Abstract: Basic meteorological data are essential for evaluating impacts of spatiotemporal variability in climate forcing on hydrology and agroecosystems. The objective of this work was to develop high-resolution grids (0.25∘ × 0.25∘) of daily precipitation, evapotranspiration, and the five climate variables generally required to estimate evapostranspiration for Brazil. These five variables are maximum and minimum temperature, solar radiation, relative humidity, and wind speed. We tested six different interpolation schemes to create the grids for these variables. The data were obtained from 3625 rain gauge and 735 weather stations for period of 1980–2013. We used a cross-validation approach that compares point observed data to point interpolated estimates to select the best interpolation scheme for each climate variable. We also present the performance of the best interpolation for each climate variable at daily timescales and for river basins. The inverse distance weighting and angular distance weighting methods produced the best results. Performance of all methods was poorer prior to 1995 because of fewer stations and available data. The performance of the interpolation varies for different seasons for almost all variables. Forecasting capability was tested for precipitation only and performed adequately for the system state (wet or dry). Variations in the interpolation schemes across river basins are primarily attributed to differences in gauge or station network density. This freely available gridded meteorological data set significantly advances the availability of climate data in Brazil.

Abstract: On the basis of the sampling data from an assemblage, estimation of species richness (observed plus undetected) is statistically difficult especially for highly-diverse assemblages with many rare species. Simple counts of species richness in samples typically underestimate and strongly depend on sampling effort and sample completeness. There are two approaches to infer species richness and make fair comparisons among multiple assemblages based on possibly unequal-sampling effort and incomplete samples that miss many species. (1) An asymptotic approach: this approach compares the estimated asymptotes of species accumulation curves. It is based on statistical sampling-theory methods of estimating species richness. Both parametric and nonparametric methods are reviewed. We focus on the nonparametric estimators which are universally valid for all species abundance distributions. (2) A non-asymptotic approach: this approach compares the estimated species richnesses of standardized samples with a common finite sample size or sample completeness. It is based on the seamless sample-sizeand coverage-based rarefaction and extrapolation sampling curves. This approach aims to compare species richness estimates for equally-large or equallycomplete samples. These two approaches allow researchers to efficiently use all data to make robust and detailed inferences about species richness. Two R packages (SpadeR and iNEXT) are applied to rainforest tree data for illustration. Species richness (i.e., the number of species) is the simplest, most intuitive and most frequently used measure for characterizing the diversity of an assemblage (see Diversity measures). Species richness possesses intuitive mathematical properties, and features prominently in foundational models of community ecology. In biogeographic studies, species range maps and local and regional floras and faunas generally provide only species presence-absence information for each locality. For these studies, species richness thus becomes the only measure that can be used to quantify diversity. Even when species abundances are available,

Abstract: Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Inspired by recent k-space interpolation methods, an annihilating filter-based low-rank Hankel matrix approach is proposed as a general framework for sparsity-driven k-space interpolation method which unifies pMRI and CS-MRI. Specifically, our framework is based on a novel observation that the transform domain sparsity in the primary space implies the low-rankness of weighted Hankel matrix in the reciprocal space. This converts pMRI and CS-MRI to a k-space interpolation problem using a structured matrix completion. Experimental results using in vivo data for single/multicoil imaging as well as dynamic imaging confirmed that the proposed method outperforms the state-of-the-art pMRI and CS-MRI.

Abstract: This paper introduces a new framework for constructing the discrete empirical interpolation method (\sf DEIM) projection operator. The interpolation node selection procedure is formulated using the QR factorization with column pivoting, and it enjoys a sharper error bound for the \sf DEIM projection error. Furthermore, for a subspace $\mathcal{U}$ given as the range of an orthonormal ${\mathsf U}$, the \sf DEIM projection does not change if ${\mathsf U}$ is replaced by ${\mathsf U} \Omega$ with arbitrary unitary matrix $\Omega$. In a large-scale setting, the new approach allows modifications that use only randomly sampled rows of ${\mathsf U}$, but with the potential of producing good approximations with corresponding probabilistic error bounds. Another salient feature of the new framework is that robust and efficient software implementation is easily developed, based on readily available high performance linear algebra packages.

