relationships between cancer cell subpopulations. These analyses also highlight that various mechanisms of resistance may coexist in a given tumor. Studies have unraveled how the microenvironment affects tumor response to treatments and how cancer cells may adapt to these treatments. Though challenging, individualized treatment based on the molecular characterization of the tumor should become the new standard of care. In the meantime, the success rate of clinical trials in oncology remains dramatically low. There is a need to do better and improve the predictability of preclinical models. This requires innovative changes in ex vivo models and the culture system currently being used. An innovative ligand design is also urgently needed. The limited arsenal of medicinal chemistry reactions and the biases of scaffold selection favor structurally similar compounds with linear shapes at the expense of disc and spherical shapes, which leave a large chemical shape space untouched. In this regard, venoms have received increasing interest as a wellspring for drug candidates. Overall, the characterization of tumor heterogeneity has contributed to advancing our understanding of the mechanisms that underlie cancer resistance to treatments. Targeting these mechanisms will require setting key milestones to significantly improve the translatability of preclinical studies to the clinic with the hope of increasing the success rate of clinical trials.

Motivated by applications from computer vision to bioinformatics, the field of shape analysis deals with problems where one wants to analyze geometric objects, such as curves, while ignoring actions that preserve their shape, such as translations, rotations, or reparametrizations. Mathematical tools have been developed to define notions of distances, averages, and optimal deformations for geometric objects. One such framework, which has proven to be successful in many applications, is based on the square root velocity (SRV) transform, which allows one to define a computable distance between spatial curves regardless of how they are parametrized. This paper introduces a supervised deep learning framework for the direct computation of SRV distances between curves, which usually requires an optimization over the group of reparametrizations that act on the curves. The benefits of our approach in terms of computational speed and accuracy are illustrated via several numerical experiments., Comment: 8 pages, 7 figures, 3 tables. Accepted to DiffCVML

We develop a methodology for classifying defects based on their morphology and induced mechanical response. The proposed approach is fairly general and relies on morphological operators (Angulo and Meyer in 9th international symposium on mathematical morphology and its applications to signal and image processing, pp. 226-237, 2009) and spherical harmonic decomposition as a way to characterize the geometry of the pores, and on the Grassman distance evaluated on FFT-based computations (Willot in C. R., Méc. 343(3):232–245, 2015), for the predicted elastic response. We implement and detail our approach on a set of trapped gas pores observed in X-ray tomography of welded joints, that significantly alter the mechanical reliability of these materials (Lacourt et al. in Int. J. Numer. Methods Eng. 121(11):2581–2599, 2020). The space of morphological and mechanical responses is first partitioned into clusters using the “k-medoids” criterion and associated distance functions. Second, we use multiple-layer perceptron neural networks to associate a defect and corresponding morphological representation to its mechanical response. It is found that the method provides accurate mechanical predictions if the training data contains a sufficient number of defects representing each mechanical class. To do so, we supplement the original set of defects by data augmentation techniques. Artificially-generated pore shapes are obtained using the spherical harmonic decomposition and a singular value decomposition performed on the pores signed distance transform. We discuss possible applications of the present method, and how medoids and their associated mechanical response may be used to provide a natural basis for reduced-order models and hyper-reduction techniques, in which the mechanical effects of defects and structures are decorrelated (Ryckelynck et al. in C. R., Méc. 348(10–11):911–935, 2020).

Shape analysis of curves in Rn is an active research topic in computer vision. While shape itself is important in many applications, there is also a need to study shape in conjunction with other features, such as scale and orientation. The combination of these features, shape, orientation and scale (size), gives different geometrical spaces. In this work, we define a new metric in the shape and size space, S2, which allows us to decompose S2 into a product space consisting of two components: S4×R, where S4 is the shape space. This new metric will be associated with a distance function, which will clearly distinguish the contribution that the difference in shape and the difference in size of the elements considered makes to the distance in S2, unlike the previous proposals. The performance of this metric is checked on a simulated data set, where our proposal performs better than other alternatives and shows its advantages, such as its invariance to changes of scale. Finally, we propose a procedure to detect outlier contours in S2 considering the square-root velocity function (SRVF) representation. For the first time, this problem has been addressed with nearest-neighbor techniques. Our proposal is applied to a novel data set of foot contours. Foot outliers can help shoe designers improve their designs.

Shape analysis of curves in Rn is an active research topic in computer vision. While shape itself is important in many applications, there is also a need to study shape in conjunction with other features, such as scale and orientation. The combination of these features, shape, orientation and scale (size), gives different geometrical spaces. In this work, we define a new metric in the shape and size space, S2, which allows us to decompose S2 into a product space consisting of two components: S4&times, R, where S4 is the shape space. This new metric will be associated with a distance function, which will clearly distinguish the contribution that the difference in shape and the difference in size of the elements considered makes to the distance in S2, unlike the previous proposals. The performance of this metric is checked on a simulated data set, where our proposal performs better than other alternatives and shows its advantages, such as its invariance to changes of scale. Finally, we propose a procedure to detect outlier contours in S2 considering the square-root velocity function (SRVF) representation. For the first time, this problem has been addressed with nearest-neighbor techniques. Our proposal is applied to a novel data set of foot contours. Foot outliers can help shoe designers improve their designs.

