Shape-based Approach Research Articles

Shape-based functional data analysis

Functional data analysis (FDA) is a fast-growing area of research and development in statistics. While most FDA literature imposes the classical L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {L}^2$$\\end{document} Hilbert structure on function spaces, there is an emergent need for a different, shape-based approach for analyzing functional data. This paper reviews and develops fundamental geometrical concepts that help connect traditionally diverse fields of shape and functional analyses. It showcases that focusing on shapes is often more appropriate when structural features (number of peaks and valleys and their heights) carry salient information in data. It recaps recent mathematical representations and associated procedures for comparing, summarizing, and testing the shapes of functions. Specifically, it discusses three tasks: shape fitting, shape fPCA, and shape regression models. The latter refers to the models that separate the shapes of functions from their phases and use them individually in regression analysis. The ensuing results provide better interpretations and tend to preserve geometric structures. The paper also discusses an extension where the functions are not real-valued but manifold-valued. The article presents several examples of this shape-centric functional data analysis using simulated and real data.

Formation flying along artificial halo orbit around Sun–Earth L2 point for interferometric observations

This paper proposes a method of using multiple spacecraft flying in formation in an artificially reduced halo orbit around the 2nd Lagrange point in the Sun–Earth system (SEL2) to make interferometric observations. One of the requirements for interferometric observations is to collect baseline vectors between telescopes or antennas. A shape-based approach is introduced to design a formation flight orbit that spirally spreads to satisfy this requirement. In this approach, orbits are designed on the basis of a linear theory. However, the formation orbits based on the linear theory quickly diverge because of the unstable dynamics around the SEL2. Therefore, the state-dependent Riccati equation, which allows for nonlinear control, is applied to orbit maintenance. The control system consists of two components: one for maintaining the reference orbit around the SEL2 and the other for controlling the relative position between the multiple spacecraft. The performance of the developed formation flight system is verified through a numerical simulation, confirming that the position accuracy requirement of the infrared interferometer is satisfied. It is also shown that both controls can be achieved with a low-thrust magnitude by using an electric propulsion system.

A novel shape-based approach to identify gestational age-adjusted growth patterns from birth to 11 years of age

Child growth patterns assessment is critical to design public health interventions. However, current analytical approaches may overlook population heterogeneity. To overcome this limitation, we developed a growth trajectories clustering pipeline that incorporates a shape-respecting distance, baseline centering (i.e., birth-size normalized trajectories) and Gestational Age (GA)-correction to characterize shape-based child growth patterns. We used data from 3945 children (461 preterm) in the 2004 Pelotas Birth Cohort with at least 3 measurements between birth (included) and 11 years of age. Sex-adjusted weight-, length/height- and body mass index-for-age z-scores were derived at birth, 3 months, and at 1, 2, 4, 6 and 11 years of age (INTERGROWTH-21st and WHO growth standards). Growth trajectories clustering was conducted for each anthropometric index using k-means and a shape-respecting distance, accounting or not for birth size and/or GA-correction. We identified 3 trajectory patterns for each anthropometric index: increasing (High), stable (Middle) and decreasing (Low). Baseline centering resulted in pattern classification that considered early life growth traits. GA-correction increased the intercepts of preterm-born children trajectories, impacting their pattern classification. Incorporating shape-based clustering, baseline centering and GA-correction in growth patterns analysis improves the identification of subgroups meaningful for public health interventions.

Rapid Suboptimal Low-Thrust Space Trajectory Design

The finite Fourier series shape-based approach for fast initial trajectory design satisfies the equations of motion and other problem constraints at discrete points by using a nonlinear programming solver to design the Fourier coefficients. In this paper, the finite Fourier series approach is extended to account for the necessary conditions for optimality during the Fourier coefficient design. The proposed method uses the approximate trajectories to analytically estimate the costates at these discrete points by employing a finite difference technique on the adjoint differential equations. Lagrange multipliers associated with any terminal state constraints are determined using an auxiliary function. Residual errors in the stationarity condition are reduced through the objective function, with the Legendre–Clebsch condition enforced as a nonlinear inequality constraint; applying these two conditions finds suboptimal solutions without an excessive loss of computational efficiency. Test cases use steering angle and thrust acceleration magnitude controls and span Earth-escape spirals, geostationary spacecraft rendezvous, and phasing maneuvers. The presented results demonstrate the proposed method’s ability to achieve trajectories closer to the optimal solution.

Correction to: Joint failure recovery for snake robot locomotion using a shape-based approach

Correction to: Joint failure recovery for snake robot locomotion using a shape-based approach

A Shape-based Approach for Recognition of Hidden Objects Using Microwave Radar Imaging System

A Shape-based Approach for Recognition of Hidden Objects Using Microwave Radar Imaging System

In Silico and In Vitro Approach to Assess Direct Allosteric AMPK Activators from Nature.

