Abstract: A comprehensive archive of Australian rainfall and climate data has been constructed from ground-based observational data. Continuous, daily time step records have been constructed using spatial interpolation algorithms to estimate missing data. Datasets have been constructed for daily rainfall, maximum and minimum temperatures, evaporation, solar radiation and vapour pressure. Datasets are available for approximately 4600 locations across Australia, commencing in 1890 for rainfall and 1957 for climate variables. The datasets can be accessed on the Internet at http://www.dnr.qld.gov.au/silo. Interpolated surfaces have been computed on a regular 0.05° grid extending from latitude 10°S to 44°S and longitude 112°E to 154°E. A thin plate smoothing spline was used to interpolate daily climate variables, and ordinary kriging was used to interpolate daily and monthly rainfall. Independent cross validation has been used to analyse the temporal and spatial error of the interpolated data. An Internet based facility has been developed which allows database clients to interrogate the gridded surfaces at any desired location.

Abstract: We develop methods for adjusting grid box average temperature time series for the effects on variance of changing numbers of contributing data. Owing to the different sampling characteristics of the data, we use different techniques over land and ocean. The result is to damp average temperature anomalies over a grid box by an amount inversely related to the number of contributing stations or observations. Variance corrections influence all grid box time series but have their greatest effects over data sparse oceanic regions. After adjustment, the grid box land and ocean surface temperature data sets are unaffected by artificial variance changes which might affect, in particular, the results of analyses of the incidence of extreme values. We combine the adjusted land surface air temperature and sea surface temperature data sets and apply a limited spatial interpolation. The effects of our procedures on hemispheric and global temperature anomaly series are small.

Abstract: A geostatistical framework for integrating lower-atmosphere state variables and terrain characteristics into the spatial interpolation of rainfall is presented. Lower-atmosphere state variables considered are specific humidity and wind, derived from an assimilated data product from the National Centers for Environmental Prediction and the National Center for Atmospheric Research (NCEP–NCAR reanalysis). These variables, along with terrain elevation and its gradient from a 1-km-resolution digital elevation model, are used for constructing additional rainfall predictors, such as the amount of moisture subject to orographic lifting; these latter predictors quantify the interaction of lower-atmosphere characteristics with local terrain. A “first-guess” field of precipitation estimates is constructed via a multiple regression model using collocated rain gauge observations and rainfall predictors. The final map of rainfall estimates is derived by adding to this initial field a field of spatially interpo...

Abstract: Hidden Markov trees in the wavelet domain are capable of accurately modeling the statistical behavior of real world signals by exploiting relationships between coefficients in different scales. The model is used to interpolate images by predicting coefficients at finer scales. Various optimizations and post-processing steps are also investigated to determine their effect on the performance of the interpolation. The interpolation algorithm was found to produce noticeably sharper images with PSNR values which outperform many other interpolation techniques on a variety of images.

Abstract: A multivariate (MV) optimal statistical interpolation method is applied to conductivity–temperature–depth (CTD) and ship-mounted acoustic doppler current profiler (ADCP) data from quasi-synoptic oceanographic surveys. MV analysis aims to improve the spatial interpolation of any particular variable (e.g., dynamic height) by including in the analysis observations of other physically related variables (e.g., current). The version used in this work also provides estimates of the non-divergent and irrotational components of the flow. The method is tested in a sharp frontal region to the north of the Western Alboran gyre. After deriving the optimal analysis parameters, we first show that MV statistical dynamic height analysis errors are significantly smaller than those derived from univariate (UV) analysis. In our region, this translates in a more realistic shape for the geostrophic relative vorticity and the vertical velocity field. The latter peaks at about 45 m/day (as given by the quasi-geostrophic omega equation), with a tendency for light water to be upwelled upstream of the gyre while denser water is downwelled downstream of the gyre. For the horizontal velocity we show the existence of large (up to 40 cm/s) ageostrophic velocities. These are mainly non-divergent and can be explained by the cyclostrophic acceleration induced by the anticyclonic gyre. The irrotational velocity component is of the order of 10 cm/s towards the dense side of the front. The robustness of the method is checked by means of several tests that evaluate the sensitivity of results with respect to the synopticity of the data, the analysis parameters, the reference level and the presence of tidal or inertial currents.