Two new species of miniature silverside fishes are described from coastal habitats in the tropical Atlantic: Membras pygmaea sp. nov., from Brus Lagoon, Honduras, and M. procera sp. nov., from the Gulf of Urabá, Colombia. These new species belong to the martinica species-group within the genus Membras Bonaparte. The monophyletic martinica species-group (see below) contains four additional species, all coastal, marine that extend from the east coast of North America to São Paolo State, Brazil. Within the martinica species-group, all but M. martinica are miniature species, ranging from 41–60 mm SL. The smallest species, M. pygmaea sp. nov., is mature at 24 mm SL. A geometric morphometric analysis shows: (i) each species of the martinica species-group occupies its own portion of shape space; and (ii) none of the miniature species possess the shapes of small immature M. martinica. While some of the literature suggests that miniaturization may involve paedomorphosis, our results show that the miniatures accelerate to adult body forms.

Miniaturized amphibians of the genus Brachycephalus are phenotypically diverse. The species of Brachycephalus have bufoniform or leptodactyliform Baupläne and any of three skeletal states: nonhyperossified, hyperossified without dorsal shield, and hyperossified with dorsal shield. We integrate high-resolution microcomputed tomography, geometric morphometrics, and an estimate of molecular phylogenetic relationships to investigate skull diversity in shape and size-shape space in selected species of Brachycephalus. Skull diversity amongst species of Brachycephalus can be partitioned into shape and size-shape space according to the four conditions of skeletal states-Baupläne, namely, nonhyperossified leptodactyliform, nonhyperossified bufoniform, hyperossified bufoniform without dorsal shield, and hyperossified bufoniform with dorsal shield. Skull diversity in shape and size-shape space in nonhyperossified leptodactyliform species of Brachycephalus is markedly larger, when compared to skull diversity in species of the three other conditions of skeletal states-Baupläne. Variation in skull shape scales with size across Brachycephalus and, therefore, can be explained by allometry. Skull diversity, Baupläne, and skeletal states covary to a large extent with monophyletic lineages of Brachycephalus, as revealed by a mitochondrial DNA species tree. Nonhyperossified bufoniform species and hyperossified bufoniform species with or without dorsal shield are monophyletic lineages, as inferred from a mitochondrial DNA species tree. Nonhyperossified leptodactyliform species of Brachycephalus do not share, however, a most recent common ancestor. The nonhyperossified leptodactyliform species of Brachycephalus, due to their marked skull diversity and lack of monophyly, emerge as evolutionarily complex. Therefore, further sampling of the nonhyperossified leptodactyliform condition of skeletal states-Baupläne will be necessary to further understand the evolutionary history of Brachycephalus.Os anfíbios miniaturizados do gênero Brachycephalus são fenotipicamente diversos. As espécies de Brachycephalus têm o plano corporal bufoniforme ou leptodactyliforme e três estados esqueléticos: não-hiperossificado, hiperossificado sem placa dorsal e hiperossificado com placa dorsal. Neste trabalho nós integramos tomografia micro-computadorizada de alta resolução, morfometria geométrica e uma estimativa de relações filogenéticas moleculares para investigar diversidade craniana nos espaços de forma e tamanho-forma em determinadas espécies de Brachycephalus. A diversidade craniana entre espécies de Brachycephalus pode ser dividida no espaço de forma e tamanho-forma segundo as quatro condições de plano corporal-esqueleto, a saber, leptodactiliforme não-hiperossificado, bufoniforme não-hiperossificado, bufoniforme hiperossificado sem placa dorsal e bufoniforme hiperossificado com placa dorsal. A diversidade craniana nos espaços de forma e tamanho-forma nas espécies de Brachycephalus leptodactiliformes não-hiperossificadas é pronunciadamente maior quando comparada àquela das espécies nas outras trĉs condições de plano corporal-esqueleto. A variação na forma craniana aumenta com o tamanho craniano em Brachycephalus e, portanto, pode ser explicada por alometria. Diversidade craniana, plano corporal e estados esqueléticos covariam consideravelmente com as linhagens monofiléticas de Brachycephalus, como estimado pela filogenia mitocondrial. As espécies de Brachycephalus leptodactiliformes não-hiperossificadas e bufoniformes hiperossificadas com ou sem placa dorsal são linhagens monofiléticas, como estimado pela filogenia mitocondrial. As espécies leptodactiliformes não-hiperossificadas não compartilham, todavia, um ancestral comum mais recente. As espécies de Brachycephalus leptodactiliformes não-hiperossificadas devido a sua pronunciada diversidade e não-monofilia emergem claramente como entidades evolutivamente complexas. Por conseguinte, a amostragem adicional de populações leptodactiliformes não-hiperossificadas será necessária para uma melhor compreensão da história evolutiva do gênero Brachycephalus.

The heat kernel on Kendall shape subspaces is approximated by an expansion. The Kendall space is useful for representing the shapes associated to collections of landmarks’positions. The Minakshisundaram-Pleijel recursion formulas are used in order to calculate the closed-form approximations of the first and second coefficients of the heat kernel expansion. Prior to the exploitation of the recursion scheme, the expression of the Laplace-Beltrami operator is adapted to the targeted space using geodesic spherical and angular coordinates.