The 5'-adenosine monophosphate-activated protein kinase (AMPK) is an important metabolic regulator. Its allosteric drug and metabolite binding (ADaM) site was identified as an attractive target for direct AMPK activation and holds promise as a novel mechanism for the treatment of metabolic diseases. With the exception of lusianthridin and salicylic acid, no natural product (NP) is reported so far to directly target the ADaM site. For the streamlined assessment of direct AMPK activators from the pool of NPs, an integrated workflow using in silico and in vitro methods was applied. Virtual screening combining a 3D shape-based approach and docking identified 21 NPs and NP-like molecules that could potentially activate AMPK. The compounds were purchased and tested in an in vitro AMPK α 1 β 1 γ 1 kinase assay. Two NP-like virtual hits were identified, which, at 30 µM concentration, caused a 1.65-fold (± 0.24) and a 1.58-fold (± 0.17) activation of AMPK, respectively. Intriguingly, using two different evaluation methods, we could not confirm the bioactivity of the supposed AMPK activator lusianthridin, which rebuts earlier reports.

Shape-based approach to attitude motion planning of reconfigurable spacecraft

Internal torques generated from shape reconfiguration can be helpful in Micro-Satellite attitude control. The configuration-attitude-coupled non-holonomic dynamics of a multi-body spacecraft is investigated. A shape-based motion trajectory in the form of water drop curve is proposed to synchronously reach target attitude and target shape configuration. With the shape-based approach, the motion planning problem is converted into a system of non-linear equations in three unknowns. The advantages of this approach is demonstrated from the views of simplicity, reachability, and efficiency. Simulations are conducted to test the planning function, and the results are compared with those obtained from the optimal control method.

Joint failure recovery for snake robot locomotion using a shape-based approach

Joint failure recovery for snake robot locomotion using a shape-based approach

A shape-based approach to conflict forecasting

ABSTRACT Do conflict processes exhibit repeating patterns over time? And if so, can we exploit the recurring shapes and structures of the time series to forecast the evolution of conflict? Theory has long focused on the sequence of events that precedes conflicts (e.g., escalation or brinkmanship). Yet, current empirical research is unable to represent these complex interactions unfolding over time because it attempts to match cases on the raw value of covariates, and not on their structure or shape. As a result, it cannot easily represent real-world relations which may, for example, follow a long alternation of escalation and détente, in various orders and at various speeds. Here, I aim to address these issues using recent machine-learning methods derived from pattern recognition in time series to study the dynamics of casualties in civil war processes. I find that the methods perform well on out-of-sample forecasts of the count of the number of fatalities per month from state-based conflict. In particular, our results yield Mean Squared Errors that are lower than the competition benchmark. We discuss the implication for conflict research and the importance of comparing entire sequences rather than isolated observations in time.

A note on the effect of material uncertainty on acoustic source localization error in anisotropic plates

The uncertainty in material properties of an anisotropic plate may influence the acoustic source localization process undertaken for the plate. To study this effect of material uncertainty, the two moduli of elasticity of an orthotropic plate material are considered in this note as independent random variables and the propagation of this material uncertainty through the wave front shape-based acoustic source localization approach is investigated. Assuming lognormal probability distributions for the two random variables, several design points in lognormal spaces are picked using Latin Hypercube Sampling. Finite element analysis is performed for each design point to simulate the elastic wave propagation due to an acoustic event and wave front shape-based approach is applied to estimate the source location. The time-of-arrivals and source localization errors obtained for each design point are considered as separate response functions at that design point and regression kriging metamodels through the responses at the design points are constructed. Monte Carlo simulations are carried out using these metamodels to obtain the distribution parameters (i.e., ranges, means and standard deviations) of the time-of-arrivals and localization errors. A global sensitivity analysis is performed to estimate the effect of each random variable on the localization errors. It is observed that for lognormally distributed moduli of elasticity with same coefficients of variation, uncertainty in the modulus of elasticity in the major direction affects the source localization accuracy more compared to the uncertainty in the modulus of elasticity in the minor direction, particularly when the ellipse-based technique is used.

Shape-Based Approach for Low-Thrust Earth–Moon Trajectories Initial Design

A robust finite Fourier series (R-FFS) approach is developed for fast generation of Earth–moon trajectories using continuous low thrust. Each component of the position vector is approximated using a finite Fourier series as a function of time; these approximations are then used to design a trajectory that satisfies the equations of motion and the constraints, at discrete points, as well as the problem boundary conditions. The R-FFS method leverages the three-body problem characteristics to achieve all the required plane change without the use of propulsion. The trajectory is divided into phases: escape, intermediate, and capture. The escape phase is further divided into segments. The phase of the trajectory near the L1 Lagrange point is designed first and is always a thrust-free phase. This thrust-free phase is optimized to achieve the required plane change, enabling planar trajectories in the other phases. The initial guess needed by the solver, in the escape and capture phases, is generated using an analytic approximation developed in this paper. The numerical results show that the R-FFS can generate three-dimensional transfers to high lunar orbits, low lunar orbits, and halo orbits, while meeting constraints on the maximum thrust level of the engine.

