Thin-plate Spline Research Articles

Differentiation of face and auricular shape resulting from diabetes and hypertension in the elderly

The prevalence global of noncommunicable chronic diseases as diabetes and hypertension worldwide has been disregarded until recently by policy makers. In addition, these diseases have growing with the aging of the population. This study sought to identify changes in face shape from the frontal and side views in elderly people diagnosed with diabetes and hypertension. 205 individuals were studied, with 60 years or more, from both sexes, with different ethnicities, and cognition intact. With a digital camera, photos were taken of the front and side and based on these images landmarks for measurement were determined. For statistical analysis, ANOVA, Canonical Variates Analysis, Mahalanobis distance and Thin-Plate Spline were realized. Given sexual dimorphism, the sexes were analyzed separately. From the ANOVA, significant differences (p<0.01) for individuals with diabetes, hypertension, and patients with both or neither of the diseases were observed. The groups were separated by the Canonical Variates and Mahalanobis distance and independent of edentulism, sex or ethnicity. A morphofacial characteristics for the front and side views (especially in the ear region) that identified individuals with these chronic diseases was observed. This methodology can contribute in a specific manner to the identification of at risk populations and help to promote preventative measures for these conditions.

Microperimetry Hill of Vision and Volumetric Measures of Retinal Sensitivity.

PurposeMean retinal sensitivity is the main output measure used in microperimetry. It is, however, of limited use in patients with poor vision because averaging is weighted toward zero in those with significant scotomas creating an artificial floor effect. In contrast, volumetric measures avoid these issues and are displayed graphically as a hill of vision.MethodsAn open-source program was created to manipulate raw sensitivity threshold data files obtained from MAIA microperimetry. Thin plate spline interpolated heat maps and three-dimensional hill of vision plots with an associated volume were generated. Retrospective analyses of microperimetry volumes were undertaken in patients with a range of retinal diseases to assess the qualitative benefits of three-dimensional visualization and volumetric measures. Simulated pathology was applied to radial grid patterns to investigate the performance of volumetric sensitivity in nonuniform grids.ResultsVolumetric analyses from microperimetry in RPGR-related retinitis pigmentosa, choroideremia, Stargardt disease, and age-related macular degeneration were analyzed. In simulated nonuniform testing grids, volumetric sensitivity was able to detect differences in retinal sensitivity where mean sensitivity could not.ConclusionsVolumetric measures do not suffer from averaging issues and demonstrate superior performance in nonuniform testing grids. Additionally, volume measures enable detection of localized retinal sensitivity changes that might otherwise be undetectable in a mean change.Translational RelevanceAs microperimetry has become an outcome measure in several gene-therapy clinical trials, three-dimensional visualization and volumetric sensitivity enables a complementary analysis of baseline disease characteristics and subsequent response to treatment, both as a signal of safety and efficacy.

Determining Shell Shape Differences in the Horse Mussels Modiolus philippinarum (Hanley 1843) and Modiolus modulaides (Röding 1798) by Morphometric Analysis

In the present study, shell morphological variations of the horse mussel species Modiolus philippinarum and Modiolus modulaides have been explored by the means of linear morphometrics for size and landmark-based geometric morphometrics for shape. Linear morphometrics revealed significant differences in shell length [t(298) = –6.29, p = 1.08 x 10–9), shell height [t(298) = 10.60, p = 1.74 x 10–22], shell width [t(298) = 2.13, p = 0.034], PAMS or posterior adductor muscle scar length [t(298) = 2.16, p = 0.032], hinge length [t(298) = 2.26, p = 0.025], umbo length [t(298) = –5.54, p = 6.73 x 10–8], and anterior length [t(298) = –5.59, p = 5.16 x 10–8] between species. However, upon the use of these morphometric characters to develop an index that will easily discriminate the species, only the relationships of shell length vs. shell width and hinge length were significant (ANCOVA, width/ length F = 18.45, p = 0.0001; hinge/length F = 7.76, p = 0.005) but an invariably high overlap between species was observed resulting in a 23.3% misclassification rate. Contrastingly, the analysis of shape variables through landmark-based geometric morphometrics revealed significant differences in shell shape between the two species [MANOVA, Wilk’s λ = 0.01, F(24,335) = 941.4, p = 3.47 x 10–291] with a 0.0% misclassification rate. Generally, M. modulaides were found to have an elongated shell while M. philippinarum was compressed and convex. Also, visualization through thin-plate spline expansion factor plots revealed that variability in shell shape between the species occurred mostly in the posterior and ventral region of the shell and was attributed to the species ecology. The findings of the present study encourage the use of geometric morphometric methods in species delineation, especially when ecotypes or sibling species are present.