Background In 2009, a novel influenza vaccine was distributed worldwide to combat the H1N1 influenza “swine flu” pandemic. However, antibodies induced by the vaccine display differences in their specificity and cross-reactivity dependent on pre-existing immunity. Here, we present a computational model that can capture the effect of pre-existing immunity on influenza vaccine responses. The model predicts the region of the virus hemagglutinin (HA) protein targeted by antibodies after vaccination as well as the level of cross-reactivity induced by the vaccine. We tested our model by simulating a scenario similar to the 2009 pandemic vaccine and compared the results to antibody binding data obtained from human subjects vaccinated with the monovalent 2009 H1N1 influenza vaccine. Results We found that both specificity and cross-reactivity of the antibodies induced by the 2009 H1N1 influenza HA protein were affected by the viral strain the individual was originally exposed. Specifically, the level of antigenic relatedness between the original exposure HA antigen and the 2009 HA protein affected antigenic-site immunodominance. Moreover, antibody cross-reactivity was increased when the individual’s pre-existing immunity was specific to an HA protein antigenically distinct from the 2009 pandemic strain. Comparison of simulation data with antibody binding data from human serum samples demonstrated qualitative and quantitative similarities between the model and real-life immune responses to the 2009 vaccine. Conclusion We provide a novel method to evaluate expected outcomes in antibody specificity and cross-reactivity after influenza vaccination in individuals with different influenza HA antigen exposure histories. The model produced similar outcomes as what has been previously reported in humans after receiving the 2009 influenza pandemic vaccine. Our results suggest that differences in cross-reactivity after influenza vaccination should be expected in individuals with different exposure histories.

Four decades of studies in visual attention and visual working memory used visual features such as colors, orientations, and shapes. The layout of their featural space is clearly established for most features (e.g., CIE-Lab for colors) but not shapes. Here, I attempted to reveal the basic dimensions of preattentive shape features by studying how shapes can be positioned relative to one another in a way that matches their perceived similarities. Specifically, 14 shapes were optimized as n-dimensional vectors to achieve the highest linear correlation (r) between the log-distances between C (14, 2) = 91 pairs of shapes and the discriminabilities (d') of these 91 pairs in a texture segregation task. These d' values were measured on a large sample (N = 200) and achieved high reliability (Cronbach's α = 0.982). A vast majority of variances in the results (r = 0.974) can be explained by a three-dimensional SCI shape space: segmentability, compactness, and spikiness.

The standard method of transforming a continuous distribution on the line to the uniform distribution on [ 0 , 1 ] is the probability integral transform. Analogous transforms exist on compact Riemannian manifolds, X , in that for each distribution with continuous positive density on X , there is a continuous mapping of X to itself that transforms the distribution into the uniform distribution. In general, this mapping is far from unique. This paper introduces the construction of an almost-canonical version of such a probability integral transform. The construction is extended to shape spaces, Cartan–Hadamard manifolds, and simplices. The probability integral transform is used to derive tests of goodness of fit from tests of uniformity. Illustrative examples of these tests of goodness of fit are given involving (i) Fisher distributions on S 2 , (ii) isotropic Mardia–Dryden distributions on the shape space Σ 2 5 . Their behaviour is investigated by simulation.

Shape analysis of curves in Rn is an active research topic in computer vision. While shape itself is important in many applications, there is also a need to study shape in conjunction with other features, such as scale and orientation. The combination of these features, shape, orientation and scale (size), gives different geometrical spaces. In this work, we define a new metric in the shape and size space, S2, which allows us to decompose S2 into a product space consisting of two components: S4×R, where S4 is the shape space. This new metric will be associated with a distance function, which will clearly distinguish the contribution that the difference in shape and the difference in size of the elements considered makes to the distance in S2, unlike the previous proposals. The performance of this metric is checked on a simulated data set, where our proposal performs better than other alternatives and shows its advantages, such as its invariance to changes of scale. Finally, we propose a procedure to detect outlier contours in S2 considering the square-root velocity function (SRVF) representation. For the first time, this problem has been addressed with nearest-neighbor techniques. Our proposal is applied to a novel data set of foot contours. Foot outliers can help shoe designers improve their designs.

Learning to reconstruct 3D shapes using 2D images is an active research topic, with benefits of not requiring expensive 3D data. However, most work in this direction requires multi-view images for each object instance as training supervision, which oftentimes does not apply in practice. In this paper, we relax the common multi-view assumption and explore a more challenging yet more realistic setup of learning 3D shape from only single-view images. The major difficulty lies in insufficient constraints that can be provided by single view images, which leads to the problem of pose entanglement in learned shape space. As a result, reconstructed shapes vary along input pose and have poor accuracy. We address this problem by taking a novel domain adaptation perspective, and propose an effective adversarial domain confusion method to learn pose-disentangled compact shape space. Experiments on single-view reconstruction show effectiveness in solving pose entanglement, and the proposed method achieves on-par reconstruction accuracy with state-of-the-art with higher efficiency., Comment: under review, code available at https://github.com/bomb2peng/learn3D