A Triple-Modality Ultrasound Computed Tomography Based on Full-Waveform Data for Industrial Processes

Ultrasound computed tomography (USCT) is gaining interests in many application areas in industrial processes. The recent scientific research focuses on the possible uses of USCT for varied fields of industry such as flow monitoring in pipes, non-destructive inspection, and monitoring of stirred tanks chemical processes. Until now, most transmission tomography (UTT) and reflection tomography (URT) have been demonstrated individually for these applications. A full waveform USCT contain large amount of information on process under evaluation. The developed approach in this paper is focusing on demonstration of a triple modality USCT. First, an optimised transmission image is formed by fusion of time-of-flight (TOF) and acoustic attenuation (AA) images. Secondly, a reflection image is being optimised by using the information from the transmission image. This triple modality method enables integration of a shape-based approach obtained by URT mode with the quantitative image-based approach UTT mode. A delicate combination of the different information provided by various features of the full-wave signal offers optimal and increased spatial resolution and provides complementary information. Verification tests have been implemented using experimental phantoms of different combinations, sizes, and shapes, to investigate the qualitative imaging features. Moreover, experiments with different concentrations solutions further validate the quantitative traits to benefit from both reflection and transmission modes. This work displays the potential of the full-waveform USCT for industrial applications.

The three-dimensional shape symmetry of the lunate and its implications.

We studied the three-dimensional (3-D) shape variations and symmetry of the lunate to evaluate whether a contralateral shape-based approach to design patient-specific implants for treatment of Kienböck's disease is accurate. A 3-D statistical shape model of the lunate was built using the computed tomography scans of 54 lunate pairs and shape symmetry was evaluated based on an intraclass correlation analysis. The lunate shape was not bilaterally symmetrical in (1) the angle scaphoid surface - radius-ulna surface, (2) the dorsal side and the length of the side adjacent to the triquetrum, (3) the orientation of the volar surface, (4) the width of the side adjacent to the scaphoid, (5) the skewness in the coronal plane and (6) the curvature of bone articulating with the hamate and capitate. These findings suggest that using the contralateral lunate to design patient-specific lunate implants may not be as accurate as it is intended.

Square-shaped sensor clusters for acoustic source localization in anisotropic plates by wave front shape-based approach

Various techniques have emerged in the past few years for localizing the acoustic source in an anisotropic plate. The wave front shape-based approach, one of the recent additions to this field of research, has the advantage of circumventing the unrealistic assumption of a straight line wave propagation path through an anisotropic medium. In their most recent versions, the two major wave front shape-based techniques (i.e., the ellipse- and the parametric curve-based techniques) are applicable to the situations with an unknown orientation of the axes of symmetry of an anisotropic plate. However, this approach still relies on estimating the angle of wave-incidence at a given location of the plate via a single L-shaped sensor cluster. The incidence angle so obtained may deviate significantly from the true angle of wave arrival. To improve the estimation accuracy of the incidence angle, in the present study a square-shaped cluster composed of four densely-spaced sensors forming the four vertices of a square is proposed to be installed at the location of interest. Essentially, a square-shaped sensor cluster contains four L-shaped clusters oriented in different directions. A formulation to estimate the angle of incidence from the signal data acquired by a squared-shaped cluster is presented. The wave front shape-based approach can then be applied to estimate the acoustic source location. A numerical study is conducted to illustrate the proposed methodology. Performance comparisons between square- and L-shaped clusters reveal that in general the square-shaped clusters lead to more accurate source location estimates than the L-shaped clusters.

Spiral trajectories induced by radial thrust with applications to generalized sails

In this study, new analytical solutions to the equations of motion of a propelled spacecraft are investigated using a shape-based approach. There is an assumption that the spacecraft travels a two-dimensional spiral trajectory in which the orbital radius is proportional to an assigned power of the spacecraft angular coordinate. The exact solution to the equations of motion is obtained as a function of time in the case of a purely radial thrust, and the propulsive acceleration magnitude necessary for the spacecraft to track the prescribed spiral trajectory is found in a closed form. The analytical results are then specialized to the case of a generalized sail, that is, a propulsion system capable of providing an outward radial propulsive acceleration, the magnitude of which depends on a given power of the Sun-spacecraft distance. In particular, the conditions for an outward radial thrust and the required sail performance are quantified and thoroughly discussed. It is worth noting that these propulsion systems provide a purely radial thrust when their orientation is Sun-facing. This is an important advantage from an engineering point of view because, depending on the particular propulsion system, a Sun-facing attitude can be stable or obtainable in a passive way. A case study is finally presented, where the generalized sail is assumed to start the spiral trajectory from the Earth’s heliocentric orbit. The main outcome is that the required sail performance is in principle achievable on the basis of many results available in the literature.

