Thin-plate Spline Interpolation Research Articles

Research on Intelligent Prefabricated Reinforced Concrete Staircase Lifting Point Setting Method Considering Multidimensional Spatial Constraint Characteristics

Prefabricated reinforced concrete staircases (PC staircases) are prefabricated components that are widely used in prefabricated buildings and are used in large quantities. During the production and construction of a PC staircase, the lifting point setting directly affects the construction safety, construction efficiency, and construction quality. In this paper, we analyze the quality problems and safety risks in the design, production, and construction of PC staircases under the constraints of multidimensional spatial characteristics, clarify the key technical difficulties of prefabricated staircase lifting under the multidimensional spatial and temporal constraints, and analyze the factors that should be considered in the setting of lifting points. In this paper, a prefabricated staircase lifting point setting database is established and a thin-plate spline interpolation algorithm is introduced to expand it. Based on the support vector machine algorithm, the process of optimization is carried out for the kernel function scale parameter and penalty factor, and it is concluded that for every increase of two in the number of cross-validation folds, the percentage reduction in minimum RMSE is 9.4%, 17.8%, and 4.2%, respectively, the percentage increase in the optimization time is 39.7%, 61.8%, and 27.3%, respectively, and a PC staircase lifting point setup method based on the small-sample database is proposed. The number of lifting points and lifting point locations of the PC staircase satisfying the multidimensional spatial feature constraints can be obtained by inputting the five design parameters of the PC staircase, namely, the number of treads, the height of the treads, the width of the treads, the width of the staircase, and the weight of the staircase, into the lifting point setup method proposed in this paper. The reliability of the precast reinforced concrete staircase lifting point setting method proposed in this paper when considering the multidimensional spatial constraint characteristics is verified by the precast staircases in deep shafts for assembly construction at the Chongqing metro station.

Virtual reconstruction and geometric morphometric analysis of the Kocabaş hominin fossil from Turkey: Implications for taxonomy and evolutionary significance

The Kocabaş specimen comes from a travertine quarry near the homonymous village in the Denizli basin (Turkey). The specimen comprises three main fragments: portions of the right and left parietal and left and right parts of the frontal bone. The fossil was assumed to belong to the Homo erectus s.l. hypodigm by some authors, whereas others see similarities with Middle Pleistocene fossils (Broken Hill 1/Kabwe, Bodo, or Ceprano). Here, we present the first attempt to make a complete reconstruction of the missing medial portion of the frontal bone and a comprehensive geometric morphometric analysis of this bone. We restored the calotte by aligning and mirroring the three preserved fragments. Afterward, we restored the missing portion by applying the thin-plate spline interpolation algorithm of target fossils onto the reconstructed Kocabaş specimen. For the geometric morphometric analyses, we collected 80 landmarks on the frontal bone (11 osteometric points, 14 bilateral curve semilandmarks, and 41 surface semilandmarks). The comparative sample includes 21 fossils from different chronological periods and geographical areas and 30 adult modern humans from different populations. Shape analyses highlighted the presence in Kocabaş of features usually related to Middle Pleistocene Homo, such as a developed supraorbital torus associated with a relatively short frontal squama and reduced post-toral sulcus. Cluster analysis and linear discriminant analysis classification procedure suggest Kocabaş being part of the same taxonomic unit of Eurasian and African Middle Pleistocene Homo. In light of our results, we consider that attributing the Kocabaş hominin to H. erectus s.l. may be unwarranted. Results of our analyses are compatible with different evolutionary scenarios, but a more precise chronological framework is needed for a thorough discussion of the evolutionary significance of this specimen. Future work should clarify its geological age, given uncertainties regarding its stratigraphic provenance.

Human calcaneal variation relative to subsistence strategy, activity level, and footwear

