Shape Constraints Research Articles

Flexural wave illusion on a curved plate

Manipulating elastic waves using a transformation approach is challenging due to the complex constitutive relationship. However, for flexural waves, approximated as scalar waves, two straightforward approaches emerge based on geometric curvature and plate thickness. Here, we develop transformation theory to establish equivalence between curved plates of different shapes and thickness profiles. Introducing tailor-made thickness profiles on a given curved shape enables illusion effects, where flexural waves propagate as if on a flat plate or on another curved plate with a totally different configuration. Numerical simulations and experimental field mapping confirm the effectiveness of these illusions. Our approach to flexural wave illusion finds applications in structural designs with material and shape constraints and holds the potential for absorption or vibration control, wavefront shaping, chaotic dynamics, and topology control.

Youth engagement in livestock production and marketing in East Africa

There is limited empirical evidence about how youth engage in livestock production in East Africa. The primary objective of this article is to better understand youth engagement in the livestock sector, namely commercialization and marketing. We compare youth to non-youth in four areas: livestock asset ownership, access to and use of services and improved practices and lastly, market participation. Our framework draws upon agricultural transformation concepts to suggest a tentative pathway through which livestock can support youth in transitions. We draw upon quantitative data and analyze and compare youth to nonyouth in intensive and extensive livestock systems in Kenya, Uganda, Ethiopia, and Tanzania and investigate four livestock systems, dairy, extensive ruminants, pig, and chicken systems. The results showed that there were no systematic youth-specific trends across the asset ownership, levels of commercialization or market participation. Also, low asset ownership did not generate observable youth specific differences in market participation. Rather, education and improved practices correlate with higher levels of market participation. Exploring how livestock are acquired and implications upon asset-based approaches is recommended to better understand the potential of livestock as a source of income during youth transitions in different livestock systems. More evidence is needed to inform and tailor policy approaches to support equitable opportunities in the livestock sector better. Research into understanding how social factors, including gender, shape youth opportunities and constraints, is needed.

A Shape-constrained Transfer Temporal Transformer Network for remaining useful life prediction of rotating machines

Predicting remaining useful life (RUL) of rotating machines can promote predictive maintenance and improve the mechanical system reliability. This paper proposes a Shape-constrained Transfer Temporal Transformer Network (SC3TN) for RUL prediction across different rotating machines. The disentangled representation learning is utilized to extract invariant features across different domains. Health indexes are constructed with invariant features considering shape constraints and all previous health states. The operating time is encoded by a Temporal Encoding in predicting process. The SC3TN is tested on two tasks, namely RUL prediction across different working conditions and different equipment. Compared to state-of-the-art methods, SC3TN reduces the mean absolute error by 4.94% and 5.47% and improves the score by 8.5% and 20.83% on two tasks. The experiments show that the proposed method can achieve more accurate RUL prediction than existing methods, which demonstrates the potential of the proposed method for predicting RUL without collecting degradation data in advance.

Shape-controllable inverse kinematics of hyper-redundant robots based on the improved FABRIK method

AbstractHyper-redundant robots have good prospects for applications in confined space due to their high flexibility and slim body size. However, the super-redundant structure brings great challenges for its inverse kinematics with shape constraints. Unfortunately, traditional Jacobian pseudo-inverse-based inverse kinematics method and forward and backward reaching inverse kinematics (FABRIK) method are difficult to constrain the arm shape and realize trajectory tracking in confined spaces. To solve this problem, we propose a shape-controllable FABRIK method to satisfy the given path and shape constraints. Firstly, the kinematic model of the hyper-redundant robot is established, and the canonical FABRIK method is introduced. Based on the preliminary works, the single-layer improved FABRIK method is developed to solve the position and pointing inverse kinematics considering path environment and joint angle constraints instead of two-layer geometric iterations. For tracking the desired end roll angles, the polygonal virtual arm is designed. The real arm roll angle is achieved by controlling its winding on the virtual arm. In this way, the shape can be controlled. Finally, we compare the proposed method with other three approaches by simulations. Results show that the proposed method is more efficient and the arm shape is controllable.