Abstract: As a key component in many computer vision systems, optical flow estimation, especially with large displacements, remains an open problem. In this paper we present a simple but powerful matching method works in a coarsetofine scheme for optical flow estimation. Inspired by the nearest neighbor field (NNF) algorithms, our approach, called CPM (Coarse-to-fine PatchMatch), blends an efficient random search strategy with the coarse-to-fine scheme for optical flow problem. Unlike existing NNF techniques, which is efficient but the results is often too noisy for optical flow caused by the lack of global regularization, we propose a propagation step with constrained random search radius between adjacent levels on the hierarchical architecture. The resulting correspondences enjoys a built-in smoothing effect, which is more suited for optical flow estimation than NNF techniques. Furthermore, our approach can also capture the tiny structures with large motions which is a problem for traditional coarse-to-fine optical flow algorithms. Interpolated by an edge-preserving interpolation method (EpicFlow), our method outperforms the state of the art on MPI-Sintel and KITTI, and runs much faster than the competing methods.

Abstract: Appropriate spatiotemporal interpolation is critical to the assessment of relationships between environmental exposures and health outcomes. A powerful assessment of human exposure to environmental agents would incorporate spatial and temporal dimensions simultaneously. This paper compares shape function (SF)-based and inverse distance weighting (IDW)-based spatiotemporal interpolation methods on a data set of PM2.5 data in the contiguous U.S. Particle pollution, also known as particulate matter (PM), is composed of microscopic solids or liquid droplets that are so small that they can get deep into the lungs and cause serious health problems. PM2.5 refers to particles with a mean aerodynamic diameter less than or equal to 2.5 micrometers. Based on the error statistics results of k-fold cross validation, the SF-based method performed better overall than the IDW-based method. The interpolation results generated by the SF-based method are combined with population data to estimate the population exposure to PM2.5 in the contiguous U.S. We investigated the seasonal variations, identified areas where annual and daily PM2.5 were above the standards, and calculated the population size in these areas. Finally, a web application is developed to interpolate and visualize in real time the spatiotemporal variation of ambient air pollution across the contiguous U.S. using air pollution data from the U.S. Environmental Protection Agency (EPA)’s AirNow program.

Abstract: We present a global optimization approach to optical flow estimation. The approach optimizes a classical optical flow objective over the full space of mappings between discrete grids. No descriptor matching is used. The highly regular structure of the space of mappings enables optimizations that reduce the computational complexity of the algorithm's inner loop from quadratic to linear and support efficient matching of tens of thousands of nodes to tens of thousands of displacements. We show that one-shot global optimization of a classical Horn-Schunck-type objective over regular grids at a single resolution is sufficient to initialize continuous interpolation and achieve state-of-the-art performance on challenging modern benchmarks.

Abstract: A curved beam element based on the Timoshenko model and non-uniform rational B-splines (NURBS) interpolation both for geometry and displacements is presented. Such an element can be used to suitably analyse plane-curved beams and arches. Some numerical results will explore the effectiveness and accuracy of this novel method by comparing its performance with those of some accurate finite elements proposed in the technical literature, and also with analytical solutions: for the cases where such closed-form solutions were not available in the literature, they have been computed by exact integration of the governing differential equations. It is shown that the presented element is almost insensitive to both membrane- and shear-locking, and that such phenomena can be easily controlled by properly choosing the number of elements or the NURBS degree.

Abstract: We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of Matlab and requiring no user input parameters. Even on a disk or interval the algorithm may outperform existing methods, and on more complicated domains it is especially competitive. The core ideas are (1) representation of the rational approximant in barycentric form with interpolation at certain support points and (2) greedy selection of the support points to avoid exponential instabilities. The name AAA stands for "adaptive Antoulas--Anderson" in honor of the authors who introduced a scheme based on (1). We present the core algorithm with a Matlab code and nine applications and describe variants targeted at problems of different kinds. Comparisons are made with vector fitting, RKFIT, and other existing methods for rational approximation.

Abstract: Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which generalizes deep kernel learning approaches to enable classification, multi-task learning, additive covariance structures, and stochastic gradient training. Specifically, we apply additive base kernels to subsets of output features from deep neural architectures, and jointly learn the parameters of the base kernels and deep network through a Gaussian process marginal likelihood objective. Within this framework, we derive an efficient form of stochastic variational inference which leverages local kernel interpolation, inducing points, and structure exploiting algebra. We show improved performance over stand alone deep networks, SVMs, and state of the art scalable Gaussian processes on several classification benchmarks, including an airline delay dataset containing 6 million training points, CIFAR, and ImageNet.