Abstract: This paper describes the spatial interpolation of daily minimum air temperature using a feed-forward back-propagation neural network Simple network configurations were trained to predict minimum temperature using as inputs: (1) date and terrain variables; (2) temperature observations at a number of neighbouring locations; (3) date, terrain variables and neighbouring temperature observations This is the first time that trend and spatial association are explicitly considered together when interpolating using a neural network The internal weights given to different inputs to the network were analysed to estimate the degree of spatial correlation between neighbouring stations in addition to the most influential variables contributing to the underlying trend The spatial distribution of daily minimum temperature was estimated with the greatest accuracy by a network trained on the most comprehensive data set (3) The best model for the prediction of temperature accounts for 93% of the variance, measured by t

Abstract: Compositional data are very common in the earth sciences. Nevertheless, little attention has been paid to the spatial interpolation of these data sets. Most interpolators do not necessarily satisfy the constant sum and nonnegativity constraints of compositional data, nor take spatial structure into account. Therefore, compositional kriging is introduced as a straightforward extension of ordinary kriging that complies with these constraints. In two case studies, the performance of compositional kriging is compared with that of the additive logratio-transform. In the first case study, compositional kriging yielded significantly more accurate predictions than the additive logratio-transform, while in the second case study the performances were comparable.

Abstract: We propose a new general algorithm for constructing interpolation weights in algebraic multigrid (AMG). It exploits a proper extension mapping outside a neighborhood about a fine degree of freedom (dof) to be interpolated. The extension mapping provides boundary values (based on the coarse dofs used to perform the interpolation) at the boundary of the neighborhood. The interpolation value is then obtained by matrix dependent harmonic extension of the boundary values into the interior of the neighborhood. We describe the method, present examples of useful extension operators, provide a two-grid analysis of model problems, and, by way of numerical experiments, demonstrate the successful application of the method to discretized elliptic problems.

Abstract: The spatial distribution of a pollutant in contaminated soils is usually highly skewed. As a result, the sample variogram often differs considerably from its regional counterpart and the geostatistical interpolation is hindered. In this study, rank-order geostatistics with standardized rank transformation was used for the spatial interpolation of pollutants with a highly skewed distribution in contaminated soils when commonly used nonlinear methods, such as logarithmic and normal-scored transformations, are not suitable. A real data set of soil Cd concentrations with great variation and high skewness in a contaminated site of Taiwan was used for illustration. The spatial dependence of ranks transformed from Cd concentrations was identified and kriging estimation was readily performed in the standardized-rank space. The estimated standardized rank was back-transformed into the concentration space using the middle point model within a standardized-rank interval of the empirical distribution function (EDF). The spatial distribution of Cd concentrations was then obtained. The probability of Cd concentration being higher than a given cutoff value also can be estimated by using the estimated distribution of standardized ranks. The contour maps of Cd concentrations and the probabilities of Cd concentrations being higher than the cutoff value can be simultaneously used for delineation of hazardous areas of contaminated soils.

Abstract: The air temperature is one of the main input data in models for water balance monitoring or crop models for yield prediction. The different phenological stages of plant growth are generally defined according to cumulated air temperature from the sowing date. When these crop models are used at the regional scale, the meteorological stations providing input climatic data are not spatially dense enough or in a similar environment to reflect the crop local climate. Hence spatial interpolation methods must be used. Climatic data, particularly air temperature, are influenced by local environment. Measurements show that the air above dry surfaces is warmer than above wet areas. We propose a method taking into account the environment of the meteorological stations in order to improve spatial interpolation of air temperature. The aim of this study is to assess the impact of these “corrected climatic data” in crop models. The proposed method is an external drift kriging where the Kriging system is modified to correct local environment effects. The environment of the meteorological stations was characterized using a land use map summarized in a small number of classes considered as a factor influencing local temperature. This method was applied to a region in south-east France (150×250 km) where daily temperatures were measured on 150 weather stations for two years. Environment classes were extracted from the CORINE Landcover map obtained from remote sensing data. Categorical external drift kriging was compared to ordinary kriging by a cross validation study. The gain in precision was assessed for different environment classes and for summer days. We then performed a sensitivity study of air temperature with the crop model STICS. The influence of interpolation corrections on the main outputs as yield or harvest date is discussed. We showed that the method works well for air temperature in summer and can lead to significant correction for yield prediction. For example, we observed by cross validation a bias reduction of 0.5 to 1.0°C (exceptionally 2.5°C for some class), which corresponds to differences in yield prediction from 0.6 to 1.5 t/ha.