Enhancing Semantic Web Technologies Using Lexical Auditing Techniques for Quality Assurance of Biomedical Ontologies

Semantic web technologies (SWT) represent data in a format that is easier for machines to understand. Validating the knowledge in data graphs created using SWT is critical to ensure that the axioms accurately represent the so-called “real” world. However, data graph validation is a significant challenge in the semantic web domain. The Shapes Constraint Language (SHACL) is the latest W3C standard developed with the goal of validating data-graphs. SHACL (pronounced as shackle) is a relatively new standard and hitherto has predominantly been employed to validate generic data graphs like WikiData and DBPedia. In generic data graphs, the name of a class does not affect the shape of a class, but this is not the case with biomedical ontology data graphs. The shapes of classes in biomedical ontology data graphs are highly influenced by the names of the classes, and the SHACL shape creation methods developed for generic data graphs fail to consider this characteristic difference. Thus, the existing SHACL shape creation methods do not perform well for domain-specific biomedical ontology data graphs. Maintaining the quality of biomedical ontology data graphs is crucial to ensure accurate analysis in safety-critical applications like Electronic Health Record (EHR) systems referencing such data graphs. Thus, in this work, we present a novel method to create enhanced SHACL shapes that consider the aforementioned characteristic difference to better validate biomedical ontology data graphs. We leverage the knowledge available from lexical auditing techniques for biomedical ontologies and incorporate this knowledge to create smart SHACL shapes. We also create SHACL shapes (baseline SHACL graph) without incorporating the lexical knowledge of the class names, as is performed by existing methods, and compare the performance of our enhanced SHACL shapes with the baseline SHACL shapes. The results demonstrate that the enhanced SHACL shapes augmented with lexical knowledge of the class names identified 176 violations which the baseline SHACL shapes, void of this lexical knowledge, failed to detect. Thus, the enhanced SHACL shapes presented in this work significantly improve the validation performance of biomedical ontology data graphs, thereby reducing the errors present in such data graphs and ensuring safe use in the life-critical applications referencing them.

Convergent evolving finite element approximations of boundary evolution under shape gradient flow

Abstract As a specific type of shape gradient descent algorithm, shape gradient flow is widely used for shape optimization problems constrained by partial differential equations. In this approach, the constraint partial differential equations could be solved by finite element methods on a domain with a solution-driven evolving boundary. Rigorous analysis for the stability and convergence of such finite element approximations is still missing from the literature due to the complex nonlinear dependence of the boundary evolution on the solution. In this article, rigorous analysis of numerical approximations to the evolution of the boundary in a prototypical shape gradient flow is addressed. First-order convergence in time and $k$th order convergence in space for finite elements of degree $k\geqslant 2$ are proved for a linearly semi-implicit evolving finite element algorithm up to a given time. The theoretical analysis is consistent with the numerical experiments, which also illustrate the effectiveness of the proposed method in simulating two- and three-dimensional boundary evolution under shape gradient flow. The extension of the formulation, algorithm and analysis to more general shape density functions and constraint partial differential equations is also discussed.

Shape-Constrained Statistical Inference

Statistical models defined by shape constraints are a valuable alternative to parametric models or nonparametric models defined in terms of quantitative smoothness constraints. While the latter two classes of models are typically difficult to justify a priori, many applications involve natural shape constraints, for instance, monotonicity of a density or regression function. We review some of the history of this subject and recent developments, with special emphasis on algorithmic aspects, adaptivity, honest confidence bands for shape-constrained curves, and distributional regression, i.e., inference about the conditional distribution of a real-valued response given certain covariates.

Semantic rule checking of cross-domain building data in information containers for linked document delivery using the shapes constraint language

Information exchange is a crucial process throughout the lifecycle of built assets. Building Information Modeling (BIM) and standardized information delivery enable exchanging, storing, and linking cross-domain information bundled in containers such as the standardized Information Container for Linked Document Delivery (ICDD). While assessing the quality of the interlinking and metadata is essential to allow all parties to interpret an information container correctly, most research efforts have focused on code compliance of domain-specific models. In order to address this gap, this paper proposes an approach for validating ICDD information containers using the Shapes Constraint Language (SHACL), the W3C recommendation for Resource Description Framework (RDF) data validation. For optimized querying and validation, a case study applies SHACL inference rules to the linking structure of ICDD to infer predicates between linked entities in four ICDD containers in varying dataset sizes and different linking methods. Afterward, the validation of these containers is analyzed using three types of validation rules with increasing complexity for another SHACL implementation. Results show the feasibility of cross-domain building information validation in ICDD with SHACL and how performance enhancements can be obtained on an inferred dataset compared to the original dataset.