Fish swim by undulating their bodies. These propulsive motions require coordinated shape changes of a body that interacts with its fluid environment, but the specific shape coordination that leads to robust turning and swimming motions remains unclear. To address the problem of underwater motion planning, we propose a simple model of a three-link fish swimming in a potential flow environment and we use model-free reinforcement learning for shape control. We arrive at optimal shape changes for two swimming tasks: swimming in a desired direction and swimming towards a known target. This fish model belongs to a class of problems in geometric mechanics, known as driftless dynamical systems, which allow us to analyze the swimming behavior in terms of geometric phases over the shape space of the fish. These geometric methods are less intuitive in the presence of drift. Here, we use the shape space analysis as a tool for assessing, visualizing, and interpreting the control policies obtained via reinforcement learning in the absence of drift. We then examine the robustness of these policies to drift-related perturbations. Although the fish has no direct control over the drift itself, it learns to take advantage of the presence of moderate drift to reach its target.

We introduce generalized partially linear models with covariates on Riemannian manifolds. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for scalar response variables with error distribution models other than a normal distribution. Partially linear models are particularly useful when some of the covariates of the model are elements of a Riemannian manifold, because the curvature of these spaces makes it difficult to define parametric models. The model was developed to address an interesting application: the prediction of children's garment fit based on three-dimensional scanning of their bodies. For this reason, we focus on logistic and ordinal models and on the important and difficult case where the Riemannian manifold is the three-dimensional case of Kendall's shape space. An experimental study with a well-known three-dimensional database is carried out to check the goodness of the procedure. Finally, it is applied to a three-dimensional database obtained from an anthropometric survey of the Spanish child population. A comparative study with related techniques is carried out.

In this article, we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector-valued one-forms. We provide a numerical framework for the computation of geodesics with respect to these metrics. The family of metrics is invariant under rigid motions and reparametrizations; hence, it induces a metric on the “shape space” of surfaces. This new class of metrics generalizes a previously studied family of elastic metrics and includes in particular the Square Root Normal Field (SRNF) metric, which has been proven successful in various applications. We demonstrate our framework by showing several examples of geodesics and compare our results with earlier results obtained from the SRNF framework Refereed/Peer-reviewed

Virtual surgery planning is a non-invasive procedure, which uses digital clinical data for diagnostic, procedure selection and treatment planning purposes, including the forecast of potential outcomes. The technique begins with 3D data acquisition, using various methods, which may or may not utilize ionizing radiation, such as 3D stereophotogrammetry, 3D cone-beam CT scans, etc. Regardless of the imaging technique selected, landmark selection, whether it is manual or automated, is the key to transforming clinical data into objects that can be interrogated in virtual space. As a prerequisite, the data require alignment and correspondence such that pre- and post-operative configurations can be compared in real and statistical shape space. In addition, these data permit predictive modeling, using either model-based, data-based or hybrid modeling. These approaches provide perspectives for the development of customized surgical procedures and medical devices with accuracy, precision and intelligence. Therefore, this review briefly summarizes the current state of virtual surgery planning.

We aimed to develop the first fully automated 3D gallbladder segmentation approach to perform volumetric analysis in volume data of magnetic resonance (MR) cholangiopancreatography (MRCP) sequences. Volumetric gallbladder analysis is performed for non-contrast-enhanced and secretin-enhanced MRCP sequences. Native and secretin-enhanced MRCP volume data were produced with a 1.5-T MR system. Images of coronal maximum intensity projections (MIP) are used to automatically compute 2D characteristic shape features of the gallbladder in the MIP images. A gallbladder shape space is generated to derive 3D gallbladder shape features, which are then combined with 2D gallbladder shape features in a support vector machine approach to detect gallbladder regions in MRCP volume data. A region-based level set approach is used for fine segmentation. Volumetric analysis is performed for both sequences to calculate gallbladder volume differences between both sequences. The approach presented achieves segmentation results with mean Dice coefficients of 0.917 in non-contrast-enhanced sequences and 0.904 in secretin-enhanced sequences. This is the first approach developed to detect and segment gallbladders in MR-based volume data automatically in both sequences. It can be used to perform gallbladder volume determination in epidemiological studies and to detect abnormal gallbladder volumes or shapes. The positive volume differences between both sequences may indicate the quantity of the pancreatobiliary reflux.

We discuss the total collision singularities of the gravitational N-body problem on shape space. Shape space is the relational configuration space of the system obtained by quotienting ordinary configuration space with respect to the similarity group of total translations, rotations, and scalings. For the zero-energy gravitating N-body system, the dynamics on shape space can be constructed explicitly and the points of total collision, which are the points of central configuration and zero shape momenta, can be analyzed in detail. It turns out that, even on shape space where scale is not part of the description, the equations of motion diverge at (and only at) the points of total collision. We construct and study the stratified total-collision manifold and show that, at the points of total collision on shape space, the singularity is essential. There is, thus, no way to evolve solutions through these points. This mirrors closely the big bang singularity of general relativity, where the homogeneous-but-not-isotropic cosmological model of Bianchi IX shows an essential singularity at the big bang. A simple modification of the general-relativistic model (the addition of a stiff matter field) changes the system into one whose shape-dynamical description allows for a deterministic evolution through the singularity. We suspect that, similarly, some modification of the dynamics would be required in order to regularize the total collision singularity of the N-body model.