Abstract: The interpolation of continuous surfaces from discrete points is supported by most GIS software packages. Some packages provide additional options for the interpolation from 3D line objects, for example surface-specific lines, or contour lines digitized from topographic maps. Demographic, social and economic data can also be used to construct and display smooth surfaces. The variables are usually published as sums for polygonal units, such as the number of inhabitants in communities or counties. In the case of point and line objects the geometric properties have to be maintained in the interpolated surface. For polygon-based data the geometric properties of the polygon boundary and the volume should be preserved, avoiding redistribution of parts of the volume to neighboring units during interpolation. The pycnophylactic interpolation method computes a continuous surface from polygon-based data and simultaneously enforces volume preservation in the polygons. The original procedure using a regular grid is extended to surface representations based on an irregular triangular network (TIN).

Abstract: In this paper, we will consider the interpolation of fuzzy data by fuzzy-valued complete splines. Finally, we will give the numerical solutions of the illustrative examples.

Abstract: Lagragne interpolation schemes are constructed based on C1 cubic splines on certain triangulations obtained from checkerboard quadrangulations.

Abstract: A method and system for image resample by spatial interpolation The method and system allow more than simple angle interpolation by allowing spatial interpolation to be performed on small angle edges Multiple interpolation directions are established Once an interpolation direction is selected, verifications are performed on the selected interpolation direction in order to rule out erroneous selection If the selected interpolation direction passes all verification, then spatial interpolation will be performed along the selected interpolation direction Otherwise, a default interpolation direction is used as the interpolation direction

Abstract: Temporal interpolation has been proposed as a solution for increasing temporal resolution or even for predicting missing or corrupted frames within a video sequence. In this paper new techniques on temporal interpolation are presented, by mainly exploiting properties of the very popular and highly efficient zonal based motion estimation algorithms, and by introducing several other techniques such as multihypothesis motion compensation, motion classification and temporal/spatial filtering. In addition we further give an analysis on when temporal interpolation should be employed, thus possibly avoiding unwanted artifacts created from this process, while at the same time significantly improving the overall performance of the interpolation.

Abstract: A technique for neural network time series prediction using radial basis functions, where the input data contain a significant proportion of missing points, is developed. This technique is intended to model the data while simultaneously providing a means of minimizing the impact upon the model of the missing points that are typical of geophysical time series. The two issues are inextricably entwined because missing data points have a significant impact upon the performance of data-derived models in terms of prediction availability and accuracy. The core of the technique is a nonlinear interpolation scheme that assigns values to gaps in the input time series. Each missing point is interpolated such that the error introduced into any specific predictive function is minimized. This interpolative technique has a general application in any instance where the effects of interpolation upon a given analysis process need to be minimized or a complete time series needs to be constructed from incomplete data. The technique has been applied to the prediction of ƒ0F2 from Slough, United Kingdom. The resultant model prediction root-mean-square (RMS) error is shown to be 2.3% better than using recurrence interpolation (in terms of overall model accuracy rather than relative to each other), 3.8% better than using persistence interpolation, and 34.3% better than not using any interpolation. Utilizing the interpolation algorithm lowers the RMS error by 26% when incomplete data, in addition to complete data, are used as an input to both the interpolated and the uninterpolated models.

Abstract: A new algorithm for the interpolation of temporal intermediate images using polyphase weighted median filters is proposed in this paper. To achieve a good interpolation quality not only in still but also in moving areas of the image, vector based interpolation techniques have to be used. However, motion estimation on natural image scenes always suffers from errors in the estimated motion vector field. Therefore it is of great importance that the interpolation algorithm possesses a sufficient robustness against vector errors. Depending on the input and output frame repetition rate, different cyclically repeated interpolation phases can be distinguished. The new interpolation algorithm uses dedicated weighted median filters for each interpolation phase (polyphase weighted median filters) which are (due to their shift property) able to achieve a correct positioning of moving edges in the interpolated image, even if the estimated vector differs from the true motion vector up to a certain degree. A new design method for these dedicated error tolerant weighted median filters is presented in the paper. Other aspects like e.g. the preservation of fine image details can also be regarded in the design process. The results of the new algorithm are compared to other existing interpolation algorithms.