Lower limb cortical and trabecular bone varies with human behavior, leading to suggestions that activity level decreases have contributed to a more gracile skeleton. Similar trends are likely present in calcaneal morphology due to its locomotor role during heel strike. Such relationships exist in calcaneal trabecular structure; however, they have yet to be investigated in external morphology. Here entire external calcaneal shape is analyzed among three human populations that vary in subsistence strategy, activity level, and footwear use (n = 93) to investigate how calcaneal morphology varies relative to these factors. Calcanei were either surface scanned or micro-CT scanned. Calcaneal external shape was analyzed using a sliding semilandmark analysis with 1,007 semilandmarks. Semilandmarks were allowed to slide along tangent vectors or planes to minimize the bending energy of the thin plate spline interpolation function relative to an updated Procrustes average. Final landmark configurations underwent a Generalized Procrustes Analysis. Shape variation of Procrustes coordinates was summarized using principal components analysis (PCA). Procrustes distances between the average calcaneus of each population were calculated, and resampling statistics run to test for significant differences. The three populations exhibit significantly different calcaneal morphologies (p<0.001 for all pairwise comparisons) and separate along the first three PCs (42.11% of variance). Hunter-gatherers have superoinferiorly taller and mediolaterally wider posterior calcanei than sedentary populations. This likely serves as an adaptation for increased load transfer through the posterior calcaneus due to more active lifestyles. This is supported further by variation among the two industrialized populations. The 19th–20thcentury industrialized population exhibits a relatively mediolaterally wider posterior calcaneus than the mid-20thcentury-born population, suggesting there has been further gracilization of the calcaneus with increases in sedentary behavior over the last century.

INCORPORATION AND RELEASE OF HAMAMELIS VIRGINIANA IN “SCAFFOLDS” PRECURSOR MATRIX: AN APPROACH WITH THE “THIN PLATE SPLINE” INTERPOLATION METHOD

In recent years, tissue engineering has been developing methodologies to potentialize the regeneration of injured tissues, such as using biomaterials to obtain scaffolds performing the controlled release of drugs. The polymers polyhydroxy butyrate (PHB) and chitosan (CHI) have been used in the production of matrices applied to scaffold production. This study aims to produce and evaluate matrices containing different proportions of PHB and CHI using the compression molding technique. These matrices can form scaffolds after drug incorporation of Hamamelis virginiana (HV). In order to predict the swelling of the matrices, the Thin Plate Spline Interpolation method (TPSIM) was used to generate three-dimensional data fitted, showing the influence of time and concentration variables on drug absorption. Results show that the percentage of CHI in the samples determines the swelling degree of the matrices. According to scanning electron microscopy analyses, increasing this polymer's quantity modifies the matrix's morphology, making it more heterogeneous. The sample with 50% by weight composition of CHI showed better-swelling results and samples loaded with HV demonstrated drug release ability. Thus, the obtained matrices have great potential to work as scaffolds and drug delivery systems, and therefore, they are promising products for application in tissue engineering.

Nolinear Static Aeroelastic Analysis and Optimization for High-Altitude Solar-Powered UAV With Large Aspect Ratio

According to the static aeroelastic characteristics of Solar-Powered UAV (SP-UAV) with large aspect ratio, this paper develops a nolinear aeroelastic analysis method which takes into account both the calculation accuracy and efficiency. Firstly, we establish the finite element model of the geometric nonlinear structure, which is verified by the static test of the whole UAV to reduce the calculation error caused by the simplified method of structure model. Then, the aerodynamic model of SP-UAV is established by using Curved Vortex Lattice (CVL), and the structure-aerodynamic coupling interpolation is realized by the Thin Plate Spline-interpolation (TPS) method, so as to complete the full static aeroelastic analysis. The analysis indicate that the calculated results of the longitudinal trim are well match the first flight condition. In particular, considering the elevator efficiency loss occurred in longitudinal trim analysis of the UAV, we design an optimization scheme to improve the efficiency of the elevator by about 15%. The simulation results show that the loss of elevator efficiency of flexible solar UAV with high aspect ratio is non-negligible, with the maximum value higher than 40% under high dynamic pressure. In actual flight, the speed of UAV must be reduced as much as possible to minimize the loss of rudder efficiency, while the elastic control method should be considered in flight control.

Fine Beam Tracking Using Spatio–Temporal Interpolation in Wireless Power Transfer Systems

The use of transmit beamforming in a radio-frequency wireless power transfer (WPT) system can improve the energy transmission efficiency by concentrating the transmit power in the angle of departure (AoD). Optimal beamforming requires information regarding the AoD or the channel between the transmitter and receiver. A previously proposed WPT system continually estimates the optimal AoD using custom-designed pilot signals, which are known as beam-steered pilot signals and are transmitted periodically at every frame. Herein, we propose a spatio–temporal interpolation technique to improve the accuracy of beam tracking for such a WPT system. Specifically, thin-plate spline interpolation is adopted in the space domain to overcome the limited angular resolution of the beam-steered pilot signals in a three-dimensional channel. In the time domain, polynomial interpolation is performed to track the changing AoD during consecutive frames. Numerical results show that the proposed technique can improve the WPT efficiency as well as the mean square error performance of the beamforming weight vector.