Abstract: Coprime arrays, consisting of two uniform linear arrays whose inter-element separations are coprime, can resolve O(MN) sources using only O(M + N) sensors. However, holes in the coarray prevent us from using the full coarray in the MUSIC algorithm for DOA estimation. Through interpolation, it may be possible to use the remaining elements of the coarray to increase the degrees of freedom beyond what is captured in the contiguous ULA section in the coarray. Techniques like positive definite Toeplitz completion, array interpolation, and sparse recovery, manage to include all the information in the coarray, but they demand extra fine-tuned parameters and have individual drawbacks. In this paper, a simple and tractable convex framework via nuclear norm minimization is presented. This approach has no extra tuning parameters and overcomes several undesired issues of other techniques. Numerical examples indicate that, in many instances, the proposed method not only increases the estimation accuracy but also distinguishes more sources than other methods.1

Abstract: Motion planning is a fundamental tool in robotics, used to generate collision-free, smooth, trajectories, while satisfying task-dependent constraints. In this paper, we present a novel approach to motion planning using Gaussian processes. In contrast to most existing trajectory optimization algorithms, which rely on a discrete state parameterization in practice, we represent the continuous-time trajectory as a sample from a Gaussian process (GP) generated by a linear time-varying stochastic differential equation. We then provide a gradient-based optimization technique that optimizes continuous-time trajectories with respect to a cost functional. By exploiting GP interpolation, we develop the Gaussian Process Motion Planner (GPMP), that finds optimal trajectories parameterized by a small number of states. We benchmark our algorithm against recent trajectory optimization algorithms by solving 7-DOF robotic arm planning problems in simulation and validate our approach on a real 7-DOF WAM arm.

Abstract: In this paper, we propose residual interpolation (RI) as an alternative to color difference interpolation, which is a widely accepted technique for color image demosaicking. Our proposed RI performs the interpolation in a residual domain, where the residuals are differences between observed and tentatively estimated pixel values. Our hypothesis for the RI is that if image interpolation is performed in a domain with a smaller Laplacian energy, its accuracy is improved. Based on the hypothesis, we estimate the tentative pixel values to minimize the Laplacian energy of the residuals. We incorporate the RI into the gradient-based threshold free algorithm, which is one of the state-of-the-art Bayer demosaicking algorithms. Experimental results demonstrate that our proposed demosaicking algorithm using the RI surpasses the state-of-the-art algorithms for the Kodak, the IMAX, and the beyond Kodak data sets.

Abstract: This review paper presents a methodological study on possible and existing meshfree methods for solving the partial differential equations (PDEs) governing solid mechanics problems, based mainly on the research work in the past two decades at the authors group. We start with a discussion on the general steps in a meshfree method based on nodes, with the displacements as the primary variables. We then examine the major techniques used in each of these steps: (1) techniques for displacement function approximations using nodes, (2) approximation of the gradient of the displacements or strains based on nodes and a background T-cells that can be automatically generated and refined, and (3) formulation techniques for producing algebraic equations. The function approximation techniques include node-based interpolation methods, cell-based interpolation methods, function smoothing techniques, and moving least squares approximation techniques. The gradient approximation includes direct differentiation, gradient smoothing, and special strain construction. Formulation techniques include strong-form, weakform, local weakform, weak-strong-form, and weakened weakform (W2). In theory, a meshfree method can be developed using a combination of function approximation, gradient approximation, and formulation techniques, which can lead to matrix of a large number of possible methods. This review attempts to provide an overall methodological review, rather than a usual review of comparing different methods. We hope to show readers the differences between the forests, and just between the trees.

Abstract: We propose Deep Feature Interpolation (DFI), a new data-driven baseline for automatic high-resolution image transformation. As the name suggests, it relies only on simple linear interpolation of deep convolutional features from pre-trained convnets. We show that despite its simplicity, DFI can perform high-level semantic transformations like "make older/younger", "make bespectacled", "add smile", among others, surprisingly well - sometimes even matching or outperforming the state-of-the-art. This is particularly unexpected as DFI requires no specialized network architecture or even any deep network to be trained for these tasks. DFI therefore can be used as a new baseline to evaluate more complex algorithms and provides a practical answer to the question of which image transformation tasks are still challenging in the rise of deep learning.