Thickness accuracy of virtually designed patient-specific implants for large neurocranial defects.

The combination of computer‐aided design (CAD) techniques based on computed tomography (CT) data to generate patient‐specific implants is in use for decades. However, persisting disadvantages are complicated design procedures and rigid reconstruction protocols, for example, for tailored implants mimicking the patient‐specific thickness distribution of missing cranial bone. In this study we used two different approaches, CAD‐ versus thin‐plate spline (TPS)‐based implants, to reconstruct extensive unilateral and bilateral cranial defects in three clinical cases. We used CT data of three complete human crania that were virtually damaged according to the missing regions in the clinical cases. In total, we carried out 132 virtual reconstructions and quantified accuracy from the original to the generated implant and deviations in the resulting implant thickness as root‐mean‐square error (RMSE). Reconstructions using TPS showed an RMSE of 0.08–0.18 mm in relation to geometric accuracy. CAD‐based implants showed an RMSE of 0.50–1.25 mm. RMSE in relation to implant thickness was between 0.63 and 0.70 mm (TPS) while values for CAD‐based implants were significantly higher (0.63–1.67 mm). While both approaches provide implants showing a high accuracy, the TPS‐based approach additionally provides implants that accurately reproduce the patient‐specific thickness distribution of the affected cranial region.

Nonlinear hydrodynamics of freely floating symmetric bodies in waves by three-dimensional fully nonlinear potential-flow numerical wave tank

This study estimated the nonlinear hydrodynamic performance of freely floating structures in nonlinear water waves. For this, a three-dimensional, fully nonlinear numerical wave tank (NWT) was developed based on potential theory and the boundary element method (BEM). The fully nonlinear NWT evaluates the hydrodynamic force acting on the instantaneous body position and free-surface elevation based on the mixed Eulerian and Lagrangian (MEL) method and acceleration-potential approach. The instantaneous nonlinear free surface was traced at each time step, and the far-field outgoing wave condition was satisfied by placing an artificial free-surface damping zone. In addition, the least square gradient reconstruction method, thin-plate spline method, and modified inverse distance weighting method were adopted to re-grid the calculation nodes and evaluate the spatial derivatives of the physical quantities robustly. The developed NWT was used to evaluate the first-order and second-order motion RAOs and excitation forces of a freely floating vertical cylinder. The results were compared systematically with previously published results using perturbation theory. Moreover, the heave-to-pitch Mathieu-instability phenomena on a deep-draft floating cylinder were demonstrated by the fully nonlinear NWT simulations. The results agreed well with the corresponding experimental observations.

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.

RBF Moment computation and meshless cubature on general polygonal regions

We obtain analytical formulas for the computation of integrals (moments) of all the most common Radial Basis Functions (usually shortened as RBFs) on polygonal regions that may be nonconvex or even multiply connected. With RBFs of finite regularity, such as Thin-Plate Splines, Wendland functions and Radial Powers, our Matlab codes, based on standard linear solvers for the corresponding moment matching systems, provide cubature rules that are reasonably accurate and numerically stable.

Deep learning for registration of region of interest in consecutive wireless capsule endoscopy frames

Background and objective: Functional gastrointestinal disorders (FGIDs) are reported as worldwide gastrointestinal (GI) diseases. GI motility assessment can assist the diagnosis of patients with intestine motility dysfunction. Wireless capsule endoscopy (WCE) can acquire images in the gastrointestinal (GI) tract including the small intestine where other conventional endoscopes cannot penetrate, and WCE images can reveal GI motility. To generally analyze WCE frames, the high-precision registration of consecutive WCE frames is an absolute necessity. It is difficult and meaningless to register entire WCE frames on a pixel level due to the unpredictable and massive non-rigid deformation between consecutive frames, the low quality of imaging and the complex intestinal environment. Thus, the registration of region of interest (ROI) functioning in a feature level has more significance than entire frame registration.Methods: In this paper we present Timecylce-WCE, an end-to-end automatic registration approach of ROIs on WCE images. The clinicians can determine a ROI by drawing a bounding box in any WCE frame to be registered. This proposed approach is based on a deep-learning model of time-consistency in recurrent-registering, skip-registering and self-registering cycle, and it is fully unsupervised without any label. We incorporate the global correlation map with the local correlation map in matching the features, and a novel overall loss function is designed to enable the convergence of the model. As the output, a thin-plate spline (TPS) transformed region in the template frame is highly aligned with the query ROI in a finer-grained level. To the best of our knowledge this is the first time that a deep-learning-based registration method is proposed for WCE imaging motion.Results: To highlight the effectiveness of the proposed approach, our proposed method is compared with the existing non-deep-learning methods and tested in a validation dataset with labeled matching points. The presented method resulted in the best PCK@10 (Percentage of Correct Key-points, i.e., the predicted and the true joint is within the threshold - 10 pixels) of 66.49%. We also demonstrate that variants of design improved registration accuracy.Conclusions: From the experimental analysis, it is clear that our proposed method outperforms the other existing methods. This lays the groundwork for subsequent studies, such as GI motility assessment, and WCE image synthesis.

