Shape Constraints Research Articles

Three-Dimensional Multi-Morphology TPMS-based Microchannel Design Method for Conformal Cooling in Injection Molding

Abstract Triply Periodic Minimal Surface (TPMS) possesses diverse morphological characteristics, such as pore sizes, porosity, and structural types. Integrating TPMS-based microchannels into micro-cellular cooling structures is advantageous for designing and controlling fluid characteristics within mold cooling channels. However, it is still difficult to design multi-morphology TPMS-based cooling microchannels that conform to the external shapes of injection molds. This work proposes a three-dimensional (3D) multi-morphology TPMS-based design method that transforms 3D constraints into a combination of two-dimensional (2D) constraints. Firstly, a beta growth algorithm based on closed-loop constraints is proposed to transition different morphologies smoothly on the plane. Subsequently, a transition optimization algorithm along the normal direction of the plane is introduced to smoothly transition multi-morphology TPMS-based microchannels in all directions. With this layered approach, multi-morphology microchannels can be obtained with first-order geometric continuity under complex shape constraints. Finally, several TPMS-based conformal cooling structures are designed for an automotive hood cover. The results of finite element simulations show that the cooling structures generated by the proposed method have a better cooling effect than the conformal channels. It can be concluded that multi-morphology TPMS-based structures perform better by contrast with conformal channels as the average temperature of the cooling surface decreases by 8.48K, and the standard deviation of temperature distribution decreases by 24.65%.

Interpretable Price Bounds Estimation with Shape Constraints in Price Optimization

Interpretable Price Bounds Estimation with Shape Constraints in Price Optimization

Measuring environmental inefficiency through machine learning: An approach based on efficiency analysis trees and by-production technology

The main objective of this study is to introduce machine learning-type extensions for the measurement of environmental inefficiency based on regression trees under shape constraints. The new methods developed are implemented using a by-production approach that distinguishes two technologies, one related to the generation of pollution and the other to the production of good outputs. In particular, we define two alternative approaches to measuring environmental inefficiency: by-production Efficiency Analysis Trees (by-production EAT) and by-production Convexified Efficiency Analysis Trees (by-production CEAT). The main advantage of the methods developed is that they do not suffer from the typical statistical problem of overfitting connected to Free Disposal Hull (FDH) and Data Envelopment Analysis (DEA). The performance of the new models is evaluated through a simulation study which shows that the new approaches outperform FDH and DEA in terms of mean squared error and bias. We also illustrate the practical usefulness of the new techniques through empirical application to 43 developing and developed countries over a fifteen-year period - from 2000 to 2014. Our empirical findings using real data clearly indicate the higher discriminating power of the by-production EAT and CEAT models as compared respectively to FDH and DEA.

Measurement of the fractional radiation length of a pixel module for the CMS Phase-2 upgrade via the multiple scattering of positrons

High-luminosity particle collider experiments such as the ones planned at the High-Luminosity Large Hadron Collider require ever-greater vertexing precision of the tracking detectors, necessitating reductions in the material budget of the detectors. Traditionally, the fractional radiation length (x/X 0) of detectors is either estimated using known properties of the constituent materials, or measured in dedicated runs of the final detector. In this paper, we present a method of direct measurement of the material budget of a CMS prototype module designed for the Phase-2 upgrade of the CMS detector using a 40–65 MeV positron beam. A total of 630 million events were collected at the Paul Scherrer Institut PiE1 experimental area using a three-plane telescope consisting of the prototype module as the central plane, surrounded by two MALTA monolithic pixel detectors. Fractional radiation lengths were extracted from scattering angle distributions using the Highland approximation for multiple scattering. A statistical technique recovered runs suffering from trigger desynchronisation, and several corrections were introduced to compensate for local inefficiencies related to geometric and beam shape constraints. Two regions of the module were surveyed and yielded average x/X 0 values of (0.72 ± 0.05)% and (0.95 ± 0.09)%, which are compatible with empirical estimates for these regions computed from known material properties of 0.753% and 0.892%, respectively. Two types of higher-granularity maps of the fractional radiation length were produced, subdivided either into rectangular regions of uniform size, or polygonal-shaped regions of uniform material composition. The results bode well for the CMS Phase-2 upgrade modules, which will play a key role in the minimisation of the material of the upgraded detector.