3D Point Cloud Instance Segmentation Considering Global Shape Contour Constraints

Aiming to solve the problem that spatially distributed similar instances cannot be distinguished in 3D point cloud instance segmentation, a 3D point cloud instance segmentation network, considering the global shape contour, was proposed. This research used the global-to-local design idea and added the global shape constraint to solve this problem. A Transformer module (Global Shape Attention, GSA) that can capture the shape contour information of the instance in the scene was designed. This module encoded the shape contour information into the Transformer structure as a Key-Value and extracted the instance fused with the global shape contour features, for instance, segmentation. At the same time, the network directly predicted the instance mask in an end-to-end mode, avoiding heavy post-processing algorithms. Many experiments have been conducted on the S3DIS, ScanNet, and STPL3D datasets, and our experimental results showed that our proposed network can efficiently capture the shape contour information of scene instances and can help to alleviate the problem of the difficulty distinguishing between spatially distributed similar instances in a scene, improving the efficiency and stability of instance segmentation.

GTV Based Automatic Delineation of Clinical Target Volume for Cervical Cancer

The delineation of gross tumor volume (GTV) and clinical target volume (CTV) are two critical steps in the radiotherapy planning for cervical cancer. GTV defines the primary treatment region for the gross tumor, while CTV is the area surrounding GTV that includes a certain probability (5% to 10%) of subclinical lesions. In contrast to GTV, CTV delineation relies on predefined and judgment-based boundaries, and the high variability among users makes this task particularly challenging. In this study, we evaluated the potential relationship between GTV and CTV and developed an automatic CTV delineation algorithm for cervical cancer based on the fusion of GTV information. We introduced position and shape constraints of GTV to improve the accuracy of CTV delineation. The GTV-Net deep learning method was used to segment the CTV images of cervical cancer. The method aimed to use the delineation results of the GTV region for one-hot coding and add human anatomy experience in the clinical field to guide the CTV segmentation. This retrospective study included 545 cervical cancer patients who received radiation therapy from June 2017 to May 2019, including postoperative and radical treatment groups. The CTV and GTV regions were manually delineated by human experts. Numerous experiments were conducted to evaluate the performance of the network. First, compared with different network architectures, the Dice similarity coefficient (DSC) and 95% Hausdorff distance (95HD) of GTV-Net were both improved. Then, we compared the GTV-Net method with two resident physicians. Our GTV-Net method outperformed both resident physicians. In the postoperative group, our method improved the DSC by 4% compared to 3D-UNet, reaching 76.55%, and increased by about 2.57% compared to V-Net's 73.98%, with an improvement of approximately 1.23% compared to the two resident physicians. In the radical treatment group, compared to 3D-UNet's 78.76%, our method increased the DSC by about 3.25%, reaching 82%, and increased by approximately 2.08% compared to V-Net's 79.92%, with an improvement of about 1.35% compared to the two resident physicians. Compared with 3D-UNet, the average 95HD in the postoperative group decreased from 1.489 to 1.457, and in the radical treatment group, it decreased from 1.454 to 1.433. The results of 95HD also showed some improvement compared to V-Net. This study is the first to introduce GTV information for automatic segmentation of the clinical target area for cervical cancer. In this experiment, we observed a positive gain in CTV target automatic delineation guided by GTV information compared to solely performing CTV segmentation, with an improvement in Dice similarity of more than 4% and Hausdorff distance of more than 6% in the experimental dataset. In addition, GTV-guided CTV automatic delineation has also shown promising results on multicenter data, which will better serve the clinical field.

Semi-supervised peripapillary atrophy segmentation with shape constraint

Peripapillary atrophy (PPA) is a clinical abnormality related to many eye diseases, such as myopia and glaucoma. The shape and area of PPA are essential indicators of disease progression. PPA segmentation is a challenging task due to blurry edge and limited labeled data. In this paper, we propose a novel semi-supervised PPA segmentation method enhanced by prior knowledge. In order to learn shape information in the network, a novel shape constraint module is proposed to restrict the PPA appearance based on active shape model. To further leverage large amount of unlabeled data, a Siamese-like model updated by exponential moving average is introduced to provide pseudo labels. The pseudo labels are further refined by region connectivity correction. Extensive experiments on a clinical dataset demonstrate that our proposed PPA segmentation method provides good qualitative and quantitative performance.

Shape-Constrained Regression Using Sum of Squares Polynomials

Shape-Constrained Regression Using Algebraic Techniques How can one fit a multivariate polynomial to data points in such a way that this polynomial is guaranteed to have certain shape constraints, such as convexity or monotonicity in some of its variables? In “Shape-constrained regression using sum-of-squares polynomials,” M. Curmei and G. Hall propose a hierarchy of semidefinite programs to address this problem. They show that polynomial functions that are optimal to any fixed level of our hierarchy form a consistent estimator of the underlying shape-constrained function, which generates the data points. As a by-product of the proof, they establish that sum-of-squares-convex polynomials are dense in the set of polynomials that are convex over an arbitrary box. They further demonstrate the performance of the regressor for the problem of computing optimal transport maps in a color transfer task and that of estimating the optimal value function of a conic program. A real-time application of the latter problem to inventory management contract negotiation is presented.

