Abstract: This paper presents the nearest neighbor value (NNV) algorithm for high resolution (H.R.) image interpolation. The difference between the proposed algorithm and conventional nearest neighbor algorithm is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. In other words, the proposed concept selects one pixel, among four directly surrounding the empty location, whose value is almost equal to the value generated by the conventional bilinear interpolation algorithm. The proposed method demonstrated higher performances in terms of H.R. when compared to the conventional interpolation algorithms mentioned.

Abstract: I introduce a unified approach for denoising and interpolation of seismic data in the frequency-wavenumber (f-k) domain. First, an angular search in the f-k domain is carried out to identify a sparse number of dominant dips, not only using low frequencies but over the whole frequency range. Then, an angular mask function is designed based on the identified dominant dips. The mask function is utilized with the least-squares fitting principle for optimal denoising or interpolation of data. The least-squares fit is directly applied in the time-space domain. The proposed method can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid. Synthetic and real data examples are provided to examine the performance of the proposed method.

Abstract: Image-zooming is a technique of producing a high-resolution image from its low-resolution counterpart. It is also called image interpolation because it is usually implemented by interpolation. Keys' cubic convolution (CC) interpolation method has become a standard in the image interpolation field, but CC interpolates indiscriminately the missing pixels in the horizontal or vertical direction and typically incurs blurring, blocking, ringing or other artefacts. In this study, the authors propose a novel edge-directed CC interpolation scheme which can adapt to the varying edge structures of images. The authors also give an estimation method of the strong edge for a missing pixel location, which guides the interpolation for the missing pixel. The authors' method can preserve the sharp edges and details of images with notable suppression of the artefacts that usually occur with CC interpolation. The experiment results demonstrate that the authors'method outperforms significantly CC interpolation in terms of both subjective and objective measures.

Abstract: [1] In this paper, improved flow duration curve (FDC) and area ratio (AR) based methods are developed to obtain better daily streamflow estimation at ungauged sites. A regression based logarithmic interpolation method which makes no assumption on the distribution or shape of a FDC is introduced in this paper to estimate regional FDCs. The estimated FDC is combined with a spatial interpolation algorithm to obtain daily streamflow estimates. Multiple source sites based AR methods, especially the geographical distance weighted AR (GWAR) method, are introduced in an effort to maximize the use of regional information and improve the standard AR method (SAR). Performances of the proposed approaches are evaluated using a jackknife procedure. The application to 109 stations in the province of Quebec, Canada indicates that the FDC based methods outperform AR based methods in all the summary statistics including Nash, root mean squared error (RMSE), and Bias. The number of sites that show better performances using the FDC based approaches is also significantly larger than the number of sites showing better performances using AR based methods. Using geographical distance weighted multiple sources sites based approaches can improve the performance at the majority of the catchments comparing with using the single source site based approaches.

Abstract: Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran’s I analysis was used to supplement the traditional geostatistics. According to Moran’s I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran’s I and the standardized Moran’s I, Z(I) reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran’s I analysis was better than traditional geostatistics. Thus, Moran’s I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals.

Abstract: Recent advances in radio environmental mapping enable novel, practical and efficient cognitive radio and dynamic spectrum access solutions. A crucial aspect of such solutions is to ensure the reliability of the constructed Radio Environmental Maps (REMs). Especially important is the accurate and up-to-date Radio Interference Field (RIF) estimation based on distributed spectrum use measurements. This paper analyzes the use of spatial interpolation techniques that allow robust, yet sufficiently reliable, RIF estimation from a limited number of field measurements. Several spatial interpolation techniques based on Inverse Distance Weighting (IDW) are analyzed and compared in terms of reliability bounds of the interpolation errors for an indoor environment. Performance evaluation using REM prototype implementation and a wireless testbed shows that the spatial interpolation techniques can provide a robust and reliable RIF estimation within the entire REM concept.