Landmark-in-facial-component: Towards occlusion-robust facial landmark localization

Despite great efforts in recent years to research robust facial landmark localization methods, occlusion remains a challenge. To tackle this challenge, we propose a model called the Landmark-in-Facial-Component Network (LFCNet). Unlike mainstream models that focus on boundary information, LFCNet utilizes the strong structural constraints inherent in facial anatomy to address occlusion. Specifically, two key modules are designed, a component localization module and an offset localization module. After grouping landmarks based on facial components, the component localization module accomplishes coarse localization of facial components. Offset localization module performs fine localization of landmarks based on the coarse localization results, which can also be seen as delineating the shape of facial components. These two modules form a coarse-to-fine localization pipeline and can also enable LFCNet to better learn the shape constraint of human faces, thereby enhancing LFCNet's robustness to occlusion. LFCNet achieves 4.82% normalized mean error on occlusion subset of WFLW dataset and 6.33% normalized mean error on Masked 300W dataset. The results demonstrate that LFCNet achieves excellent performance in comparison to state-of-the-art methods, especially on occlusion datasets.

3D Vessel Segmentation With Limited Guidance of 2D Structure-Agnostic Vessel Annotations.

Delineating 3D blood vessels of various anatomical structures is essential for clinical diagnosis and treatment, however, is challenging due to complex structure variations and varied imaging conditions. Although recent supervised deep learning models have demonstrated their superior capacity in automatic 3D vessel segmentation, the reliance on expensive 3D manual annotations and limited capacity for annotation reuse among different vascular structures hinder their clinical applications. To avoid the repetitive and costly annotating process for each vascular structure and make full use of existing annotations, this paper proposes a novel 3D shape-guided local discrimination (3D-SLD) model for 3D vascular segmentation under limited guidance from public 2D vessel annotations. The primary hypothesis is that 3D vessels are composed of semantically similar voxels and often exhibit tree-shaped morphology. Accordingly, the 3D region discrimination loss is firstly proposed to learn the discriminative representation measuring voxel-wise similarities and cluster semantically consistent voxels to form the candidate 3D vascular segmentation in unlabeled images. Secondly, the shape distribution from existing 2D structure-agnostic vessel annotations is introduced to guide the 3D vessels with the tree-shaped morphology by the adversarial shape constraint loss. Thirdly, to enhance training stability and prediction credibility, the highlighting-reviewing-summarizing (HRS) mechanism is proposed. This mechanism involves summarizing historical models to maintain temporal consistency and identifying credible pseudo labels as reliable supervision signals. Only guided by public 2D coronary artery annotations, our method achieves results comparable to SOTA barely-supervised methods in 3D cerebrovascular segmentation, and the best DSC in 3D hepatic vessel segmentation, demonstrating the effectiveness of our method.

A hierarchical constrained density regression model for predicting cluster‐level dose‐response

AbstractWith the advent of new alternative methods for rapid toxicity screening of chemicals comes the need for new statistical methodologies which appropriately synthesize the large amount of data collected. For example, transcriptomic assays can be used to assess the impact of a chemical on thousands of genes, but current approaches to analyzing the data treat each gene separately and do not allow sharing of information among genes within pathways. Furthermore, the methods employed are fully parametric and do not account for changes in distribution shape that may occur at high exposure levels. To address the limitations of these methods, we propose Constrained Logistic Density Regression (COLDER) to model expression data from different genes simultaneously. Under COLDER, the dose‐response function for each gene is assigned a prior via a discrete logistic stick‐breaking process (LSBP) whose weights depend on gene‐level characteristics (e.g., pathway membership) and atoms consist of different dose‐response functions subject to a shape constraint that ensures biological plausibility. The posterior distribution for the benchmark dose among genes within the same pathways can be estimated directly from the model, which is another advantage over current methods. The ability of COLDER to predict gene‐level dose‐response is evaluated in a simulation study and the method is illustrated with data from a National Toxicology Program study of Aflatoxin B1.