Recent paleontological collection in submerged caves in the eastern Dominican Republic has yielded new specimens of Antillothrix bernensis. Here we describe a complete cranium of an adult individual (MHD 20) and provide phenetic comparisons to other endemic Caribbean taxa and extant mainland platyrrhines using three-dimensional geometric morphometric methods (3DGM). Qualitative and quantitative comparisons support conclusions based on other recently described fossil material: Antillothrix has a dentition lacking clear dietary specialization, an elongated brain case with strong temporal lines, and a vertically oriented nuchal plane. MHD 20 shares a combination of traits with a previously published subadult specimen (MHD 01) including a deep depression at glabella, dorsoventrally elongated orbits, and a relatively large face. This shared morphology reinforces the taxonomic affinity of the two specimens, with differences between the two likely reflecting the younger ontogenetic age of MHD 01. Comparisons to the extant platyrrhines paint a complicated picture as the results of between-group principal components analyses (bgPCA) indicate that Antillothrix does not share a suite of morphological features exclusively with any one genus. Depending on which bgPC axes are visualized, and which subset of landmarks is included (i.e., only those describing the shape of the face/palate for inclusion of Xenothrix), MHD 20 is most similar in shape to the atelids, Alouatta, Lagothrix, and Brachyteles, or an otherwise "empty" region of shape space. It groups neither with Cebus nor Callicebus, two taxa that Antillothrix has been associated with in previous studies based on much less complete material. The Antillothrix cranium does not exhibit any of the derived characters classically used to diagnose or define any single clade; rather its morphology shares features with multiple platyrrhine groups. This is consistent with the interpretation that Antillothrix preserves a primitive morphology, which accords with the hypothesis positing an early arrival of platyrrhines in the Caribbean.

We present a novel algorithm for generating the mean structure of non-rigid stretchable shapes. Following an alignment process, which supports local affine deformations, we translate the search of the mean shape into a diagonalization problem where the structure is hidden within the kernel of a matrix. This is the first step required in many practical applications, where one needs to model bendable and stretchable shapes from multiple observations.

In this paper we consider the shape space as the set of smooth simple closed curves in R 2 (parameterized curves), modulo translations, rotations and scale changes. An algorithm to obtain the intrinsic average of a sample data (set of planar shape realizations), from the identification of the shape space with an infinite dimensional Grassmannian is proposed using a gradient descent type algorithm. A simulation study is carried out to check the performance of the algorithm. HighlightsWe propose an algorithm to obtain the intrinsic mean of sample data (planar shapes).Shape space is identified with a Grassmann manifold of infinite dimension.The Frechet mean for manifolds and the gradient descent algorithm are used.A simulation study is carried out to check the performance of the methodology.

The nature, extent and causes of shape variation within and between Acheulean handaxe assemblages represent one of the most heavily theorised aspects of Lower Palaeolithic archaeology. To date, however, handaxe shape variation has only ever been studied within an artefact-based comparative context. Here, the 2D and 3D shape of 698 Acheulean handaxes, selected from ten assemblages, is contextualised within a theoretically possible range of forms defined by two intentionally highly diverse modern replica biface sets. Results demonstrate that handaxe artefacts are highly diverse in their 2D plan-view shape, displaying near complete overlap with the shape space of the intentionally diverse replica tools, along with similar levels of variation. The 3D shape of handaxe artefacts, however, displays much stronger form limitations, occupying under 50% of the shape space created by the replica bifaces. Principally, flat and more ‘tabular’ handaxe forms that display low thickness to width ratios were revealed as absent from the archaeological record. It is argued that while there is considerable diversity and variability in the shape of Acheulean handaxe artefacts, their form is nonetheless restricted by strong material volume and ‘refinement’ limits.

The paper reviews various topics in shape analysis. In particular, matching configurations using regression is emphasized. Connections with general shape spaces and shape distances are discussed. Kendall’s shape space and the affine shape space are considered in particular detail. Matching two configurations and the extension to generalized matching are illustrated with applications in electrophoresis and biology. Shape distributions are briefly discussed and inference in tangent spaces is considered. Finally, some robustness and smoothing issues are highlighted.

Existing methods for reconstructing 3D faces from multiple unconstrained images mainly focus on generating a canonical identity shape. This paper instead aims to optimize both the identity shape and the deformed shapes unique to individual images. To this end, we disentangle 3D face shapes into identity and residual components and leverage facial landmarks on the 2D images to regress both component shapes in shape space directly. Compared with existing methods, our method reconstructs more personal-ized and visually appealing 3D face shapes thanks to its ability to effectively explore both common and different shape characteristics among the multiple images and to cope with various shape deformation that is not limited to expression changes. Quantitative evaluation shows that our method achieves lower reconstruction errors than state-of-the-art methods.