Abstract: Image sequence interpolation, or to obtain an up-sampled image sequence equivalently from a corresponding low-resolution image sequence, is an ill-posed inverse problem. In this study, three processing steps, namely, regularization, discretization and optimization, are used to convert the image sequence interpolation problem into a solvable optimization problem. In regularization, a fitness function combining a set of spatial and temporal performance measures for rating the quality of the interpolated (up-sampled) images is defined, which is used to convert the original ill-posed interpolation problem into a well-posed optimization problem. Discretization transforms the well-posed problem into a discrete one so that it can be solved numerically. Genetic algorithms (GAs) are used to optimize the solution in the discrete solution space using three basic operations, namely, reproduction, crossover and mutation. In the proposed approach, instead of only the spatial information within the current image frame employed in most existing methods, both the spatial and temporal information within the image sequence can be employed. Based on the experimental results obtained in this study, the interpolation results by the proposed approach are always better than those from the three existing approaches used for comparison. This shows the feasibility of the proposed approach.

Abstract: Multilevel scattered data interpolation requires decomposing the given data into a hierarchy of nested subsets. This paper concerns the efficient construction of such hierarchies. To this end, a recursive filter scheme for scattered data is proposed which generates hierarchies of locally optimal nested subsets. The scheme is a composition of greedy thinning, a recursive point removal strategy, and exchange, a local optimization procedure. The utility of the filter scheme for multilevel interpolation using radial basis functions is shown by numerical examples.

Abstract: In order to assess the impact of natural and anthropogenic stresses on forest ecosystems, it is necessary to interpolate air temperature and tropospheric ozone (O3) exposure values at high spatial resolution over complex terrain. The proposed interpolation approach was selected because of its ability to (1) account for the effect of elevation on temperature and their effects on tropospheric ozone, (2) use auxiliary data at higher spatial resolution than the variables of interest to improve the precision and accuracy of the prediction surfaces, (3) handle large amounts of data, and (4) provide not only a prediction at nonsampled locations but also a prediction standard deviation. The approach used auxiliary digital elevation model (DEM) data at 1 km resolution to improve the precision and resolution of the predictions for temperature and O3 exposure in the western United States. Initially, the study area was stratified into O3 regions based on seasonality and variability of monthly SUM06 values at 111 stations for the period 1990–1992 using rotated principal component analysis. Monthly mean daily maximum air temperatures were spatially interpolated using loess nonparametric regression and kriging of the loess residuals and interpolated to 2 km grid points of a DEM and to the ambient air quality monitoring points. Monthly O3 exposures were spatially interpolated using loess fits to relate O3 levels to elevation, predicted temperature, and the geographic coordinates and interpolated to 2 km grid points of a DEM. The elevation-based spatial interpolation procedure produced accurate and precise temperature and O3 exposure surfaces which had desirable statistical properties and were logically consistent with local topographical features and atmospheric conditions known to influence O3 formation and transport. The leave-one-out cross-validation mean absolute error was 0.93°C for the monthly mean daily maximum temperature and 1.93 ppm-h for the monthly SUM06 index for June 1990 for the western United States, comparable to published results for other regions at smaller spatial scales with less complex terrain.

Abstract: Generally, it is not easy to judge automatically and correctly whether the attribute of an image is the one belonging to logos and illustrations or the one belonging to natural pictures. Due to incorrect judgment, sometimes, unsuitable interpolation execution has occurred. Pixels interpolated by the first interpolation processing and pixels interpolated by the second interpolation processing are blended, based on a predetermined evaluation function, and placed on a source image. Because the evaluation function depends on the attribute of the image, a blending ratio between the pixels interpolated separately in two modes of interpolation can be determined, according to the image attribute, with high percentages assigned to more suitable interpolation processing. The merit of each mode of interpolation processing becomes more noticeable, whereas the demerit of each becomes mild. Consequently, the invention can prevent an error in selecting an interpolation method, based on the appraised attribute of the image for which interpolation is executed.

Abstract: Image interpolation is of great importance in biomedical visualization and analysis. In this paper, we present a novel gray-level interpolation method called Directional Coherence Interpolation (DCI). The principle advantage of the proposed approach is that it leads to significantly higher visual quality in 3D rendering when compared with traditional image interpolation methods. The basis of DCI is a form of directional image-space coherence. DCI interpolates the missing image data along the maximum coherence directions (MCD), which are estimated from the local image intensity yet constrained by a generic smoothness term. Since the edges of the image and the contents of the objects are well preserved along the MCDs, DCI can incorporate image shape and structure information without the prior requirement of explicit representation of object boundary/surface. A number of experiments were performed on both synthetic and real medical images to evaluate the proposed approach. The experimental results show that in addition to the substantial improvement of visual effects (qualitative evaluation), the quantitative error measures of DCI are also better than the conventional gray level linear interpolation. Comparing with the shape-based interpolation scheme applied on gray-level images, DCI has much lower computation cost.