The Application of Fast Multipole Boundary Element Method to the Calculation of Slamming Load of Three-Dimensional Elastic Sphere

An efficient fluid-structure interaction (FSI) method is established to quickly and accurately calculate the fluid load of three-dimensional (3D) elastic structure in the process of water slamming. In this method, the boundary element method (BEM) and computational structural dynamics (CSD) are coupled by thin plate spline (TPS) interpolation method and flow field reconstruction. In order to improve the calculation efficiency, the fast multipole algorithm is introduced into the BEM, the finite element mesh of the wetted part of the structure is directly used as the flow field boundary, and the structural dynamic response is analyzed by the direct integration method of state equation based on modal superposition. The numerical results are compared with the results of Nisewanger’s sphere water entry test and the existing literature, which proves the accuracy of the numerical calculation method established in this paper. The effects of time-domain iteration step size, mesh size, slamming velocity, fluid density and structural elastic effect on water slamming load are studied. The results show that the slamming velocity and fluid density have a great influence on the simulation results; the iteration step size has little influence on the accuracy of simulation calculation, and the mesh size has a certain influence on the accuracy of simulation calculation; elastic effect reduces the peak value of slamming load, considering elastic effect is necessary for accurate calculation of slamming load.

Spatial Distribution of Multi-Fractal Scaling Behaviours of Atmospheric XCO2 Concentration Time Series during 2010-2018 over China.

Exploring the spatial distribution of the multi-fractal scaling behaviours in atmospheric CO2 concentration time series is useful for understanding the dynamic mechanisms of carbon emission and absorption. In this work, we utilise a well-established multi-fractal detrended fluctuation analysis to examine the multi-fractal scaling behaviour of a column-averaged dry-air mole fraction of carbon dioxide (XCO2) concentration time series over China, and portray the spatial distribution of the multi-fractal scaling behaviour. As XCO2 data values from the Greenhouse Gases Observing Satellite (GOSAT) are insufficient, a spatio-temporal thin plate spline interpolation method is applied. The results show that XCO2 concentration records over almost all of China exhibit a multi-fractal nature. Two types of multi-fractal sources are detected. One is long-range correlations, and the other is both long-range correlations and a broad probability density function; these are mainly distributed in southern and northern China, respectively. The atmospheric temperature and carbon emission/absorption are two possible external factors influencing the multi-fractality of the atmospheric XCO2 concentration. Highlight: (1) An XCO2 concentration interpolation is conducted using a spatio-temporal thin plate spline method. (2) The spatial distribution of the multi-fractality of XCO2 concentration over China is shown. (3) Multi-fractal sources and two external factors affecting multi-fractality are analysed.

A Knuckle‐Walking Signal in the Trabecular Architecture of the African Ape Scaphoid

African ape (Panand Gorilla) carpals have few diagnostic features in their external morphology reflecting knuckle‐walking hand postures, and whether the internal trabecular architecture of their carpals yields a functional signal for knuckle‐walking is unclear. Here we perform a high‐density, multiple‐VOI analysis of trabecular architecture in the scaphoid of knuckle‐walking African apes and non‐knuckle‐walkers (Pongo, Macaca,and Papio). We predict that (1) Gorilla, the taxon with largest body mass, will have the highest trabecular thickness (Tb.Th) and trabecular spacing (Tb.Sp) because Tb.Th and Tb.Sp have been shown to be correlated with body size, (2) bone volume fraction (BV/TV) will be higher in habitually terrestrial taxa than in arboreal taxa, as the forelimb is thought to experience relatively high compressive loads during terrestrial locomotion, (3) Pongo will have the lowest degree of anisotropy (DA) as they engage in variable locomotor behaviors, and (4) pattern of DA distribution will differ between knuckle‐walking and non‐knuckle‐walking taxa, as the consistency and direction of wrist joint loading likely differs among primates with different quadrupedal hand postures.Fifty‐four scaphoids were scanned using high‐resolution µCT (voxel range: 48‐27 μm). Surface models were created from image data and then subjected to a weighted spherical harmonic analysis. Volumes of interest (VOIs) were manually placed into a surface model of the average scaphoid, and then warped to individual specimens using the thin plate spline interpolation function. Trabecular properties were calculated using the BoneJ plugin for ImageJ and MATLAB, and variation in distribution of trabecular parameters among taxa was summarized using a principal component analysis (PCA). Parameter values among species were compared with non‐parametric MANOVAs using a randomized residual permutation procedure, and PC scores were compared using Kruskal‐Wallis ANOVAs. The parameter distribution within each bone was visualized by comparing species‐average color maps of average parameter values.As predicted, Tb.Th and Tb.Sp are greatest in Gorilla, indicating that these parameters are related in part to body size. In contrast, results indicate that BV/TV and DA magnitudes do not follow predictions. Specifically, habitually terrestrial taxa do not have significantly higher BV/TV than arboreal taxa, and taxa that engage in more variable locomotor behaviors (i.e., Pongo) do not have the lowest values of DA. Finally, results indicate that knuckle‐walking African apes can be distinguished from other taxa studied here by pattern of DA distribution, and these differences appear to reflect differences in habitual hand postures and locomotor modes. If this pattern is unique to knuckle‐walking apes among hominoids, and is also identified in the scaphoid of fossil hominoids, then it may be used to indicate whether fossil taxa were habitual knuckle‐walkers.