This paper is focused on kernel regression when the response variable is the shape of a 3D object represented by a configuration matrix of landmarks. Regression methods on this shape space are not trivial because this space has a complex finite-dimensional Riemannian manifold structure (non-Euclidean). Papers about it are scarce in the literature, the majority of them are restricted to the case of a single explanatory variable, and many of them are based on the approximated tangent space. In this paper, there are several methodological innovations. The first one is the adaptation of the general method for kernel regression analysis in manifold-valued data to the three-dimensional case of Kendall’s shape space. The second one is its generalization to the multivariate case and the addressing of the curse-ofdimensionality problem. Finally, we propose bootstrap confidence intervals for prediction. A simulation study is carried out to check the goodness of the procedure, and a comparison with a current approach is performed. Then, it is applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children’s wear.

Several operating and control strategies with the purpose of manipulating the size and shape of crystals exhibiting needle-like morphology are presented using an ex situ wet mill as the actuator. A model-based operating policy and different model-free controllers are discussed. These controllers were coupled with an online particle size and shape monitoring tool. First, the attainable region in the size and shape space for a wet milling operation was evaluated in a simulation framework using a multidimensional population balance model describing the breakage phenomenon. Second, the operating and control strategies were tested experimentally in a lab-scale setup using two different milling configurations and two different compounds, namely, β l-glutamic acid and γ d-mannitol. The goal of the experiments was to drive various seed populations of the two compounds to several target average lengths in the size and shape space. It was observed that the model-based operating policy, run without any feedback action, was not able to achieve this goal for arbitrary seed populations. The model-free controllers incorporating feedback were able to do so without relying on any multidimensional breakage model. These controllers enable the robust operation of wet milling stages in complex crystal size and shape modification processes., Crystal Growth & Design, 19 (5), ISSN:1528-7483, ISSN:1528-7505

Although we can all agree that interference induces forgetting, there is surprisingly little consensus regarding what type of interference most likely disrupts memory. We previously proposed that the similarity of interference differentially impacts the representational detail of color memory. Here, we extend this work by applying the Validated Circular Shape Space (Li et al., 2020) for the first time to a continuous retrieval task, in which we quantified both the visual similarity of distracting information as well as the representational detail of shape memory. We found that the representational detail of memory was systematically and differentially altered by the similarity of distracting information. Dissimilar distractors disrupted both fine- and coarse-grained information about the target, akin to memory erasure. In contrast, similar distractors disrupted fine-grained target information but increased reliance on coarse-grained information about the target, akin to memory blurring. Notably, these effects were consistent across two mixture models that each implemented a different scaling metric (either angular distance or perceived target similarity), as well as a parameter-free analysis that did not fit the mixture model. These findings suggest that similar distractors will help memory in cases where coarse-grained information is sufficient to identify the target. In other cases where precise fine-grained information is needed to identify the target, similar distractors will impair memory. As these effects have now been observed across both stimulus domains of shape and color, and were robust across multiple scaling metrics and methods of analyses, we suggest that these results provide a general set of principles governing how the nature of interference impacts forgetting.

OBJECTIVES: To assess the potential of predicting adult facial types at different stages of mandibular development. SETTING AND SAMPLE POPULATION: 941 participants from the Bolton-Brush, Denver, Fels, Iowa, Michigan, and Oregon growth studies with longitudinal lateral cephalograms (total of 7,166) between ages 6–21 years. MATERIAL & METHODS: Each participant was placed into one of three facial types based on mandibular plane angle (MPA) from cephalograms taken closest to 18 years of age (range of 15–21 years): hypo-divergent (MPA39°). Cephalograms were categorized into 13 age groups 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18–21. Twenty-three two-dimensional anatomical landmarks were digitized on the mandible and superimposed using generalized Procrustes analysis, which projects landmarks into a common shape space. Data were analyzed within age categories using stepwise discriminant analysis to identify landmarks that distinguish adult facial types and by jackknife cross-validation to test how well young individuals can be re-classified into their adult facial types. RESULTS: Although each category has multiple best discriminating landmarks among adult types, three landmarks were common across nearly all age categories: menton, gonion, and articulare. Individuals were correctly classified better than chance, even among the youngest age category. Cross-validation rates improved with age, and hyper- and hypo-divergent groups have better reclassification rates than the normo-divergent group. CONCLUSIONS: The discovery of important indicators of adult facial type in the developing mandible helps improve our capacity to predict adult facial types at a younger age.

Continuous image morphing is a classical task in image processing. The metamorphosis model proposed by Trouv\'e, Younes and coworkers casts this problem in the frame of Riemannian geometry and geodesic paths between images. The associated metric in the space of images incorporates dissipation caused by a viscous flow transporting image intensities and its variations along motion paths. In many applications, images are maps from the image domain into a manifold (e.g. in diffusion tensor imaging (DTI) the manifold of symmetric positive definite matrices with a suitable Riemannian metric). In this paper, we propose a generalized metamorphosis model for manifold-valued images, where the range space is a finite-dimensional Hadamard manifold. A corresponding time discrete version was presented by Neumayer et al. based on the general variational time discretization proposed by Berkels et al. Here, we prove the Mosco--convergence of the time discrete metamorphosis functional to the proposed manifold-valued metamorphosis model, which implies the convergence of time discrete geodesic paths to a geodesic path in the (time continuous) metamorphosis model. In particular, the existence of geodesic paths is established. In fact, images as maps into Hadamard manifold are not only relevant in applications, but it is also shown that the joint convexity of the distance function which characterizes Hadamard manifolds is a crucial ingredient to establish existence of the metamorphosis model.