A shape-supervised feature fusion U-Net for tubular structure segmentation

Accurate segmentation of tubular structures, such as blood vessels and bile ducts, is pivotal for clinical diagnosis and subsequent treatment. However, challenges arise from their unique structure and morphology. These structures are thin and elongated, and often exhibit complex branching patterns, making precise delineation difficult. Additionally, the intricate and often noisy backgrounds in medical images complicate the extraction of detailed and shape features. These challenges collectively hinder the effectiveness of automated segmentation methods. To address these issues, this paper introduces the shape-supervised feature fusion U-Net (SFU-Net), a novel approach that extends the traditional U-Net architecture. Our network incorporates a feature fusion module that effectively combines different semantic information in both the encoder and decoder paths, facilitating the capture of detailed geometric representations of tubular structures. Furthermore, a novel distance-based tubularity loss is designed to capture boundary information and supervise segmentation integrity by imposing shape constraints. We conducted comprehensive experiments on three tubular structure segmentation tasks in medical imaging, including the dilated biliary tree, hepatic vessel, and pulmonary artery. The experimental results illustrate that the proposed SFU-Net achieves the best performance in terms of accuracy and completeness, with Dice scores of 76.14%, 80.42%, and 83.79%, and HD95 values of 8.59 mm, 6.43 mm, and 4.31 mm across three datasets, respectively. Compared to traditional U-Net-based segmentation methods and other tubular segmentation approaches, our method exhibits superior performance, underscoring its effectiveness in medical image segmentation with tubular structures.

Hierarchical Bayesian spectral regression with shape constraints for multi-group data

We propose a hierarchical Bayesian (HB) model for multi-group analysis with group–specific, flexible regression functions. The lower–level (within group) and upper–level (between groups) regression functions have hierarchical Gaussian process priors. HB smoothing priors are developed for the spectral coefficients. The HB priors smooth the estimated functions within and between groups. The HB model is particularly useful when data within groups are sparse because it shares information across groups, and provides more accurate estimates than fitting separate nonparametric models to each group. The proposed model also allows shape constraints, such as monotone, U and S–shaped, and multi-modal constraints. When appropriate, shape constraints improve estimation by recognizing violations of the shape constraints as noise. The model is illustrated by two examples: monotone growth curves for children, and happiness as a convex, U-shaped function of age in multiple countries. Various basis functions could also be used, and the paper also implements versions with B-splines and orthogonal polynomials.

SMFS‐GAN: Style‐Guided Multi‐class Freehand Sketch‐to‐Image Synthesis

AbstractFreehand sketch‐to‐image (S2I) is a challenging task due to the individualized lines and the random shape of freehand sketches. The multi‐class freehand sketch‐to‐image synthesis task, in turn, presents new challenges for this research area. This task requires not only the consideration of the problems posed by freehand sketches but also the analysis of multi‐class domain differences in the conditions of a single model. However, existing methods often have difficulty learning domain differences between multiple classes, and cannot generate controllable and appropriate textures while maintaining shape stability. In this paper, we propose a style‐guided multi‐class freehand sketch‐to‐image synthesis model, SMFS‐GAN, which can be trained using only unpaired data. To this end, we introduce a contrast‐based style encoder that optimizes the network's perception of domain disparities by explicitly modelling the differences between classes and thus extracting style information across domains. Further, to optimize the fine‐grained texture of the generated results and the shape consistency with freehand sketches, we propose a local texture refinement discriminator and a Shape Constraint Module, respectively. In addition, to address the imbalance of data classes in the QMUL‐Sketch dataset, we add 6K images by drawing manually and obtain QMUL‐Sketch+ dataset. Extensive experiments on SketchyCOCO Object dataset, QMUL‐Sketch+ dataset and Pseudosketches dataset demonstrate the effectiveness as well as the superiority of our proposed method.

