Enhanced spatial error concealment with directional entropy based interpolation switching

This paper describes a spatial error concealment method that uses edge related information for concealing missing macroblocks in a way that not only preserves existing edges but also avoids introducing new strong ones. The method relies on a novel switching algorithm which uses the directional entropy of neighboring edges for choosing between two interpolation methods, a directional along detected edges or a bilinear using the nearest neighboring pixels. Results show that the performance of the proposed method is subjectively and objectively (PSNR wise) better compared to both 'single interpolation' and to edge strength based switching methods.This paper describes a spatial error concealment method that uses edge related information for concealing missing macroblocks in a way that not only preserves existing edges but also avoids introducing new strong ones. The method relies on a novel switching algorithm which uses the directional entropy of neighboring edges for choosing between two interpolation methods, a directional along detected edges or a bilinear using the nearest neighboring pixels. Results show that the performance of the proposed method is subjectively and objectively (PSNR wise) better compared to both 'single interpolation' and to edge strength based switching method

Distance in spatial interpolation of daily rain gauge data

Spatial interpolation of rain gauge data is important in forcing of hydrological simulations or evaluation of weather predictions, for example. The spatial density of available data sites is often changing with time. This paper investigates the application of statistical distance, like one minus common variance of time series, between data sites instead of geographical distance in interpolation. Here, as a typical representative of interpolation methods the inverse distance weighting interpolation is applied and the test data is daily precipitation observed in Austria. Choosing statistical distance instead of geographical distance in interpolation of an actually available coarse observation network yields more robust interpolation results at sites of a denser network with actually lacking observations. The performance enhancement is in or close to mountainous terrain. This has the potential to parsimoniously densify the currently available observation network. Additionally, the success further motivates search for conceptual rain-orography interaction models as components of spatial rain interpolation algorithms in mountainous terrain

GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 2: User's manual and program listing

An efficient computer program, called GRID2D/3D, was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. The theory and method used in GRID2D/3D is described

GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 1: Theory and method

An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D

Interpolation methods for geographical data: Housing and commercial establishment markets

The estimation of commercial property prices in a touristic city can be explored through spatial interpolation methods, but in the presence of small sample sizes, auxiliary stochastic processes that are correlated with the prices of commercial establishments are needed. The aim of this paper is to compare the various estimates of commercial establishment prices in Toledo (Spain) provided by methods based on inverse distance weighting, 2-D shape functions for triangles, kriging and cokriging (the housing prices being the auxiliary stochastic process). The results indicate that kriging improves the classical interpolation methods and that cokriging has a clear advantage over kriging.

Interpolating point spread function anisotropy

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

An Ensemble Approach to Space-Time Interpolation

There has been much excitement and activity in recent years related to the relatively sudden availability of earth-related data and the computational capabilities to visualize and analyze these data. Despite the increased ability to collect and store large volumes of data, few individual data sets exist that provide both the requisite spatial and temporal observational frequency for many urban and/or regional-scale applications. The motivating view of this paper, however, is that the relative temporal richness of one data set can be leveraged with the relative spatial richness of another to fill in the gaps. We also note that any single interpolation technique has advantages and disadvantages. Particularly when focusing on the spatial or on the temporal dimension, this means that different techniques are more appropriate than others for specific types of data. We therefore propose a space- time interpolation approach whereby two interpolation methods – one for the temporal and one for the spatial dimension – are used in tandem in order to maximize the quality of the result. We call our ensemble approach the Space-Time Interpolation Environment (STIE). The primary steps within this environment include a spatial interpolator, a time-step processor, and a calibration step that enforces phenomenon-related behavioral constraints. The specific interpolation techniques used within the STIE can be chosen on the basis of suitability for the data and application at hand. In the current paper, we describe STIE conceptually including the structure of the data inputs and output, details of the primary steps (the STIE processors), and the mechanism for coordinating the data and the 1 processors. We then describe a case study focusing on urban land cover in Phoenix Arizona. Our empirical results show that STIE was effective as a space-time interpolator for urban land cover with an accuracy of 85.2% and furthermore that it was more effective than a single technique.