Abstract: Geographically weighted regression algorithm (GWR) has been applied to derive the spatial structure of urban heat island (UHI) in the city of Wroclaw, SW Poland. Seven UHI cases, measured during various meteorological conditions and characteristic of different seasons, were selected for analysis. GWR results were compared with global regression models (MLR), using various statistical procedures including corrected Akaike Information Criterion, determination coefficient, analysis of variance, and Moran’s I index. It was found that GWR is better suited for spatial modeling of UHI than MLR models, as it takes into account non-stationarity of the spatial process. However, Monte Carlo and F3 tests for spatial stationarity of the independent variables suggest that for several spatial predictors a mixed GWR–MLR approach is recommended. Both local and global models were extended by the interpolation of regression residuals and used for spatial interpolation of the UHI structure. The interpolation results were evaluated with the cross-validation approach. It was found that the incorporation of the spatially interpolated residuals leads to significant improvement of the interpolation results for both GWR and MLR approaches. Because GWR is better justified in terms of statistical specification, the combined GWR + interpolated regression residuals (GWR residual kriging; GWRK) approach is recommended for spatial modeling of UHI, instead of widely applied MLR models.

Abstract: Achieving accurate interpolation is an important requirement for many signal-processing applications. While nearest-neighbor and linear interpolation methods are popular due to their native GPU support, they unfortunately result in severe undesirable artifacts. Better interpolation methods are known but lack a native GPU support. Yet, a particularly attractive one is prefiltered cubic-spline interpolation. The signal it reconstructs from discrete samples has a much higher fidelity to the original data than what is achievable with nearest-neighbor and linear interpolation. At the same time, its computational load is moderate, provided a sequence of two operations is applied: first, prefilter the samples, and only then reconstruct the signal with the help of a B-spline basis. It has already been established in the literature that the reconstruction step can be implemented efficiently on a GPU. This article focuses on an efficient GPU implementation of the prefilter, on how to apply it to multidimensional samples (e.g. RGB color images), and on its performance aspects.

Abstract: In a world of increasing exposure of populations to natural hazards, the mapping of extreme rainfall remains a key subject of study. Such maps are required for both flood risk management and civil engineering structure design, the challenge being to take into account the local information provided by point rainfall series as well as the necessity of some regional coherency. Two approaches based on the extreme value theory are compared here, with an application to extreme rainfall mapping in West Africa. The first approach is a local fit and interpolation (LFI) consisting of a spatial interpolation of the generalized extreme value (GEV) distribution parameters estimated independently at each station. The second approach is a spatial maximum likelihood estimation (SMLE); it directly estimates the GEV distribution over the entire region by a single maximum likelihood fit using jointly all measurements combined with spatial covariates. Five LFI and three SMLE methods are considered, using the information provided by 126 daily rainfall series covering the period 1950-1990. The methods are first evaluated in calibration. Then the predictive skills and the robustness are assessed through a cross validation and an independent network validation process. The SMLE approach, especially when using the mean annual rainfall as covariate, appears to perform better for most of the scores computed. Using the Niamey 104 year time series, it is also shown that the SMLE approach has the capacity to deal more efficiently with the effect of local outliers by using the spatial information provided by nearby stations.

Abstract: Directional data arise in various contexts such as oceanography (wave directions) and meteorology (wind directions), as well as with measurements on a periodic scale (weekdays, hours, etc.). Our contribution is to introduce a model-based approach to handle periodic data in the case of measurements taken at spatial locations, anticipating structured dependence between these measurements. We formulate a wrapped Gaussian spatial process model for this setting, induced from a customary linear Gaussian process. We build a hierarchical model to handle this situation and show that the fitting of such a model is possible using standard Markov chain Monte Carlo methods. Our approach enables spatial interpolation (and can accommodate measurement error). We illustrate with a set of wave direction data from the Adriatic coast of Italy, generated through a complex computer model.

Abstract: Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs.