Higher-order diffraction forces on vertical circular cylinders by using a three-dimensional fully-nonlinear potential numerical wave tank

The aim of this study is to evaluate higher-order diffraction forces on vertical circular cylinders by using an author-developed three-dimensional fully-nonlinear numerical wave tank (NWT). The nonlinear NWT is based on the potential theory, boundary element method, and mixed Eulerian Lagrangian (MEL) approach. The acceleration-potential method is used to calculate the hydrodynamic pressure accurately. The artificial damping zone is adopted to prevent reflected waves from bodies and side walls. The least square gradient reconstruction method and the thin plate spline method are applied to evaluate the spatial derivatives of physical quantities and updated locations of interpolation points. The third-order stokes monochromatic or bichromatic waves are inputted as incident-wave boundary condition. From the nonlinear NWT simulations with FFT, first-order, second-order, and third-order diffraction forces are simultaneously calculated and the results are systematically compared with published experimental and perturbation-based numerical results. The sensitivity of the nonlinear NWT results with the respective orders of Stokes monochromatic or bichromatic input waves is also investigated. The increase of third-order sum-frequency force in shallow water long wave is noticed.

Transporting Deformations of Face Emotions in the Shape Spaces: A Comparison of Different Approaches

Studying the changes of shape is a common concern in many scientific fields. We address here two problems: (1) quantifying the deformation between two given shapes and (2) transporting this deformation to morph a third shape. These operations can be done with or without point correspondence, depending on the availability of a surface matching algorithm, and on the type of mathematical procedure adopted. In computer vision, the re-targeting of emotions mapped on faces is a common application. We contrast here four different methods used for transporting the deformation toward a target once it was estimated upon the matching of two shapes. These methods come from very different fields such as computational anatomy, computer vision and biology. We used the large diffeomorphic deformation metric mapping and thin plate spline, in order to estimate deformations in a deformational trajectory of a human face experiencing different emotions. Then we use naive transport (NT), linear shift (LS), direct transport (DT) and fanning scheme (FS) to transport the estimated deformations toward four alien faces constituted by 240 homologous points and identifying a triangulation structure of 416 triangles. We used both local and global criteria for evaluating the performance of the 4 methods, e.g., the maintenance of the original deformation. We found DT, LS and FS very effective in recovering the original deformation while NT fails under several aspects in transporting the shape change. As the best method may differ depending on the application, we recommend carefully testing different methods in order to choose the best one for any specific application.

Toward Realistic Virtual Try-on Through Landmark Guided Shape Matching

Image-based virtual try-on aims to synthesize the customer image with an in-shop clothes image to acquire seamless and natural try-on results, which have attracted increasing attentions. The main procedures of image-based virtual try-on usually consist of clothes image generation and try-on image synthesis, whereas prior arts cannot guarantee satisfying clothes results when facing large geometric changes and complex clothes patterns, which further deteriorates the afterwards try-on results. To address this issue, we propose a novel virtual try-on network based on landmark-guided shape matching (LM-VTON). Specifically, the clothes image generation progressively learns the warped clothes and refined clothes in an end-to-end manner, where we introduce a landmark-based constraint in Thin-Plate Spline (TPS) warping to inject finer deformation constraints around the clothes. The try-on process synthesizes the warped clothes with personal characteristics via a semantic indicator. Qualitative and quantitative experiments on two public datasets validate the superiority of the proposed method, especially for challenging cases such as large geometric changes and complex clothes patterns. Code will be available at https://github.com/lgqfhwy/LM-VTON.