We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone., Comment: 15 pages, 3 figures

In a previous contribution, a new Riemannian shape space, named TPS space, was introduced to perform statistics on shape data. This space was endowed with a Riemannian metric and a flat connection, with torsion, compatible with the given metric. This connection allows the definition of a Parallel Transport of the deformation compatible with the three-fold decomposition in spherical, deviatoric, and non-affine components. Such a parallel transport also conserves the Γ-energy, strictly related to the total elastic strain energy stored by the body in the original deformation. A new approach is here presented in order to calculate the bending energy on the body alone (body bending energy) and to restrict it exclusively within physical boundaries of objects involved in the deformation analysis. The novelty of this new procedure resides in the fact that we propose a new metric to be preserved during the TPS direct transport. This allows transporting the shape change more coherently with the mechanical meaning of the deformation. The geometry of the TPS space is then further discussed in order to better represent the relationship between the Γ-energy, the strain energy, and the so-called bending energy densities.

Background In horses, the morphological changes induced by the process of domestication are reportedly less pronounced than in other species, such as dogs or pigs – although the horses’ disparity has rarely been empirically tested. We investigated shape differences and modularity of domesticated horses, Przewalski’s horses, donkeys and zebras. Mandibular and tooth shape have been shown to be valuable features for differentiating wild and domesticated forms in some mammals. Results Both mandible and teeth, show a pattern of shape space occupation analogous to that of the cranium, with domesticated horses occupying a similar extension in shape space to that of wild equids. Only cranial shape data exhibit a tendency to separate domesticated horses and Przewalski’s horses from donkeys and zebras. Maximum likelihood model-based tests confirm the horse cranium is composed of six developmental modules, as reported for placental mammals in general. The magnitude of integration in domesticated horse skull was lower than in wild equids across all six cranial modules, and lower values of integration were associated with higher disparity values across all modules. Conclusion This is the first study that combines different skeletal features for the description and comparison of shape changes in all living equid groups using geometric morphometrics. We support Darwin’s hypothesis that the shape variation in the skull of domesticated horses is similar to the shape variation of all wild equid species existing today. Lower magnitudes of module integration are recovered in domesticated horses compared to their wild relatives. Electronic supplementary material The online version of this article (10.1186/s12983-018-0258-9) contains supplementary material, which is available to authorized users.

Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed points of self-maps defined on the shape space, and some results on the inverse problem in dimension $1$, i.e. finding (positive or real) masses which make a given collinear configuration central. This survey article introduces readers to the recent results of the author, also unpublished, showing an application of the fixed point theory.

Shape analysis of curves in Rn is an active research topic in computer vision. While shape itself is important in many applications, there is also a need to study shape in conjunction with other features, such as scale and orientation. The combination of these features, shape, orientation and scale (size), gives different geometrical spaces. In this work, we define a new metric in the shape and size space, S2, which allows us to decompose S2 into a product space consisting of two components: S4×R, where S4 is the shape space. This new metric will be associated with a distance function, which will clearly distinguish the contribution that the difference in shape and the difference in size of the elements considered makes to the distance in S2, unlike the previous proposals. The performance of this metric is checked on a simulated data set, where our proposal performs better than other alternatives and shows its advantages, such as its invariance to changes of scale. Finally, we propose a procedure to detect outlier contours in S2 considering the square-root velocity function (SRVF) representation. For the first time, this problem has been addressed with nearest-neighbor techniques. Our proposal is applied to a novel data set of foot contours. Foot outliers can help shoe designers improve their designs.

Focusing on geometric morphometrics (GMM), we review methods for acquiring morphometric data from 3-D objects (including fossils), algorithms for producing shape variables and morphospaces, the mathematical properties of shape space, especially how they relate to morphogenetic and evolutionary factors, and issues posed by working with fossil objects. We use the Raupian shell-coiling equations to illustrate the complexity of the relationship between such factors and GMM morphospaces. The complexity of these issues re-emphasize what are arguably the two most important recommendations for GMM studies: 1) always use multivariate methods and all of the morphospace axes in an analysis; and 2) always anticipate the possibility that the factors of interest can have complex, nonlinear relationships with shape.

Morphospaces are spatial depictions of morphological variation among biological forms that have become an integral part of the analytical toolkit of evolutionary biologists and palaeobiologists. Nevertheless, the term morphospace brings together a great variety of spaces with different geometries. In particular, many morphospaces lack the metric properties underlying the notions of distance and direction, which are, however, central to the analysis of morphological differences and evolutionary transitions. The problem is illustrated here with the iconic morphospace of coiled shells implemented by Raup 50 years ago. The model, which allows the description of shell coiling geometry of various invertebrate taxa, is a seminal reference in theoretical morphology and morphospace theory, but also a morphometric framework frequently used in empirical studies, particularly of ammonoids. Because of the definition of its underlying parameters, Raup's morphospace does not possess a Euclidean structure and a meaningful interpretation of the spread and spacing of taxa within it is not guaranteed. Focusing on the region of the morphospace occupied by most ammonoids, I detail a landmark-based morphospace circumventing this problem and built from the same input measurements required for the calculation of Raup's parameters. From simulations and a reanalysis of Palaeozoic ammonoid shell disparity, the properties of these morphospaces are compared and their algebraic and geometric relationships highlighted. While Raup's model remains a valuable tool for describing ammonoid shells and relating their shapes to the coiling process, it is demonstrated that quantitative analyses of morphological patterns should be carried out within the landmark-based framework. Beyond this specific case, the increasing use and diversity of morphospaces in evolutionary morphology call for caution when interpreting patterns and comparing results drawn from different types of morphospaces.