Abstract: A method is proposed to reconstruct the instantaneous velocity field from time-resolved volumetric particle tracking velocimetry (PTV, e.g., 3D-PTV, tomographic PTV and Shake-the-Box), employing both the instantaneous velocity and the velocity material derivative of the sparse tracer particles. The constraint to the measured temporal derivative of the PTV particle tracks improves the consistency of the reconstructed velocity field. The method is christened as pouring time into space, as it leverages temporal information to increase the spatial resolution of volumetric PTV measurements. This approach becomes relevant in cases where the spatial resolution is limited by the seeding concentration. The method solves an optimization problem to find the vorticity and velocity fields that minimize a cost function, which includes next to instantaneous velocity, also the velocity material derivative. The velocity and its material derivative are related through the vorticity transport equation, and the cost function is minimized using the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. The procedure is assessed numerically with a simulated PTV experiment in a turbulent boundary layer from a direct numerical simulation (DNS). The experimental validation considers a tomographic particle image velocimetry (PIV) experiment in a similar turbulent boundary layer and the additional case of a jet flow. The proposed technique (‘vortex-in-cell plus’, VIC+) is compared to tomographic PIV analysis (3D iterative cross-correlation), PTV interpolation methods (linear and adaptive Gaussian windowing) and to vortex-in-cell (VIC) interpolation without the material derivative. A visible increase in resolved details in the turbulent structures is obtained with the VIC+ approach, both in numerical simulations and experiments. This results in a more accurate determination of the turbulent stresses distribution in turbulent boundary layer investigations. Data from a jet experiment, where the vortex topology is retrieved with a small number of tracers indicate the potential utilization of VIC+ in low-concentration experiments as for instance occurring in large-scale volumetric PTV measurements.

Abstract: In this paper, we present an accurate and efficient isogeometric topology optimization method that integrates the non-uniform rational B-splines based isogeometric analysis and the parameterized level set method for minimal compliance problems. The same NURBS basis functions are used to parameterize the level set function and evaluate the objective function, and therefore the design variables are associated with the control points. The coefficient matrix that parameterizes the level set function is set up by a collocation method that uses the Greville abscissae. The zero-level set boundary is obtained from the interpolation points corresponding to the vertices of the knot spans. Numerical examples demonstrate the validity and efficiency of the proposed method.

Abstract: Available climatological information of Distrito Federal does not satisfy the requirements for detailed climate diagnosis, as they do not provide the necessary spatial resolution for water resources management purposes. Annual and seasonal climatology (1971–2000) of precipitation from 6 meteorological stations and 54 rain gauges from Central Brazil were used to test eight different spatial interpolation methods. Geographical factors (i.e., altitude, longitude and latitude) explain a large portion of precipitation in the region, and therefore, multivariate models were included. The performance of estimations was assessed through independent validation using mean square error, correlation coefficient and Nash–Sutcliffe efficiency criterion. Inverse distance weighting (IDW), ordinary kriging (OK) and the multivariate regression with interpolation of residuals by IDW (MRegIDW) and OK (MRegOK) have performed the lowest errors and the highest correlation and Nash–Sutcliffe efficiency criterion. In general, interpolation methods provide similar spatial distributions of rainfall wherever observation network is dense. However, the inclusion of geographical variables to the interpolation method should improve estimates in areas where the observation network density is low. Nevertheless, the assessment of uncertainties using a geostatistical method provides supplementary and qualitative information which should be considered when interpreting the spatial distribution of rainfall.

Abstract: Monge--Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities---it quantifies the cost of transporting a mass distribution into another. In particular, it provides natural options for interpolation of distributions (displacement interpolation) and for modeling flows. As such it has been the cornerstone of recent developments in physics, probability theory, image processing, time-series analysis, and several other fields. In spite of extensive work and theoretical developments, the computation of OMT for large-scale problems has remained a challenging task. An alternative framework for interpolating distributions, rooted in statistical mechanics and large deviations, is that of the Schroźdinger bridge problem (SBP), which leads to entropic interpolation. SBP may be seen as a stochastic regularization of OMT, and can be cast as the stochastic control problem of steering the probability density of the state-vector of a dynamical system between two marginals. The actual computation of entropic flows, however, has received hardly any attention. In our recent work on Schroźdinger bridges for Markov chains and quantum channels, we showed that the solution can be efficiently obtained from the fixed point of a map which is contractive in the Hilbert metric. Thus, the purpose of this paper is to show that a similar approach can be taken in the context of diffusion processes which (i) leads to a new proof of a classical result on SBP and (ii) provides an efficient computational scheme for both SBP and OMT. We illustrate this new computational approach by obtaining interpolation of densities in representative examples such as interpolation of images.

