Thin-plate Spline Interpolation Research Articles

Image Vectorization With Real-Time Thin-Plate Spline

The vector graphics with gradient mesh can be attributed to their compactness and scalability; however, they tend to fall short when it comes to real-time editing due to a lack of real-time rasterization and an efficient editing tool for image details. In this paper, we encode global manipulation geometries and local image details within a hybrid vector structure, using parametric patches and detailed features for localized and parallelized thin-plate spline interpolation in order to achieve good compressibility, interactive expressibility, and editability. The proposed system then automatically extracts an optimal set of detailed color features while considering the compression ratio of the image as well as reconstruction error and its characteristics applicable to the preservation of structural and irregular saliency of the image. The proposed real-time vector representation makes it possible to construct an interactive editing system for detail-maintained image magnification and color editing as well as material replacement in cross mapping, without maintaining spatial and temporal consistency while editing in a raster space. Experiments demonstrate that our representation method is superior to several state-of-the-art methods and as good as JPEG, while providing real-time editability and preserving structural and irregular saliency information.

An Improved Flexible Spatiotemporal DAta Fusion (IFSDAF) method for producing high spatiotemporal resolution normalized difference vegetation index time series

The Normalized Difference Vegetation Index (NDVI) is one of the most commonly used vegetation indices for monitoring ecosystem dynamics and modeling biosphere processes. However, global NDVI products are usually provided with relatively coarse spatial resolutions that lack important spatial details. Producing NDVI time-series data with high spatiotemporal resolution is indispensable for monitoring land surfaces and ecosystem changes, especially in spatiotemporally heterogeneous areas. The Improved Flexible Spatiotemporal DAta Fusion (IFSDAF) method was developed in this study to fill this need. In accord with the distinctive characteristics of NDVIs with large data variance and high spatial autocorrelation compared with raw reflectance bands, the IFSDAF method first produces a time-dependent increment with linear unmixing and a space-dependent increment via thin plate spline interpolation. It then makes a final prediction by optimal integration of these two increments with the constrained least squares method. Moreover, the IFSDAF was developed with the capacity to use all available finer-scaled images, including those partly contaminated by clouds. NDVI images with coarse spatial resolution (MODIS) and fine spatial resolution (Landsat and Sentinel) in areas with great spatial heterogeneity and significant land cover changes were used to test the performance of the IFSDAF method. The root mean square error and relative root mean square error of predicted relative to observed results were 0.0884 and 22.12%, respectively, in heterogeneous areas, and 0.0546 and 25.77%, respectively, in areas of land-cover change. These promising results demonstrated the strength and robustness of the IFSDAF method in providing reliable NDVI datasets with high spatial and temporal resolution to support research on land surface processes. The efficiency of the proposed IFSDAF method can be greatly improved by using only the space-dependent increment. This simplification will make IFSDAF a feasible method for monitoring global vegetation.

Swelling degree prediction of polyhydroxybutyrate/chitosan matrices loaded with “Arnica‐do‐Brasil”

ABSTRACTPolyhydroxybutyrate and chitosan have been studied as materials for drug delivery systems (DDSs) due to their biodegradability and biocompatibility. The aim of this work was to produce amphiphilic polyhydroxybutyrate/chitosan matrices that form porous structures (scaffolds) after swelling in water and arnica extract. The matrices were analyzed by TGA, SEM, XDR, DSC, and FTIR. Thin plate spline interpolation method (TPSIM) was used to predict the swelling of the matrices generating three‐dimensional data fitted, showing the influence of time and concentration variables on both fluids absorption. Polyhydroxybutyrate/chitosan samples containing 60 wt % (weight percent) of chitosan formed a porous structure as they were submitted to arnica loading, and the obtained device was able to deliver arnica in physiological medium. Thus, the produced matrices have a strong potential to perform both as scaffolds and DDS © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47838.

Magnetometer Calibration and Field Mapping through Thin Plate Splines.