Abstract: Digital elevation models (DEMs) of river channels, built by interpolation between samples of topographic survey points, are widely used to represent surfaces and to derive land-surface parameters. Differencing between successive DEMs permits quantification of change, which in gravel-bed rivers is used to construct a morphological budget of lower bound estimates of sediment flux and bed-stability surrogate. Choice of DEM interpolation method strongly influences DEM quality and realistic representation of channel forms. When comparing morphological budgets between multiple contrasting reaches, e.g. for rapid ecological appraisal, an effective and consistent means of DEM construction is required to avoid digitally generated inconsistencies. An appropriate interpolation method should be suitable for accurate representation of channels contrasting in substrate and hydraulic conditions, surveys of varying data density and distribution, and avoidance of site-specific parameterization. This paper investigates representation of channel form using a series of DEMs generated within Surfer® by triangulation with linear interpolation, natural neighbours, point kriging, universal kriging, multiquadratic radial basis function, modified Shepard's method and inverse distance to a power on the example of four reaches of mountain streams in New Zealand. These reaches represent a diversity of channel forms, substrate and hydraulic properties. DEMs from triangulation with linear interpolation revealed consistently the best results and this method is recommended for geomorphological and ecological studies of multiple reaches. The main advantage over point kriging and radial basis function is better representation of channel margins and bedforms without introduction of breaklines, while it outperforms natural neighbours in honouring measured points. Copyright © 2010 John Wiley & Sons, Ltd.

Abstract: The paper proposes an interpolation error expansion reversible watermarking algorithm. The main novelty of the paper is a modified rhombus interpolation scheme. The four horizontal and vertical neighbors are considered and, depending on their values, the interpolated pixel is computed as the average of the horizontal pixels, of the vertical pixels or of the entire set of four pixels. Experimental results are provided. The proposed scheme outperforms the results obtained by using the average on the four horizontal and vertical neighbors and the ones obtained by using well known predictors as MED or GAP.

Abstract: Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). We also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics $\sigma_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones.

Abstract: In this paper, we address the problem of image bit-depth expansion and present a novel method to generate high bit-depth (HBD) images from a single low bit-depth (LBD) image. We expand image bit-depth by reconstructing the least significant bits (LSBs) for the LBD image after it is rescaled to high bit-depth. For image regions whose intensities are neither locally maximum nor minimum, neighborhood flooding is applied to convert 2D interpolation problem into 1D interpolation, for local maxima/minima (LMM) regions where interpolation is not applicable, a virtual skeleton marking algorithm is proposed to convert problematic 2D extrapolation problem into 1D interpolation. At last, a content-adaptive reconstruction model is proposed to obtain the output HBD image. The experimental results show that proposed method significantly outperforms existing methods in PSNR and SSIM without contouring artifacts.

Abstract: We employed an informatics mathematical approach, namely: the ArcMap [a component of ESRI’s ArcGIS Geographical Information System (GIS), for Microsoft Windows],

Abstract: Point spread function (PSF) modelling is a central part of any astronomy data analysis relying on measuring the shapes of objects. It is especially crucial for weak gravitational lensing, in order to beat down systematics and allow one to reach the full potential of weak lensing in measuring dark energy. A PSF modelling pipeline is made of two main steps: the first one is to assess its shape on stars, and the second is to interpolate it at any desired position (usually galaxies). We focus on the second part, and compare different interpolation schemes, including polynomial interpolation, radial basis functions, Delaunay triangulation and Kriging. For that purpose, we develop simulations of PSF fields, in which stars are built from a set of basis functions defined from a principal components analysis of a real ground-based image. We find that Kriging gives the most reliable interpolation, significantly better than the traditionally used polynomial interpolation.We also note that although a Kriging interpolation on individual images is enough to control systematics at the level necessary for current weak lensing surveys, more elaborate techniques will have to be developed to reach future ambitious surveys’ requirements.

Abstract: New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naive approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to ...