Shape-Guided Dual Consistency Semi-Supervised Learning Framework for 3-D Medical Image Segmentation

Popular semi-supervised 3D medical image segmentation networks commonly suffer from two limitations: First, the geometry shape constraint of targets is frequently disregarded, leading to coarse segmentation results. Second, semi-supervision is only performed on the last layer of the decoder, resulting in the insufficient representation learning of 3D convolution neural network. To address these issues, we propose a shape-guided dual consistency semi-supervised learning (SDC-SSL) framework for 3D medical image segmentation. Indeed, the proposed framework has two dominating advantages. Initially, a geometry-aware shape constraint is presented and used to learn the shape representation, which converts the differences between two networks into an unsupervised loss and lets the framework learn the boundary distance information of targets in unlabeled challenging regions. Additionally, a deep-supervised knowledge transfer strategy is developed and employed by the proposed framework, which can upgrade the generalization ability of our framework without increasing any extra parameters and computation costs in the inference phase. Experimental results demonstrate that the proposed framework outperforms state-of-the-art methods on two challenging 3D medical image segmentation tasks due to effective geometry-aware shape constraint on unlabeled data and the strong ability of knowledge mining on labeled data. The code is available at: https://github.com/SUST-reynole/SDC-SSL.

Additively manufactured high permeability Fe-Ni alloys and novel bi-metallic magnetic shields

The sensitivity and sophistication of spacecraft for Earth Science and Planetary Science missions are increasing with each successive mission. Advances in instrumentation, robotics, remote sensing, avionics and controls are allowing un-crewed missions to be incredibly sophisticated. Effective electromagnetic shielding is critical for high fidelity functioning of the spacecraft and onboard instrumentation. Moreover, the geometrical complexity of the shielding arrangement and the constraints of size and shape, make additive manufacturing (AM) a critical, enabling technology for current and future missions. Two AM approaches - directed energy deposition (DED) and laser powder bed fusion (LPBF) - were used to produce Fe-80Ni-5Mo alloy rings and shields. The microstructure and magnetic properties of the materials produced through these processes are reported in this paper. A mechanism relating the microstructure to the soft magnetic performance of the material is proposed. The AM material produced in this work demonstrated the highest reported magnetic permeability and lowest reported coercivity of any additively manufactured soft magnetic material. Two different combinations of bi-metallic shields, Fe-80Ni-5Mo/FeCo-2V and Fe-80Ni-5Mo/Fe-49Ni, were fabricated using the DED process. The creation of these shields as monoliths in general, and for space-related applications in particular, is a novel aspect of this work. These multi-alloy, multi-layer shields showed a nearly 10 dB increase in shielding performance over Fe-80Ni-5Mo single alloy shielding, a significant improvement. For the DED builds, the coercivity decreases and permeability increases (better soft magnetic performance) with increasing build power. With increasing build power in the DED process, the grain size in the printed part increases. The corresponding reduction in the grain boundary area results in fewer obstacles to the movement of magnetic domain walls.

IOP-FL: Inside-Outside Personalization for Federated Medical Image Segmentation.

Federated learning (FL) allows multiple medical institutions to collaboratively learn a global model without centralizing client data. It is difficult, if possible at all, for such a global model to commonly achieve optimal performance for each individual client, due to the heterogeneity of medical images from various scanners and patient demographics. This problem becomes even more significant when deploying the global model to unseen clients outside the FL with unseen distributions not presented during federated training. To optimize the prediction accuracy of each individual client for medical imaging tasks, we propose a novel unified framework for both Inside and Outside model Personalization in FL (IOP-FL). Our inside personalization uses a lightweight gradient-based approach that exploits the local adapted model for each client, by accumulating both the global gradients for common knowledge and the local gradients for client-specific optimization. Moreover, and importantly, the obtained local personalized models and the global model can form a diverse and informative routing space to personalize an adapted model for outside FL clients. Hence, we design a new test-time routing scheme using the consistency loss with a shape constraint to dynamically incorporate the models, given the distribution information conveyed by the test data. Our extensive experimental results on two medical image segmentation tasks present significant improvements over SOTA methods on both inside and outside personalization, demonstrating the potential of our IOP-FL scheme for clinical practice. Code is available at https://github.com/med-air/IOP-FL.