While the undisturbed Earth’s magnetic field represents a fundamental information source for orientation purposes, magnetic distortions have been mostly considered as a source of error. However, when distortions are temporally stable and spatially distinctive, they could provide a unique magnetic landscape that can be used in different applications, from indoor localization to sensor fusion algorithms for attitude estimation. The main purpose of this work, therefore, is to present a method to characterize the 3D magnetic vector in every point of the measurement volume. The possibility of describing the 3D magnetic field map through Thin Plate Splines (TPS) interpolation is investigated and demonstrated. An algorithm for the simultaneous estimation of the parameters related to magnetometer calibration and those describing the magnetic map, is proposed and tested on both simulated and real data. Results demonstrate that an accurate description of the local magnetic field using TPS interpolation is possible. The proposed procedure leads to errors in the estimation of the local magnetic direction with a standard deviation lower than 1 degree. Magnetometer calibration and magnetic field mapping could be integrated into different algorithms, for example to improve attitude estimation in highly distorted environments or as an aid to indoor localization.

An Improved Skewness Balancing Filtering Algorithm Based on Thin Plate Spline Interpolation

Most filtering algorithms suffer from complex parameter settings or threshold adjusting. To solve this problem, this paper proposes an improved skewness balancing filtering algorithm based on thin plate spline (TPS) interpolation. The proposed algorithm filters the nonground points in an iterative manner. A reference surface that reflects the fluctuation of the terrain is generated using the TPS interpolation method. Accordingly, the elevation difference from each point to the surface can be calculated. By applying the skewness balancing principle to these elevation differences, nonground points can be removed automatically. To verify the validity and robustness of the proposed method, the datasets provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) were adopted. The experimental results show that this presented method can adapt to complex environments and achieve a higher filtering accuracy than the traditional skewness balancing algorithm. Moreover, in comparison with the other eight filtering methods tested by the ISPRS and four improved filtering methods proposed recently, the proposed method achieved an average total error of 5.39%, which is smaller than that of most of these other methods.

Methods for Spatial Prediction of Crop Yield Potential

Core Ideas We compared five methods for applying crop models to predict yield potential. A global weather database was divided into training and test sites. Metamodels and weather generation approaches performed best. Nearest neighbor interpolation can be replaced by superior and computationally efficient methods. Opportunities for and constraints to crop production can be assessed with crop growth simulation models. Most crop simulation models require daily weather data as input but such data are generally not available at a high spatial resolution. Several approaches have been developed to estimate yield potential (Yp) at locations without daily weather data (weather stations) but these have not been compared. We used two crop simulation models (WOFOST and LINTUL) to compute Yp for two crops for the entire world. A global weather database was divided into 856 training and 12,808 testing sites. We predicted Yp at the testing sites by using five main methods (eight methods if one considers within‐method variants): (i) weather interpolation followed by simulation; (ii) nearest neighbor interpolation; (iii) thin plate spline interpolation, either with or without covariates; (iv) Random Forest‐based metamodels with either climatic or bioclimatic variables; and (v) weather generation from either climate data or interpolated climate data, followed by simulation. The metamodel with bioclimatic variables performed best [average root mean square error (RMSE) = 667 ± 111 kg ha−1], followed by weather generation from climate data, weather interpolation, and spatial interpolation of yield with climatic covariables. The most commonly used method, nearest neighbor interpolation, performed worst (RMSE = 1763 ± 472 kg ha−1). The optimal method for a particular study will depend on the simulation model, the region, weather station density, and other variables but these results suggest that for estimating Yp, alternatives to nearest neighbor interpolation should be considered.

Using historical normals to improve modern monthly climate normal surfaces for Madagascar

High‐resolution, spatially continuous climate models are an essential first step in assessing fine‐scale impacts of climate and projected future climates. Observational weather station networks supporting such models are often inadequate and are spread unevenly throughout the globe, particularly in developing regions such as Madagascar, since network establishment and maintenance requires significant investment. Quality climate models are greatly needed for the assessment of conservation, agricultural productivity and socio‐economic studies of climate vulnerability.With the aim of generating improved modern climate normal surfaces for Madagascar, we have developed a method for augmenting the existing sparse climate normal network with spatial patterns of climate change derived from more densely distributed historical climate normals. Thin plate smoothing splines and kriging were applied to the spatial analysis of the climate difference patterns and their performances were compared.We found that the augmented data improved the spatial consistency of the climate interpolations when compared with the interpolations using only the existing observed data. Our analysis confirmed the robustness and accuracy of thin plate spline interpolation when applied to long‐term differences in climate normals. Further, the investigation indicated that long‐term differences in rainfall normals have broader spatial coherence and are less susceptible to local differences when compared to temperature normals. This suggests that long term change patterns in rainfall are better supported by sparse data networks, despite the usually acknowledged greater inherent spatial and temporal variability of rainfall.The augmented data capture distinct spatial patterns in temperature and rainfall that differ markedly from the patterns in interpolations of observed data alone. The derived change patterns are consistent with observed global trends. This technique might be used to improve understanding of the current climate in other data‐poor regions and the outputs used in spatial environmental and socio‐economic studies, such as species distribution mapping and climate change resilience mapping.