The potential and limits of Thin-Plate Spline retrodeformation on asymmetrical objects:simulation of taphonomic deformations andapplication on a fossil sample of limb long bones

In this study, we suggest a method adapted to the retrodeformation of asymmetrical objects – such as limb bones – by quantitatively estimating the effectiveness of the Thin-Plate Splines (TPS) interpolation function as a retrodeformation tool. To do so, taphonomic deformations were first simulated on a single horse femur. The original bone was then used as a reference in order to drive the retrodeformation using anatomical landmarks. This approach, based on a single bone, enabled us to evaluate the performance of the retrodeformation procedure. Then, the same approach was performed on a sample of rhino femora but using a different specimen (from the same species) as the reference in order to account for morphological variation. We also added sliding semi-landmarks on anatomical curves. Finally, retrodeformation was applied on a sample of sauropodomorph dinosaur femora by building a mean shape based on several well-preserved fossil specimens. Results show that entirely flattened and stretched bones are more efficiently retrodeformed than bent and twisted bones. Introduction of morphological variation increased the efficiency of retrodeformation for bent and locally stretched bones. The application to the sample of fossils produced similar results but also highlighted the difficulty of retrodeforming bones with a combination of different deformations. TPS interpolation is an efficient tool of retrodeformation for asymmetrical objects, especially for bones with only one affine deformation such as flattening or stretching. Finding a threshold of landmark number to use for this process would be the next step because it would allow us to ensure the quality of retrodeformation while keeping available a reasonable number of landmarks in order to perform shape analysis on retrodeformed bones. Twisted and bent fossils are frequently discovered and we suggest that these kinds of deformations should be studied with caution, especially when combined with other types of taphonomic distortions.

Progressive Morphological Filtering Algorithm Combined with Thin-Plate Spline Interpolation for Airborne LiDAR

Progressive Morphological Filtering Algorithm Combined with Thin-Plate Spline Interpolation for Airborne LiDAR

Two-dimensional prediction of the interface of geological formations: A comparative study

The location of the interface of geological formations is an important piece of information for tunneling construction. As site investigation data are usually limited, the uncertainties in locating geological interfaces for the sections between boreholes can be large and challenging to estimate. A suitable geostatistical method is thus needed for spatial prediction of the geological interfaces. In this paper, the performance of three commonly used spatial prediction methods, namely the multivariate adaptive spline regression (MARS), conditional random field (CRF) method, and thin-plate spline interpolation (TPSI) methods, are evaluated for two-dimensional cases using the boreholes data from three sites in Singapore. The prediction accuracies, patterns of the predicted surfaces, and prediction uncertainties obtained from the three methods are compared. A zonation is also proposed to improve the prediction accuracy of the MARS method. The results indicate that the MARS method can show the spatial trend of the geological interface more clearly than the other two methods. The TPSI method produces undesirable oscillations of the surface of geological interfaces and the CRF method may underestimate the extreme values of the geological interface elevations. In general, the prediction accuracy of the MARS method is similar to that of the CRF method, but higher than that of the TPSI method. For cases with very limited data in geologically complex areas, the MARS may have larger errors than the CRF method. However, the accuracy of the former can be significantly improved if a reasonable zonation is performed.

Medical image alignment based on landmark- and approximate contour-matching.