We study the field of rational differential invariants of the left \(\mathbf {PSL}_{2}\left( \mathbb {R}\right) \)-action on the homogeneous space \(\mathbf { Diff(S}^{1})/\mathbf {PSL}_{2}\left( \mathbb {R}\right) \) and use them to give an alternative discription of the shape space and fingerprints, introduced by Mumford and Sharon (Int J Comput Vis 70(1):55–75, 2006).

A statistical framework was developed for parametric modeling of human body shapes.We developed a non-linear optimization-based optimal body shape modeling technique.New body shapes were generated by inputting linear anthropometric parameters.Resultant models were segmented into 16 key regions of the human body.Resultant models contained information on 15 key skeleton joints. This paper proposes a new example-based statistical modeling framework to conduct the parametric modeling of 3D human body shapes from linear anthropometric parameters. The modeling framework consists of the following three phases: construction of a training database of human body shapes, statistical analysis of human body shapes and human body shape modeling. In the training database construction phase, a consistent parameterization was carried out on 3D whole-body scan data of 80 males and 80 females with a wide variety of body shapes as the examples for this study. The surface-fitting process, which was improved relative to existing methods, was used to guarantee the high-quality parameterization in this phase and to generate an articulated body shape model in the modeling phase. To characterize the range of body shape variation, the training database was analyzed statistically. Additionally, a correlation between the body shapes and the anthropometric parameters was learned in the statistical analysis phase to estimate body shapes from intuitive and semantic parameters. A new technique to generate an optimal body shape model that precisely satisfies user input body dimensions was developed in the model generation phase. This technique enables the estimation of body shape variation, not only within the body shape space that was learned statistically, but also outside of the body shape space, while maintaining body shapes that stay in the human shape space. Our approach produced reasonable results having a high modeling accuracy satisfying user-specified anthropometric parameters, and high visual quality in expressing realistic body shapes. The resultant models were then segmented into 16 key regions of the human body, and had information on 15 key joints, and thus they could be a useful tool in various industries. Compared with other statistical modeling approaches, the proposed method contributes to related areas by introducing an improved surface-fitting process and a non-linear optimization-based optimal body shape modeling technique.

Being a class of effective feature descriptors for action recognition, action representations based on skeleton sequences have yielded excellent recognition results. Most methods used to construct these action representations are based on the information from all the joint positions in actions. Unfortunately, some joints in the actions do not improve the accuracy of action recognition, and may even cause unnecessary inter-class errors. In this study, the authors propose a new method for action recognition by selecting active joints which are closely related to the movement of the body as the first step. Further, a skeleton is characterized as a set of its active-joint positions, and the set can be mapped to a point on pre-shape space to filter out the scale and translation variability. Then, a skeleton sequence (an action) can be regarded as points on the space. Because the timing-sequence relationship between skeletons is very valuable for action recognition, a tensor-based linear dynamical system (tLDS) is employed to model the temporal information of the action. To avoid using a finite-order sequence to estimate the infinite-order feature descriptor of a tLDS, the descriptor is mapped to a point on an infinite Grassmannian composed of the extended observability subspaces. The action is classified using sparse coding and dictionary learning (SCDL) on the infinite Grassmannian. Experimental results demonstrate that the recognition accuracies of the proposed method outperform state-of-the-art ones on four different action datasets.

The handaxes of north-western Europe are some of the most varied in the Acheulean world, with the meanings of that variation debated since the late nineteenth century. To reassess handaxe form in this region, we performed a 3D morphometric analysis of 150 handaxes from five British Acheulean assemblages: Boxgrove, High Lodge, Hitchin, Swanscombe Middle Gravels, and Broom. Regression analyses indicate the importance of the effects of allometry and the assemblage to which the handaxe belongs on shape variation. Marine Isotope Stage (MIS) 11c assemblages Hitchin and Swanscombe occupy significantly different shape space from both the MIS13 assemblages Boxgrove and High Lodge, and the MIS9 assemblage of Broom. Handaxe types such as ovates, cordates, limandes, triangular, and ficrons occupy unique areas of shape space in plan form. Twisted-profile and plano-convex handaxes are distinctive in their profile forms from handaxes with similar plan forms. We suggest that the distinctive and difficult to produce handaxes types that characterize the British Late Acheulean were reproduced according to normative expectations of what handaxes should look like. Different occupation phases in MIS13, MIS11c, and MIS9 are characterized by different suites of handaxe types, likely as the result of different waves of colonization with different normative social traditions.