Thinplate Splines on the Sphere

In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a widely used tool in myriad applications. The analogues for ${\mathbb S}^{d-1}$ are the thin plate splines for the sphere. The topic was first discussed by Wahba in the early 1980's, for the ${\mathbb S}^2$ case. Wahba presented the associated semi-reproducing kernels as infinite series. These semi-reproducing kernels play a central role in expressions for the solution of the associated spline interpolation and smoothing problems. The main aims of the current paper are to give a recurrence for the semi-reproducing kernels, and also to use the recurrence to obtain explicit closed form expressions for many of these kernels. The closed form expressions will in many cases be significantly faster to evaluate than the series expansions. This will enhance the practicality of using these thinplate splines for the sphere in computations.

Skull ontogeny of extant caimans: a three-dimensional geometric morphometric approach

Ontogenetic variation of cranial characters used in crocodylian phylogenetic systematics has never been studied. Furthermore, the relationship between diet and skull morphological transformation during ontogeny has not been properly explored yet. We quantify the inter- and intraspecific skull morphological variation in extant caiman species focusing on those areas relevant to systematics and, also investigate the relation between diet and morphological changes during ontogeny. We applied a three-dimensional approach of geometric morphometrics on post-hatching ontogenetic cranial series of Caiman latirostris and C. yacare. In order to incorporate incomplete material, we additionally tested four different methods of missing landmark estimation and apply the thin-plate spline interpolation. We detected morphological changes between species and during ontogeny (snout and pterygoid flanges increase their proportions and, orbits, temporal fenestrae, skull roof and foramen magnum decrease their relative size) that constitutes part of a general morphological change in the cranial ontogeny of crocodylians. Moreover, the negative allometry of the fenestrae and neurocranium and the positive allometry of the splanchnocranium in both caiman species are the plesiomorphic condition, at least, for tetrapods. Shape changes during growth were found to be related to ontogenetic changes in the diet. Dissimilarities between species seem to be related to different mechanical requirements and different use of the habitat. We found inter- and intraspecific variation in some morphological characters with systematic implications (the contact of nasals with naris, the contact of prefrontals in the midline, and the bones that border the suborbital fenestra and the proportion in which one of them participates) that are not currently considered in phylogenetic analyses.

Optimization of Premix Powders for Tableting Use.

Direct compression is a popular choice as it provides the simplest way to prepare the tablet. It can be easily adopted when the active pharmaceutical ingredient (API) is unstable in water or to thermal drying. An optimal formulation of preliminary mixed powders (premix powders) is beneficial if prepared in advance for tableting use. The aim of this study was to find the optimal formulation of the premix powders composed of lactose (LAC), cornstarch (CS), and microcrystalline cellulose (MCC) by using statistical techniques. Based on the "Quality by Design" concept, a (3,3)-simplex lattice design consisting of three components, LAC, CS, and MCC was employed to prepare the model premix powders. Response surface method incorporating a thin-plate spline interpolation (RSM-S) was applied for estimation of the optimum premix powders for tableting use. The effect of tablet shape identified by the surface curvature on the optimization was investigated. The optimum premix powder was effective when the premix was applied to a small quantity of API, although the function of premix was limited in the case of the formulation of large amount of API. Statistical techniques are valuable to exploit new functions of well-known materials such as LAC, CS, and MCC.