FontRL: Chinese Font Synthesis via Deep Reinforcement Learning

Automatic generation of Chinese fonts is a valuable but challenging task in areas of AI and Computer Graphics, mainly due to the huge amount of Chinese characters and their complex glyph structures. In this paper, we propose FontRL, a novel method for Chinese font synthesis by using deep reinforcement learning. Specifically, we first train a deep reinforcement learning model to obtain the Thin-Plate Spline (TPS) transformation that is able to modify the reference stroke skeleton in a mean font style into the skeleton of a required style for each stroke of every unseen Chinese character. Afterwards, we utilize a CNN model to predict the location and scale information of these strokes, and then assemble them to get the skeleton of the corresponding character. Finally, we convert each synthesized character skeleton into the glyph image via an image-to-image translation model. Both quantitative and qualitative experimental results demonstrate the superiority of the proposed FontRL compared to the state of the art. Our code is available at https://github.com/lsflyt-pku/FontRL.

Elemental composition of biochars is affected by methods used for its determination

Ultimate analysis, energy dispersive X-ray spectroscopy (EDX), and X-ray photoelectron spectroscopy (XPS) are widely used methods for the determination of elemental composition of biomaterials such as biochar. However, models that describe the relationship in elemental composition between ultimate and spectroscopic methods are lacking. Elemental composition of biochars determined using ultimate analysis, EDX, and XPS methods was used to develop relationships among these methods using linear regression and generalized additive modelling. The relationships were evaluated using min/max accuracy and cross-validation. Based on Akaike information criterion and generalized cross-validation scores, the generalized additive model with a thin plate spline (TPS) best described the relationships. Model performance significantly improved by adding a feedstock-dependent grouping variable. Elemental carbon concentration determined by the different methods was significantly related (R2 = 0.82−0.88) by the TPS. Although not detected by EDX, nitrogen concentration was significantly related by TPS (R2 = 0.77) between the ultimate and XPS methods. For oxygen concentration, a strongly significant relationship (R2 = 0.83−0.86) was found between the ultimate and both spectroscopic methods, but a weak one (R2 < 0.54) between the XPS and EDX methods. Min/max accuracy, reaching 80 % and above during testing, confirmed that the best-fit models would predict carbon, nitrogen and oxygen concentrations with small variations for several biochars. We conclude that the elemental composition of biochars is affected by the method used for its determination and the generalized additive models developed can be used to calibrate the elemental composition analyzed using different methods.

A linked geomorphological and geophysical modelling methodology applied to an active landslide

Moisture-induced landslides are a global geohazard; mitigating the risk posed by landslides requires an understanding of the hydrological and geological conditions present within a given slope. Recently, numerous geophysical studies have been attempted to characterise slow-moving landslides, with an emphasis on developing geoelectrical methods as a hydrological monitoring tool. However, landslides pose specific challenges for processing geoelectrical data in long-term monitoring contexts as the sensor arrays can move with slope movements. Here we present an approach for processing long-term (over 8 years) geoelectrical monitoring data from an active slow-moving landslide, Hollin Hill, situated in Lias rocks in the southern Howardian Hills, UK. These slope movements distorted the initial setup of the monitoring array and need to be incorporated into a time-lapse resistivity processing workflow to avoid imaging artefacts. We retrospectively sourced seven digital terrain models to inform the topography of our imaging volumes, which were acquired by either Unmanned Aerial Vehicle (UAV)-based photogrammetry or terrestrial laser ranging systems. An irregular grid of wooden pegs was periodically surveyed with a global position system, from which distortions to the terrain model and electrode positions can be modelled with thin plate splines. In order to effectively model the time-series electrical resistivity images, a baseline constraint is applied within the inversion scheme; the result of the study is a time-lapse series of resistivity volumes which also incorporate slope movements. The workflow presented here should be adaptable for other studies focussed on geophysical/geotechnical monitoring of unstable slopes.

A Multimethod Analysis for Average Annual Precipitation Mapping in the Khorasan Razavi Province (Northeastern Iran)

The spatial distribution of precipitation is one of the most important climatic variables used in geographic and environmental studies. However, when there is a lack of full coverage of meteorological stations, precipitation estimations are necessary to interpolate precipitation for larger areas. The purpose of this research was to find the best interpolation method for precipitation mapping in the partly densely populated Khorasan Razavi province of northeastern Iran. To achieve this, we compared five methods by applying average precipitation data from 97 rain gauge stations in that province for a period of 20 years (1994–2014): Inverse Distance Weighting, Radial Basis Functions (Completely Regularized Spline, Spline with Tension, Multiquadric, Inverse Multiquadric, Thin Plate Spline), Kriging (Simple, Ordinary, Universal), Co-Kriging (Simple, Ordinary, Universal) with an auxiliary elevation parameter, and non-linear Regression. Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the Coefficient of Determination (R2) were used to determine the best-performing method of precipitation interpolation. Our study shows that Ordinary Co-Kriging with an auxiliary elevation parameter was the best method for determining the distribution of annual precipitation for this region, showing the highest coefficient of determination of 0.46% between estimated and observed values. Therefore, the application of this method of precipitation mapping would form a mandatory base for regional planning and policy making in the arid to semi-arid Khorasan Razavi province during the future.