Heatmap-Based Active Shape Model for Landmark Detection in Lumbar X-ray Images.

Medical staff inspect lumbar X-ray images to diagnose lumbar spine diseases, and the analysis process is currently automated using deep-learning techniques. The detection of landmarks is necessary in the automatic process of localizing the position and identifying the morphological features of the vertebrae. However, detection errors may occur owing to the noise and ambiguity of images, as well as individual variations in the shape of the lumbar vertebrae. This study proposes a method to improve the robustness of landmark detection results. This method assumes that landmarks are detected by a convolutional neural network-based two-step model consisting of Pose-Net and M-Net. The model generates a heatmap response to indicate the probable landmark positions. The proposed method then corrects the landmark positions using the heatmap response and active shape model, which employs statistical information on the landmark distribution. Experiments were conducted using 3600 lumbar X-ray images, and the results showed that the landmark detection error was reduced by the proposed method. The average value of maximum errors decreased by 5.58% after applying the proposed method, which combines the outstanding image analysis capabilities of deep learning with statistical shape constraints on landmark distribution. The proposed method could also be easily integrated with other techniques to increase the robustness of landmark detection results such as CoordConv layers and non-directional part affinity field. This resulted in a further enhancement in the landmark detection performance. These advantages can improve the reliability of automatic systems used to inspect lumbar X-ray images. This will benefit both patients and medical staff by reducing medical expenses and increasing diagnostic efficiency.

Distributed continuous-time algorithm for time-varying optimization with desired shape constraints

Distributed continuous-time algorithm for time-varying optimization with desired shape constraints

Capacitive Touch Sensing on General 3D Surfaces

Mutual-capacitive sensing is the most common technology for detecting multi-touch, especially on flat and simple curvature surfaces. Its extension to a more complex shape is still challenging, as a uniform distribution of sensing electrodes is required for consistent touch sensitivity across the surface. To overcome this problem, we propose a method to adapt the sensor layout of common capacitive multi-touch sensors to more complex 3D surfaces, ensuring high-resolution, robust multi-touch detection. The method automatically computes a grid of transmitter and receiver electrodes with as regular distribution as possible over a general 3D shape. It starts with the computation of a proxy geometry by quad meshing used to place the electrodes through the dual-edge graph. It then arranges electrodes on the surface to minimize the number of touch controllers required for capacitive sensing and the number of input/output pins to connect the electrodes with the controllers. We reach these objectives using a new simplification and clustering algorithm for a regular quad-patch layout. The reduced patch layout is used to optimize the routing of all the structures (surface grooves and internal pipes) needed to host all electrodes on the surface and inside the object's volume, considering the geometric constraints of the 3D shape. Finally, we print the 3D object prototype ready to be equipped with the electrodes. We analyze the performance of the proposed quad layout simplification and clustering algorithm using different quad meshing and characterize the signal quality and accuracy of the capacitive touch sensor for different non-planar geometries. The tested prototypes show precise and robust multi-touch detection with good Signal-to-Noise Ratio and spatial accuracy of about 1mm.

Finite element analysis with deformed shape constraints generated by laser‐scanned point clouds

AbstractThis article proposes a computational method for finite element analysis with deformed shape constraints for analyzing constructed structures to account for deformations that occur before shape measurement by a terrestrial laser scanner (TLS). In this method, point clouds obtained by a TLS are considered as a partial surface of the deformed structure. An analysis model is assumed to be created from CAD data or drawings. The analysis is performed under deformed shape constraints, namely, the deformed surface constraints or the normal vector constraints, which are generated by the point clouds. These constraints are introduced to reproduce the current displacements and stresses for the structure through the analysis. This method was applied to analyses of a plate and a desk using point clouds, which were created virtually on a computer or obtained by a TLS in the numerical examples. The results showed that this method can consider unexpected deformations that occur before laser scanning. Although the computed stresses oscillated when the scanned point cloud was used due to measurement errors and conventional point cloud processing methods, the stress values were responsive enough to indicate unnatural shapes of the deformed structure. Moreover, the oscillation was observed only in areas with constraints, whereas it was not seen in areas without constraints.