ATMAD: robust image analysis for Automatic Tissue MicroArray De-arraying

BackgroundOver the last two decades, an innovative technology called Tissue Microarray (TMA), which combines multi-tissue and DNA microarray concepts, has been widely used in the field of histology. It consists of a collection of several (up to 1000 or more) tissue samples that are assembled onto a single support – typically a glass slide – according to a design grid (array) layout, in order to allow multiplex analysis by treating numerous samples under identical and standardized conditions. However, during the TMA manufacturing process, the sample positions can be highly distorted from the design grid due to the imprecision when assembling tissue samples and the deformation of the embedding waxes. Consequently, these distortions may lead to severe errors of (histological) assay results when the sample identities are mismatched between the design and its manufactured output. The development of a robust method for de-arraying TMA, which localizes and matches TMA samples with their design grid, is therefore crucial to overcome the bottleneck of this prominent technology.ResultsIn this paper, we propose an Automatic, fast and robust TMA De-arraying (ATMAD) approach dedicated to images acquired with brightfield and fluorescence microscopes (or scanners). First, tissue samples are localized in the large image by applying a locally adaptive thresholding on the isotropic wavelet transform of the input TMA image. To reduce false detections, a parametric shape model is considered for segmenting ellipse-shaped objects at each detected position. Segmented objects that do not meet the size and the roundness criteria are discarded from the list of tissue samples before being matched with the design grid. Sample matching is performed by estimating the TMA grid deformation under the thin-plate model. Finally, thanks to the estimated deformation, the true tissue samples that were preliminary rejected in the early image processing step are recognized by running a second segmentation step.ConclusionsWe developed a novel de-arraying approach for TMA analysis. By combining wavelet-based detection, active contour segmentation, and thin-plate spline interpolation, our approach is able to handle TMA images with high dynamic, poor signal-to-noise ratio, complex background and non-linear deformation of TMA grid. In addition, the deformation estimation produces quantitative information to asset the manufacturing quality of TMAs.

An eFTD-VP framework for efficiently generating patient-specific anatomically detailed facial soft tissue FE mesh for craniomaxillofacial surgery simulation.

Accurate surgical planning and prediction of craniomaxillofacial surgery outcome requires simulation of soft tissue changes following osteotomy. This can only be achieved by using an anatomically detailed facial soft tissue model. The current state-of-the-art of model generation is not appropriate to clinical applications due to the time-intensive nature of manual segmentation and volumetric mesh generation. The conventional patient-specific finite element (FE) mesh generation methods are to deform a template FE mesh to match the shape of a patient based on registration. However, these methods commonly produce element distortion. Additionally, the mesh density for patients depends on that of the template model. It could not be adjusted to conduct mesh density sensitivity analysis. In this study, we propose a new framework of patient-specific facial soft tissue FE mesh generation. The goal of the developed method is to efficiently generate a high-quality patient-specific hexahedral FE mesh with adjustable mesh density while preserving the accuracy in anatomical structure correspondence. Our FE mesh is generated by eFace template deformation followed by volumetric parametrization. First, the patient-specific anatomically detailed facial soft tissue model (including skin, mucosa, and muscles) is generated by deforming an eFace template model. The adaptation of the eFace template model is achieved by using a hybrid landmark-based morphing and dense surface fitting approach followed by a thin-plate spline interpolation. Then, high-quality hexahedral mesh is constructed by using volumetric parameterization. The user can control the resolution of hexahedron mesh to best reflect clinicians' need. Our approach was validated using 30 patient models and 4 visible human datasets. The generated patient-specific FE mesh showed high surface matching accuracy, element quality, and internal structure matching accuracy. They can be directly and effectively used for clinical simulation of facial soft tissue change.

Thin Plate Splines Method for 3D Reconstruction of the Left Ventricle with Use a Limited Number of Ultrasonic Sections

This paper addresses the testing of thin plate splines (TPS) interpolation method for the left ventricle (LV) 3D-reconstruction based on a limited number of ultrasonic sections obtained during echocardiography to apply the global and regional cardiac structure and function. With the use of TPS technique, the LV inner and outer surfaces were reconstructed based on three short-axes and one long-axes sections of the LV standard transthoracic imaging. The LV 3D-reconstruction by means of the heart transesophageal examination was chosen as a reference point. To evaluate the accuracy of LV 3D-reconstruction on TPS approach, the mean relative error (R) of LV surfaces interpolation and the relative change of cardiac wall thickness (dH/H) during the end (passive) phase of LV diastolic filling as a measure of the myocardium diastolic stiffness were calculated. According to ~8% value of R and qualitative distribution of dH/H in LV wall regions, we concluded that the proposed method of LV 3D-reconstruction shows a sufficient accuracy for practical use and future development.