Purpose: Our goal is to propose a landmark- and contour-matching (LCM) registration method that uses both landmark information and approximate point correspondences to boost the similarity between image pairs with sparse landmark information. Approach: A model for registering two-dimensional (2D) medical images with landmark information and contour-approximating landmarks was proposed. The model was also extended to accommodate the registration of three-dimensional (3D) cardiac images. We validated the LCM method on 2D hand x-rays and 3D porcine cardiac magnetic resonance images. The following metrics were used to assess the quality of specific aspects of the registered images: Dice similarity coefficient for the overall image overlap, target registration error for pointwise correspondence, and interior angle for local curvature. Results: Target registrations were reduced from 27.12 to 0.01mm post-LCM registration. Implementing the proposed algorithm also led to a 112% average improvement in image similarity in terms of Dice coefficients. In addition, interior angle measurements indicate that the proposed method preserved the local curvature at major reference landmarks and mitigated the appearance of deformities in the registered images. Conclusions: The proposed method addressed several issues associated with purely landmark-based techniques, such as iterative closest point registration and thin plate spline interpolation. Furthermore, it provided accurate registration results even in the presence of landmark localization errors.

The regression detectability index RDI for mammography images of breast phantoms with calcification-like objects and anatomical background

Currently, quality assurance measurements in mammography are performed on unprocessed images. For diagnosis, however, radiologists are provided with processed images. This image processing is optimised for images of human anatomy and therefore does not always perform satisfactorily with technical phantoms. To overcome this problem, it may be possible to use anthropomorphic phantoms reflecting the anatomic structure of the human breast in place of technical phantoms when carrying out task-specific quality assessment using model observers. However, the use of model observers is hampered by the fact that a large number of images needs to be acquired. A recently published novel observer called the regression detectability index (RDI) needs significantly fewer images, but requires the background of the images to be flat. Therefore, to be able to apply the RDI to images of anthropomorphic phantoms, the anatomic background needs to be removed. For this, a procedure in which the anatomical structures are fitted by thin plate spline (TPS) interpolation has been developed. When the object to be detected is small, such as a calcification-like lesion, it is shown that the anatomic background can be removed successfully by subtracting the TPS interpolation, which makes the background-free image accessible to the RDI. We have compared the detectability obtained by the RDI with TPS background subtraction to results of the channelized Hotelling observer (CHO) and human observers. With the RDI, results for the detectability can be obtained using 75% fewer images compared to the CHO, while the same uncertainty of is achieved. Furthermore, the correlation of (RDI) with the results of human observers is at least as good as that of (CHO) with human observers.

Design and Optimization of Scored Tablets with Concave Surface and Application of Bayesian Estimation for Solving Scaleup Problem.

From the viewpoint of self-medication, it is valuable to develop patient-friendly scored tablets that possess dividing uniformity. In this context, we attempted to optimize the preparation conditions for a tablet with a unique shape, such as a concavely curved scored tablet (CCST). Employing a design of experiment and a response surface method incorporating a thin-plate spline interpolation, and a bootstrap resampling technique, the optimal preparation conditions for CCST were successfully developed. To make it possible to scaleup the optimal solution estimated on a trial-scale, a Bayesian estimation was applied. Credible ranges of critical responses in large-scale manufacturing were estimated as a posterior probability from the trial-scale experiment as a prior probability. In terms of the large-scale manufacturing, the possibility of solving the scaleup problem was suggested using Bayesian estimation. Furthermore, a simulation study using a finite element method revealed that strong tensile stresses generated along the tip of the score line in CCST when an outer force was applied to the back surface of CCST. An advantage in dividing uniformity is indicated by the unique shape of CCST.

Investigation of age-related facial variation among Angelman syndrome patients

Angelman syndrome (AS) is one of the common genetic disorders that could emerge either from a 15q11–q13 deletion or paternal uniparental disomy (UPD) or imprinting or UBE3A mutations. AS comes with various behavioral and phenotypic variability, but the acquisition of subjects for experiment and automating the landmarking process to characterize facial morphology for Angelman syndrome variation investigation are common challenges. By automatically detecting and annotating subject faces, we collected 83 landmarks and 10 anthropometric linear distances were measured from 17 selected anatomical landmarks to account for shape variability. Statistical analyses were performed on the extracted data to investigate facial variation in each age group. There is a correspondence in the results achieved by relative warp (RW) of the principal component (PC) and the thin-plate spline (TPS) interpolation. The group is highly discriminated and the pattern of shape variability is higher in children than other groups when judged by the anthropometric measurement and principal component.