Abstract: When using motion fields to interpolate between two consecutive images in an image sequence, a major problem is to handle occlusions and disclusions properly. However, in most cases, one of both images contains the information that is either discluded or occluded; if the first image contains the information (i.e., the region will be occluded), forward interpolation shall be employed, while for information that is contained in the second image (i.e., the region will be discluded), one should use backward interpolation. Hence, we propose to improve an existing approach for image sequence interpolation by incorporating an automatic segmentation in the process, which decides in which region of the image forward or backward interpolation shall be used. Our approach is a combination of the optimal transport approach to image sequence interpolation and the segmentation by the Chan-Vese approach. We propose to solve the resulting optimality condition by a segregation loop, combined with a level set approach. We provide examples that illustrate the performance both in the interpolation error and in the human perception.

Abstract: Two methods of the spatial interpolation [Inverse Distance Weighting (IDW) and the Kriging], often used in the Geographical Information System (GIS), have been applied on the mapping of the annual amount of precipitation in Bosnia and Herzegovina. For that purpose the monthly precipitation data obtained from meteorological network in the period 1960-2011. The validation of the analyzed data has been carried out by using 20-meter resolution Digital Elevation Model (DEM). The methods, which are suitable for the spatial interpolation for Bosnia and Herzegovina area, particularly for the orographic regions, were analyzed. First, the IDW linear interpolator was considered. However, in the mountain region, this method can give unrealistic results („Bulls Eyes“ effect). Namely, this effect leads to occurrence of the isohyets, which are closed around the meteorological station that is not acceptable in analysis of the pluviometric regime in the real relief. In contrast to this method the Kriging method is much more acceptable because of its (i) adaptability to the relief configuration, (ii) fast data processing and (iii) high precision in calculating the precipitation and corresponding climate indexes for the high resolution of the grid cell. An acceptable annual pluviometric model with the 50x50 m resolution has been obtained by the application of the Kriging method, which was applicable at the local spatial scale, particularly in the orographic regions. More precisely, the designed annual pluviometric model is characterized by the high precision in the areas with the pronounced relief dynamics, where the energetic classes are above 6th category.

Abstract: In this paper, we tackle the problem of spatial interpolation for distributed estimation in Wireless Sensor Networks by using a geostatistical technique called kriging. We present a novel Distributed Iterative Kriging Algorithm (DIKA) which is composed of two main phases. First, the spatial dependence of the field is exploited by calculating semivariograms in an iterative way. Second, the kriging system of equations is solved by an initial set of nodes in a distributed manner, providing some initial interpolation weights to each node. In our algorithm, the estimation accuracy can be improved by iteratively adding new nodes and updating appropriately the weights, which leads to a reduction in the kriging variance. As a consequence, each cluster is constructed adaptively by the set of nodes that achieves the best estimation over the sub-area covered by them. We analyze the most influential parameters to implement this algorithm. Finally, we evaluate the performance of our algorithm and we also analyze its complexity.

Abstract: Air temperature represents a key parameter for snow hydrology, as it controls the precipitation phase, as well as snow accumulation and snowmelt. Hydrological modelling in mountain regions like the Alps needs high-resolution temperature fields as input, preferably at sub-daily time steps. The estimation of such temperature fields is challenging due to the spatio-temporal variability of environmental lapse rates (i.e. the decreasing of temperature with altitude) associated to complex topography. In this study, 10 years (2000–2009) of data from about 200 temperature stations were interpolated at 0, 6, 12 and 18 h Universal Time Coordinated (UTC) over a 1-km resolution grid covering a window of 71 500 km2 in the Northern French Alps. Three different kriging methods were tested. Kriging with elevation as external drift gave the best results in terms of mean absolute error, root mean square error and kriging standard deviation. Adding potential solar radiation as an additional external variable did not improve significantly the interpolation results. Prediction errors showed dependence on elevation and season, as well as on the time of interpolation, with globally better results in summer and daytime than in winter and night-time. Despite some shortcomings that are discussed in the paper, the interpolated temperature fields look promising for further snowmelt and snow cover dynamics modelling studies. Copyright © 2012 John Wiley & Sons, Ltd.

Abstract: Comment on discussions provided for "Bayesian Computation Using Design of Experiments-Based Interpolation Technique," which have compared the DoIt approximation to several alternative methods for Bayesian computation.