On the Interpolation of Electromagnetic Near Field Without Prior Knowledge of the Radiating Source

A method is proposed to interpolate the electromagnetic near field when no information on the radiating source is available. In the absence of a priori knowledge, general properties of the electromagnetic field are exploited to estimate the field, namely, the minimum complexity of the field, and the continuity of the first derivatives. These properties are enforced by minimizing the nuclear norm and using the thin plate spline interpolation results, respectively. The proposed procedure is validated experimentally by interpolating the planar electrical near field radiated by three antennas. The quality of the interpolation and its robustness to noise are investigated. Despite its simplicity, the interpolation method is able to properly estimate the near field from a random coarse sampling of $2 \lambda $ . The quality of the near-field interpolation is also confirmed by deriving the far-field. These promising results pave the way for the development of fast antenna measurement procedures.

Automatically tracking neurons in a moving and deforming brain.

Advances in optical neuroimaging techniques now allow neural activity to be recorded with cellular resolution in awake and behaving animals. Brain motion in these recordings pose a unique challenge. The location of individual neurons must be tracked in 3D over time to accurately extract single neuron activity traces. Recordings from small invertebrates like C. elegans are especially challenging because they undergo very large brain motion and deformation during animal movement. Here we present an automated computer vision pipeline to reliably track populations of neurons with single neuron resolution in the brain of a freely moving C. elegans undergoing large motion and deformation. 3D volumetric fluorescent images of the animal’s brain are straightened, aligned and registered, and the locations of neurons in the images are found via segmentation. Each neuron is then assigned an identity using a new time-independent machine-learning approach we call Neuron Registration Vector Encoding. In this approach, non-rigid point-set registration is used to match each segmented neuron in each volume with a set of reference volumes taken from throughout the recording. The way each neuron matches with the references defines a feature vector which is clustered to assign an identity to each neuron in each volume. Finally, thin-plate spline interpolation is used to correct errors in segmentation and check consistency of assigned identities. The Neuron Registration Vector Encoding approach proposed here is uniquely well suited for tracking neurons in brains undergoing large deformations. When applied to whole-brain calcium imaging recordings in freely moving C. elegans, this analysis pipeline located 156 neurons for the duration of an 8 minute recording and consistently found more neurons more quickly than manual or semi-automated approaches.

Spatial, temporal and latitudinal components of historical fire regimes in mixed conifer forests, California

AbstractAimThis study seeks to document and compare historical temporal and spatial components of fire regimes in two watersheds in mixed conifer forests of the western slope of the Sierra Nevada, California, USA.LocationWatersheds in the southern Sierra Nevada (Sugar Pine, 2358 ha) and north‐central Sierra Nevada (Last Chance, 3021 ha), California, USA are compared.MethodsTemporal (frequency, return interval, season) and spatial (extent, fire rotation, spatial mean fire interval) fire regime metrics were reconstructed from fire scar samples. Superposed epoch analysis (SEA) was used to examine relationships between fire occurrence and the Palmer drought severity index (PDSI) at each site. Thin plate splines were introduced as a tool for interpolating historical fire extent from dendroecological data. Point fire return intervals were compared between sites to better understand possible influences of historical Native American burning practices.ResultsDifferences emerged between sites in temporal and spatial fire regime metrics. The northern site had longer fire return intervals, more synchronized fire years, fewer point intervals < 4 years, longer fire rotation period and longer spatial mean fire interval. The northern site showed a significant reduction in PDSI values during fire years, whereas this climate–fire relationship in the southern site was likely decoupled by frequent Native American burning. Thin plate spline interpolation effectively reduced discontinuities at sample points compared to inverse distance weighting methods.Main conclusionsDifferences in both temporal and spatial fire regime metrics between sites were likely due to interplay in latitudinal influence on climate as well as differential Native American burning practices. Reconstruction of historical fire areas via geographical interpolation of fire scar data holds great promise for spatially explicit fire frequency reconstruction. The use of thin plate spline interpolation methods has the potential to reduce the impact of ‘false negatives’ in dendroecological data from frequent‐fire forests.