Robust nonparametric frontier estimation in two steps

We propose a robust methodology for estimating production frontiers with multi-dimensional input via a two-step nonparametric regression, in which we estimate the level and shape of the frontier before shifting it to an appropriate position. Our main contribution is to derive a novel frontier estimation method under a variety of flexible models which is robust to the presence of outliers and possesses some inherent advantages over traditional frontier estimators. Our approach may be viewed as a simplification, yet a generalization, of those proposed by Martins-Filho and coauthors, who estimate frontier surfaces in three steps. In particular, outliers, as well as commonly seen shape constraints of the frontier surfaces, such as concavity and monotonicity, can be straightforwardly handled by our estimation procedure. We show consistency and asymptotic distributional theory of our resulting estimators under standard assumptions in the multi-dimensional input setting. The competitive finite-sample performances of our estimators are highlighted in both simulation studies and empirical data analysis.

Face alignment combined with shape constraints and Gaussian heatmap

Face alignment combined with shape constraints and Gaussian heatmap

Schrödinger Dynamics and Berry Phase of Undulatory Locomotion.

Spectral mode representations play an essential role in various areas of physics, from quantum mechanics to fluid turbulence, but they are not yet extensively used to characterize and describe the behavioral dynamics of living systems. Here, we show that mode-based linear models inferred from experimental live-imaging data can provide an accurate low-dimensional description of undulatory locomotion in worms, centipedes, robots, and snakes. By incorporating physical symmetries and known biological constraints into the dynamical model, we find that the shape dynamics are generically governed by Schrödinger equations in mode space. The eigenstates of the effective biophysical Hamiltonians and their adiabatic variations enable the efficient classification and differentiation of locomotion behaviors in natural, simulated, and robotic organisms using Grassmann distances and Berry phases. While our analysis focuses on a widely studied class of biophysical locomotion phenomena, the underlying approach generalizes to other physical or living systems that permit a mode representation subject to geometric shape constraints.

An unsupervised learning-based generalization of Data Envelopment Analysis

In this paper, we introduce an unsupervised machine learning method for production frontier estimation. This new approach satisfies fundamental properties of microeconomics, such as convexity and free disposability (shape constraints). The new method generalizes Data Envelopment Analysis (DEA) through the adaptation of One-Class Support Vector Machines with piecewise linear transformation mapping. The new technique aims to reduce the overfitting problem occurring in DEA. How to measure technical inefficiency through the directional distance function is also introduced. Finally, we evaluate the performance of the new technique via a computational experience, showing that the mean squared error in the estimation of the frontier is up to 83% better than the standard DEA in certain scenarios.

Constructing Coupling Model of Generalized B-Spline Curve and Crown (CMGBCC) to Explore the 3D Modeling of Chinese Fir Polymorphism

Crown simulation based on basis spline (b-spline) interpolation is a compatible method to simulate tree polymorphism at present. However, there are two problems when it simulates the crown: the first problem is that the derivative value at the top point needs to be given manually, and the second is that the type of value point needs to be collected equidistantly. To solve the above problems and realize convenient and accurate tree polymorphism simulation, this study took Chinese fir as the study object, set the crown morphological feature as the model value point, and constructed a coupling model of generalized B-spline curve and crown (CMGBCC) as the constraint condition of the crown shape to simulate the polymorphism in the process of a tree three-dimensional (3D) model. The position and size of the distribution on the 3D model of the branches were constrained by the curve, and the 3D modeling of a Chinese fir polymorphism was constructed. According to the collection of Chinese fir-type value points in the sample plot, the study realized the detailed types of value points’ precise simulation for three polymorphisms of the Chinese fir crown, including natural pruning, crown displacement, and crown shape difference. At the same time, the different withered existence states of the branches were considered preliminarily. Compared to the 3D model with the field survey data, indicating that constructed models could simulate the difference in tree crown morphology precisely, the branch models were separated by convenience to simulate the process of Chinese fir growth. In the process of construction, CMGBCC did not need to add the derivative value in a manual way and could collect the type of value points according to the characteristics of the crown morphological changes completely. Compared to the results of the crown curve constructed, which were based on generalized B-spline (GB-spline) interpolation and b-spline interpolation, it showed that the number of crown value points collected by the GB-spline interpolation method decreased by 18% on average. The precision of the crown shape constraint was improved by 7.63% compared to b-spline interpolation. The 3D modeling of tree polymorphism was combined with the relationship between tree morphology and environment. At the same time, it was convenient to simulate the behavior of forest management measures, such as pruning.