Abstract: We introduce a new light-field dataset of materials, and take advantage of the recent success of deep learning to perform material recognition on the 4D light-field. Our dataset contains 12 material categories, each with 100 images taken with a Lytro Illum, from which we extract about 30,000 patches in total. To the best of our knowledge, this is the first mid-size dataset for light-field images. Our main goal is to investigate whether the additional information in a light-field (such as multiple sub-aperture views and view-dependent reflectance effects) can aid material recognition. Since recognition networks have not been trained on 4D images before, we propose and compare several novel CNN architectures to train on light-field images. In our experiments, the best performing CNN architecture achieves a 7% boost compared with 2D image classification (70% to 77%). These results constitute important baselines that can spur further research in the use of CNNs for light-field applications. Upon publication, our dataset also enables other novel applications of light-fields, including object detection, image segmentation and view interpolation.

Abstract: We propose a new pipeline for optical flow computation, based on Deep Learning techniques. We suggest using a Siamese CNN to independently, and in parallel, compute the descriptors of both images. The learned descriptors are then compared efficiently using the L2 norm and do not require network processing of patch pairs. The success of the method is based on an innovative loss function that computes higher moments of the loss distributions for each training batch. Combined with an Approximate Nearest Neighbor patch matching method and a flow interpolation technique, state of the art performance is obtained on the most challenging and competitive optical flow benchmarks.

Abstract: Filtering is one of the core post-processing steps for airborne LiDAR point cloud. In recent years, the morphology-based filtering algorithms have proven to be a powerful and efficient tool for filtering airborne LiDAR point cloud. However, most traditional morphology-based algorithms have difficulties in preserving abrupt terrain features, especially when using larger filtering windows. In order to suppress the omission error caused by protruding terrain features, this paper proposes an improved morphological algorithm based on multi-level kriging interpolation. This algorithm is essentially a combination of progressive morphological filtering algorithm and multi-level interpolation filtering algorithm. The morphological opening operation is performed with filtering window gradually downsizing, while kriging interpolation is conducted at different levels according to the different filtering windows. This process is iterative in a top to down fashion until the filtering window is no longer greater than the preset minimum filtering window. Fifteen samples provided by the ISPRS commission were chosen to test the performance of the proposed algorithm. Experimental results show that the proposed method can achieve promising results not only in flat urban areas but also in rural areas. Comparing with other eight classical filtering methods, the proposed method obtained the lowest omission error, and preserved protruding terrain features better.

Abstract: Division of focal plane (DoFP) polarimeters operate by integrating micro-polarizer elements with a focal plane. These polarization imaging sensors reduce spatial resolution output and each pixel has a varying instantaneous field of view (IFoV). These drawbacks can be mitigated by applying proper interpolation methods. In this paper, we present a new interpolation method for DoFP polarimeters by using intensity correlation. We employ the correlation of intensity measurements in different orientations to detect edges and then implement interpolation along edges. The performance of the proposed method is compared with several previous methods by using root mean square error (RMSE) comparison and visual comparison. Experimental results showed that our proposed method can achieve better visual effects and a lower RMSE than other methods.

Abstract: Selection of appropriate interpolation methods for the conversion of discrete samples into continuous maps is a controversial issue in the environmental researches. The main objective of this study was to analyze the suitability of three interpolation methods for the discrimination of groundwater with respect to the water quality index (WQI). The groundwater quality data consisted of 17 variables associated with 65 wells located in Andimeshk-Shush Plain. Three spatial interpolation methods including ordinary kriging (OK), empirical Bayesian kriging (EBK), and inverse distance weighting (IDW) were utilized for modeling the groundwater contamination. In addition, different cross-validation indicators were applied to assess the performance of different interpolation methods. The results showed that the performance differed slightly among different methods, although the best performed interpolation method in this study was the empirical Bayesian kriging. Among the interpolation methods, IDW with weighting power of 4 estimated the most contaminated area, while OK estimated the lowest contaminated area. The weighting power of IDW had a significant influence on the estimation, meaning that the estimated contaminated area was increased when a greater weighting power was selected. The subtraction results indicated that there are slightly spatial differences among the contamination assessment results. Results of both standard deviation (SD) and coefficient of variation (CV) also showed that uncertainty was highest in the southern part of the study area, where the distribution of wells were more intensive than that of the northern part.