Robust Automatic Feature Tracking on Beating Human Hearts for Minimally Invasive CABG Surgery

This paper presents a robust algorithm for automatic tracking of feature points on the human heart. The emphases and key contributions of the proposed algorithm are uniform distribution of the feature points and sustained tolerable tracking error. While in many methods in the literature, detection takes place independently from the tracking procedure, adopting a different approach, we selected a data-driven detection stage, which works based on the feedback from tracking results from the Lucas–Kanade (LK) tracking algorithm to avoid unacceptable tracking errors. To ensure a uniform spatial distribution of the total detected feature points for tracking, a cost function is employed using the simulated annealing optimizer, which prevents the newly detected points from accumulating near the previously located points or stagnant regions. Implementing the proposed algorithm on a real human heart dataset showed that the presented algorithm yields more robust tracking and improved motion reconstruction, compared with the other available methods. Furthermore, to predict the motion of feature points for handling short-term occlusions, a state space model is utilized, and thin-plate spline (TPS) interpolation was also employed to estimate motion of any arbitrary point on the heart surface.

Combining thin-plate spline interpolation with a lapse rate model to produce daily air temperature estimates in a data-sparse alpine catchment

Insufficient availability of weather stations recording air temperature is a common problem in many alpine regions. The low station density combined with the high variability of air temperature means that interpolated fields based on simple or more complex interpolation techniques are unlikely to be representative of the real patterns of air temperature. In this study, a novel method was developed to tackle this problem, following initial investigation of lapse rate variability in the study domain: the alpine Clutha catchment, New Zealand. Owing to a series of complexities in lapse rate variability, a multi-layer approach was adopted to produce 1 km2 daily fields of maximum (Tmax) and minimum air temperature (Tmin). The first layer of the Tmax and Tmin models was calculated using a trivariate thin-plate spline, which was constrained to the elevations of the continuous network to avoid unrealistic extrapolation. To compensate for missing continuous high elevation records, two lapse rate models were implemented to scale air temperature above the first layer. The two lapse rate models were based on the dominant processes driving lapse rate variation, which were found to be cold air ponding (Tmin) and spatial differences in relative humidity (Tmax). Independent station records were used to assess accuracy and compare the resultant fields to an existing product (the Virtual Climate Station Network) and a more conventional method based on a bivariate spline and a constant lapse rate. The validation revealed that the new methods developed here have led to a substantial improvement in producing spatial estimates of Tmax, with a mean root mean square error (RMSE) of 2.38 °C, while progress in regard to Tmin was more limited (mean RMSE of 2.93 °C). As such, this work demonstrates that inclusion of the driving processes controlling lapse rates in interpolation routines can lead to improvements in accuracy.

AN ELEMENTARY PROOF OF THE OPTIMAL RECOVERY OF THE THIN PLATE SPLINE RADIAL BASIS FUNCTION

In many practical applications, we face the problem of reconstruction of an un- known function sampled at some data points. Among infinitely many possible reconstructions, the thin plate spline interpolation is known to be the least oscillatory one in the Beppo-Levi semi norm, when the data points are sampled in R 2 . The traditional proofs supporting the argu- ment are quite lengthy and complicated, keeping students and researchers off its understanding. In this article, we introduce a simple and short proof for the optimal reconstruction. Our proof is unique and reguires only elementary mathematical background.

MULTI-PARAMETER INTERPOLATION OF BETA RADIATION DOSE RATES USING RADIAL BASIS FUNCTIONS.

In this study, the interpolation problem for a set of Monte Carlo simulations of dose rate per activity of beta-emitting radionuclides is considered. The simulations were carried out for various conditions: for circular areal sources of different diameters and radionuclides, and for various distances from the source. Calculations were done for both operational quantities as well as organ doses: Hp(0.07), Hp(3), Hp(10), Hskin and Hlens Interpolation is needed for practical applications because it is often necessary to evaluate the dose quantities at parameter values that do not correspond exactly to the ones that were used for the simulation. To solve this problem, the method of radial basis function thin-plate spline interpolation is used. The method used for the interpolation and a software application called BetaDosim, which allows users to get the interpolated values, are described. BetaDosim is freely available.