Data Validation Utilizing Expert Knowledge and Shape Constraints

Data validation is a primary concern in any data-driven application, as undetected data errors may negatively affect machine learning models and lead to suboptimal decisions. Data quality issues are usually detected manually by experts, which becomes infeasible and uneconomical for large volumes of data. To enable automated data validation, we propose “shape constraint-based data validation,” a novel approach based on machine learning that incorporates expert knowledge in the form of shape constraints. Shape constraints can be used to describe expected (multivariate and nonlinear) patterns in valid data and enable the detection of invalid data that deviates from these expected patterns. Our approach can be divided into two steps: (1) shape-constrained prediction models are trained on data, and (2) their training error is analyzed to identify invalid data. The training error can be used as an indicator for invalid data because shape-constrained models can fit valid data better than invalid data. We evaluate the approach on a benchmark suite consisting of synthetic datasets, which we have published for benchmarking similar data validation approaches. Additionally, we demonstrate the capabilities of the proposed approach with a real-world dataset consisting of measurements from a friction test bench in an industrial setting. Our approach detects subtle data errors that are difficult to identify even for domain experts.

Buckling mode constraints for topology optimization using eigenvector aggregates

Buckling-constrained structural design problems have conventionally prioritized optimizing the buckling load factor with less consideration given to the buckling mode shape. In this work, mode shape constraints are imposed within a topology optimization problem using an eigenvector aggregate constraint that is a weighted sum of homogeneous quadratic functions of the linearized buckling eigenvectors. A generalized formulation of the eigenvector aggregate is introduced, extending previous work. A new adjoint-based derivative evaluation technique is derived that is valid even in the presence of repeated eigenvalues. Numerical examples, including a clamped beam, a compressed column, and a square plate, demonstrate the effectiveness of the proposed approach. The results show the ability of the eigenvector aggregate to handle repeated eigenvalues, enable design space exploration, and capture mode shape switching.

Semi-supervised learning framework with shape encoding for neonatal ventricular segmentation from 3D ultrasound.

Three-dimensional (3D) ultrasound (US) imaging has shown promise in non-invasive monitoring of changes in the lateral brain ventricles of neonates suffering from intraventricular hemorrhaging. Due to the poorly defined anatomical boundaries and low signal-to-noise ratio, fully supervised methods for segmentation of the lateral ventricles in 3D US images require a large dataset of annotated images by trained physicians, which is tedious, time-consuming, and expensive. Training fully supervised segmentation methods on a small dataset may lead to overfitting and hence reduce its generalizability. Semi-supervised learning (SSL) methods for 3D US segmentation may be able to address these challenges but most existing SSL methods have been developed for magnetic resonance or computed tomography (CT) images. To develop a fast, lightweight, and accurate SSL method, specifically for 3D US images, that will use unlabeled data towards improving segmentation performance. We propose an SSL framework that leverages the shape-encoding ability of an autoencoder network to enforce complex shape and size constraints on a 3D U-Net segmentation model. The autoencoder created pseudo-labels, based on the 3D U-Net predicted segmentations, that enforces shape constraints. An adversarial discriminator network then determined whether images came from the labeled or unlabeled data distributions. We used 887 3D US images, of which 87 had manually annotated labels and 800 images were unlabeled. Training/validation/testing sets of 25/12/50, 25/12/25 and 50/12/25 images were used for model experimentation. The Dice similarity coefficient (DSC), mean absolute surface distance (MAD), and absolute volumetric difference (VD) were used as metrics for comparing to other benchmarks. The baseline benchmark was the fully supervised vanilla 3D U-Net while dual task consistency, shape-aware semi-supervised network, correlation-aware mutual learning, and 3D U-Net Ensemble models were used as state-of-the-art benchmarks with DSC, MAD, and VD as comparison metrics. The Wilcoxon signed-rank test was used to test statistical significance between algorithms for DSC and VD with the threshold being p<0.05 and corrected to p<0.01 using the Bonferroni correction. The random-access memory (RAM) trace and number of trainable parameters were used to compare the computing efficiency between models. Relative to the baseline 3D U-Net model, our shape-encoding SSL method reported a mean DSC improvement of 6.5%, 7.7%, and 4.1% with a 95% confidence interval of 4.2%, 5.7%, and 2.1% using image data splits of 25/12/50, 25/12/25, and 50/12/25, respectively. Our method only used a 1GB increase in RAM compared to the baseline 3D U-Net and required less than half the RAM and trainable parameters compared to the 3D U-Net ensemble method. Based on our extensive literature survey, this is one of the first reported works to propose an SSL method designed for segmenting organs in 3D US images and specifically one that incorporates unlabeled data for segmenting neonatal cerebral lateral ventricles. When compared to the state-of-the-art SSL and fully supervised learning methods, our method yielded the highest DSC and lowest VD while being computationally efficient.