The Use of tpsDig in Re-Describing Morphometry of Barbodes binotatus Caught in Java Island, Indonesia

Barbodes binotatus is a group of freshwater fish and this species is an endemic and most dominant category of freshwater species in Indonesia. Morphological examinations at the level of intraspecific populations by involving extensive sampling localities have never been conducted before. Morphological characteristics through truss morphometry analysis of body shape can be used to analyze shape changes during growth, discriminate genera or species as well as identify good quality of population for fish broodstock. This aims of research were to determine the relationship between fluctuating asymmetry and morphological character of B. binotatus across different regions from Java. A total of 650 samples were analyzed and collected from a total of 24 sampling sites around Java Island. Individual specimens for each population were analyzed using thin plate spline (tpsDig) method with a total of 14 anatomical landmarks. The result of this research inform that PCA analysis showed highly significant different of each population. Research with genetic approach is needed to determine population groupings across distribution area.

Which spatial interpolators I should use? A case study applying to marine species

Species are spread in space, whereas sampling is sparse. Thus, to describe and map along environmental gradients, it is necessary to interpolate the species abundance. Considering the plethora of valid methods, the researcher gets easily puzzled to choose the most appropriate interpolation approach with reference to the ecological question being asked.We propose a procedure to select among alternative spatial distribution models and we illustrate it with 175 marine species distributions (35 species * 5 years). In a first step, the distribution of the variance explained by the predictive model (VEcv) given by 10-fold cross validation is estimated for each interpolation method. When the inter-quartile range of the VEcv distribution of the different methods overlap, the selection passes to a second step, using 11 measures belonging to three criteria: 1) error based measures, 2) spatial equivalence measures (center of gravity, inertia, isotropy and index of aggregation) and 3) measures based on the data integrity after interpolation, for example the percentage of area over the maximum sampled data.We applied our approach to marine species sampled using either stratified random survey (trawl) or systematic survey (acoustic). We found that 87% of all species distributions had overlapping VEcv and thus passed the first selection. In the second selection step, the best method varied with species and year, although general additive model (GAM), Thin Plate Spline (TPS), Universal Kriging (UKr) and Random Forest (Rfor) performed better for the trawl data and TPS, Ordinary Kriging (OKri) and UKr for the acoustic data. Further, the results differed within methods (e.g. kriging neighborhood and type of kriging) and small modifications on the specifications can have a large impact on the surfaces produced.The proposed approach 1) is accessible and intuitive, and does not require any complex software or sophisticated methodology; 2) shows exactly in what aspects each interpolation model is prevalent over the others and permits to make a decision accordingly to the objectives of the study; 3) takes into account different criteria to evaluate each, properties of an interpolation method; 4) is universal and does not depend on the method used or the data characteristics. A detailed review on the subject is also included.

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.

Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system

In the present paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the solution of pattern formation in nonlinear reaction-diffusion systems. Firstly, we obtain a time discrete scheme by approximating the time derivative via a finite difference formula, then we use the SMRPI approach to approximate the spatial derivatives. This method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. In the current work, the thin plate splines (TPS) are used as the basis functions and in order to eliminate the nonlinearity, a simple predictor-corrector (P-C) scheme is performed. The effect of parameters and conditions are studied by considering the well known Brusselator model. Two test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme.

Illumination compensation for microscope images based on illumination difference estimation

The DNA ploidy analysis which measures the relative content of DNA in cells by image processing has a wide range of applications in cancer diagnosis. However, the measured results of the same cell in different positions are different because of uneven illumination, which may reduce the measurement accuracy and the diagnosis performance. Many methods are proposed to compensate for uneven illumination, but they are generally aimed at image enhancement, segmentation, or recognition and therefore not suitable for cell measurement. To solve this problem, a compensation method without using white-referencing images is proposed in this paper. This method first grabs images with cells and then removes the cells after locating them on the slide by image segmentation. Next, the regions of removed cells are filled by the thin-plate spline interpolation to obtain background images. Then, two methods used for estimating illumination difference from the background images are provided. Finally, the illumination compensation is made by adding the input image and the illumination difference image. Experiments show that the methods proposed can remove uneven illumination without using white-referencing images.