Shape-based approach for solar sail trajectory optimization

The analysis of the optimal control law that steers a solar sail-based spacecraft from a given initial condition toward a final target state is typically carried out using either indirect or direct approaches. Both these methods are usually time-consuming and require good initial guesses of costates or state vector. This paper presents a procedure requiring minimum user-computer interaction to compute an approximate three-dimensional optimal trajectory using a shape-based approach. To that end, novel shaping functions are introduced to describe the time evolution of the spacecraft state vector. The optimization problem is solved using a genetic algorithm, in which a set of shape coefficients and the initial and final spacecraft position are computed while enforcing suitable constraints on the magnitude and direction of the propulsive acceleration vector. Numerical simulations of transfers from Earth to potentially hazardous asteroids show that this method provides good estimates of solar sail trajectories, which can be used as guesses for more refined direct optimization approaches.

Multivariate time series clustering and forecasting for building energy analysis: Application to weather data quality control

In recent years, several tools for building energy analysis and simulation have been developed to assist in increasing building energy performance, harvesting its computing capabilities for a reliable and accurate energy performance prediction. To perform this analysis, energy tools typically require crucial data regarding the building's surrounding environment, which is acquired from neighbouring weather stations. However, these stations often experience hardware malfunctions, resulting in either erroneous or missing data. Traditionally, these values are rectified through empirical and geostatistical methods, which, while reflecting several decades of practice, may prove to be inadequate when considering a purely data-driven approach. To this end, the present study introduces a machine learning methodology proposing the application of regression algorithms to rectify the erroneous values in datasets, and the clustering of weather stations, based on their recorded climatic conditions, to enhance the regression models. A shape-based approach for clustering time series of different climatic parameters and weather stations is pursued, using the k-medoids algorithm alongside dynamic time warping as the similarity measure. Both Artificial Neural Networks (ANN) and Support Vector Regression (SVR) models are evaluated as exemplary regression algorithms, with different sets of predictors. Mean Squared Error is used as the performance metric. A data set of different climatic parameters from southeastern Brazil was used, with air temperature being chosen as the response variable, given its importance in energy consumption. Results indicate that a machine learning approach to the problem is indeed viable. ANN slightly outperforms SVR in the prediction of the studied weather variable.

A Multilevel Road Alignment Model for Spatial-Query-by-Sketch

A sketch map represents an individual’s perception of a specific location. However, the information in sketch maps is often distorted and incomplete. Nevertheless, the main roads of a given location often exhibit considerable similarities between the sketch maps and metric maps. In this work, a shape-based approach was outlined to align roads in the sketch maps and metric maps. Specifically, the shapes of main roads were compared and analyzed quantitatively and qualitatively in three levels pertaining to an individual road, composite road, and road scene. An experiment was performed in which for eight out of nine maps sketched by our participants, accurate road maps could be obtained automatically taking as input the sketch and the metric map. The experimental results indicate that accurate matches can be obtained when the proposed road alignment approach Shape-based Spatial-Query-by-Sketch (SSQbS) is applied to incomplete or distorted roads present in sketch maps and even to roads with an inconsistent spatial relationship with the roads in the metric maps. Moreover, highly similar matches can be obtained for sketches involving fewer roads.

A hybrid shape-based image clustering using time-series analysis

Clustering of different shapes of the same object has an inordinate impact on various domains, including biometrics, medical science, biomedical signal analysis, and forecasting, for the analysis of huge volume of data into different groups. In this work, we present a novel shape-based image clustering approach using time-series analysis, to guarantee the robustness over the conventional clustering techniques. To evaluate the performance of the proposed procedure, we employed a dataset consists of various real-world irregular shaped objects. The shapes of different objects are first extracted from the entire dataset based on similar pattern using mean structural similarity index. Furthermore, we performed radical scan on the extracted shapes for converting them to one-dimensional (1D) time-series data. Finally, the time series are clustered to form subgroups using hierarchical divisive clustering approach with average linkage, and Pearson as distance metrics. A comparative study with other conventional distance metrices was also conducted. The results established the superiority of using Pearson correlation measure, which provided the maximum F1-score with exact number of shapes under a sub-cluster, while the corresponding outcomes of other approaches results in a poor and inappropriate clustering.