Pedestrian-ground contact injury protection method under the constraint of the vehicle-front end shape and its robust analysis

This research paper introduces a novel approach for protecting pedestrians from ground contact injuries through incorporating vehicle front-end shape constraints in the braking control method. The feasibility of the proposed method is evaluated through simulations, and its resilience to different disturbances is studied. Results indicate that the proposed method effectively manages vehicle movement by monitoring the first head-vehicle contact time (t1 ) between the pedestrian’s head and the vehicle. The simulations show that the proposed method reduces ground-related Weighted Injury Cost (WIC) by up to 84%, and the proportion of ‘safe’ mechanisms increases to 74%. The robustness of the braking control method is also evidenced by its high performance during disturbances such as changes in friction coefficient, lag time, and t1 . Furthermore, the anti-disturbance abilities of each vehicle shape are comparable except for t1 disturbance. There are no significant variations in the braking control protection effect between different friction coefficients and each t1 , but noticeable differences exist between lag times. Further analysis reveals that parameter disturbances affect the deceleration of the vehicle and the impact speed of the pedestrian and vehicle, leading to changes in the Vz (Vertical head-to-ground impact velocity), thorax acceleration, pelvic lateral impact force, and knee lateral bending angle, which subsequently increases the risk of pedestrian ground contact injuries. The proposed method offers an efficient solution for protecting pedestrians from ground contact injuries by controlling vehicle braking, highlighting its practical utility.

A method for processing multispectral radiometric thermometry data based on BP-Alpha constraints

Multispectral radiometric thermometry is a commonly used method for infrared temperature measurement. The biggest challenge in processing multispectral data is the unknown emissivity. The traditional method of modeling emissivity assumptions is inadequate in dealing with emissivity instability, particularly when there is a rapid change in emissivity due to varying degrees of oxidation during metal heating. To address the temperature measurement challenge, this paper converts the multispectral temperature measurement problem into a constrained optimization problem. This is achieved by constructing a new type of constraints, using a BP neural network to establish the emissivity range constraints, and constructing an Alpha spectral model to establish the emissivity shape constraints. The improved Lichtenberg algorithm is then used to solve the problem, resulting in significantly improved temperature inversion accuracy. The method’s effectiveness was verified through simulations and GH3044 alloy experiments. The temperature inversion’s maximum absolute and relative errors were 9.5 K and 0.92%, respectively.

Universal Inference Meets Random Projections: A Scalable Test for Log-Concavity

Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival modeling, and reliability theory. However, there do not currently exist valid tests for whether the underlying density of given data is log-concave. The recent universal inference methodology provides a valid test. The universal test relies on maximum likelihood estimation (MLE), and efficient methods already exist for finding the log-concave MLE. This yields the first test of log-concavity that is provably valid in finite samples in any dimension, for which we also establish asymptotic consistency results. Empirically, we find that a random projections approach that converts the d-dimensional testing problem into many one-dimensional problems can yield high power, leading to a simple procedure that is statistically and computationally efficient.