Development of high spatial resolution weather data using daily meteorological observations over Indian region

Finer spatial resolution interpolated weather data is essential to enable utilization of satellite-based images in studies related to crop growth dynamics, etc. Satellite data are available daily at 1 × 1 km or at the most within 5 × 5 km grid. To make the weather data timely available at the same spatial scale, the procedure has been developed to generate the spatially interpolated weather data product over India. Daily weather data (minimum & maximum temperature and rainfall) available at point scale on India Meteorology Department web site have been used in this study. A semi-automated user interactive Graphical User Interface (GUI) has been developed which quality checks the temperature data sets by filling the missing data sets as well as providing a platform to correct erroneous data which have been identified using statistical methods taking spatial as well as temporal incompatibility into account. Daily spatially interpolated product is generated in image form using thin plate spline interpolation technique that uses the quality checked weather data as well as elevation information from CARTODEM data in order to account for effect of elevation on temperature. The validation was performed using “Jack-knife testing method” for three different seasons i.e., monsoon, summer and winter. The mean absolute errors for decadal averaged products were found to vary within 1.2-1.5 °C for maximum temperature, 1.1-1.7 °C for minimum temperature, 1.0-7.0 mm for rainfall considering all seasons with higher error observed in monsoon for maximum temperature and rainfall and in winter for minimum temperature. It was found that errors were close to 1 °C for stations with elevation less than 550 m whereas in central portion of India, mean absolute errors were found to be less than 1 °C.

An Adaptive Surface Interpolation Filter Using Cloth Simulation and Relief Amplitude for Airborne Laser Scanning Data

Separating point clouds into ground and nonground points is an essential step in the processing of airborne laser scanning (ALS) data for various applications. Interpolation-based filtering algorithms have been commonly used for filtering ALS point cloud data. However, most conventional interpolation-based algorithms have exhibited a drawback in terms of retaining abrupt terrain characteristics, resulting in poor algorithmic precision in these regions. To overcome this drawback, this paper proposes an improved adaptive surface interpolation filter with a multilevel hierarchy by using a cloth simulation and relief amplitude. This method uses three hierarchy levels of provisional digital elevation model (DEM) raster surfaces with thin plate spline (TPS) interpolation to separate ground points from unclassified points based on adaptive residual thresholds. A cloth simulation algorithm is adopted to generate sufficient effective initial ground seeds for constructing topographic surfaces with high quality. Residual thresholds are adaptively constructed by the relief amplitude of the examined area to capture complex landscape characteristics during the classification process. Fifteen samples from the International Society for Photogrammetry and Remote Sensing (ISPRS) commission are used to assess the performance of the proposed algorithm. The experimental results indicate that the proposed method can produce satisfying results in both flat areas and steep areas. In a comparison with other approaches, this method demonstrates its superior performance in terms of filtering results with the lowest omission error rate; in particular, the proposed approach retains discontinuous terrain features with steep slopes and terraces.

Multi-objective design optimization of additively manufactured lattice structures for improved energy absorption performance

This paper aims to improve the energy absorption performance of stiffness-optimized lattice structures by utilizing a multi-objective surrogate-based size optimization that considers the additive manufacturing (AM) constraints such as the minimum printable size. A truss optimization is first utilized at the unit cell level under static compressive loads for stiffness maximization and two optimized lattice configurations called the Face-Body Centered Cubic (FBCC) lattice and the Octet Cubic (OC) are obtained. A multi-objective size optimization process is then carried out to improve the energy absorption capabilities of those lattice designs using non-linear compression simulations with Nylon12 material to be fabricated by the Multi Jet Fusion (MJF) AM process. Thin plate spline (TPS) interpolation method is found to produce very high accuracy as the surrogate model to predict the highly nonlinear response surfaces of energy absorption objectives in the optimization. Compared to the lattice designs with uniform strut diameters, by using the optimization process, the maximum energy absorption efficiency ( EAEm) and the crush stress efficiency ( CSE) of the OC lattice design are further improved up to 33% and 37%, respectively. The FBCC lattice design is also found to have superior EAEm performance compared to the existing lattice types considered for fabricating by the MJF process in the literature.

Interpolation Algorithm for Motion Vector Field of CTA Image and Accelerated Implementation Based on Uniform Grid and Multi-level B-spline

In order to solve the problems of slow operation speed and low registration accuracy of thin plate spline (TPS) interpolation method for motion vector field in coronary computed tomography angiography (CTA), a multi-level B-spline interpolation method (MBS) with uniform grid is proposed. On the one hand, the interpolation method used local B-spline to refine the sparse mesh layer by layer in a multiscale way to improve the accuracy of registration. On the other hand, it used the splitting matrix method to interpolate the motion vector field, greatly reducing the operation time of interpolation. The experimental results show that the proposed method can be used for CTA image registration efficiently.