Abstract: As the use of Quantitative Structure Activity Relationship (QSAR) models for chemical management increases, the reliability of the predictions from such models is a matter of growing concern. The OECD QSAR Validation Principles recommend that a model should be used within its applicability domain (AD). The Setubal Workshop report provided conceptual guidance on defining a (Q)SAR AD, but it is difficult to use directly. The practical application of the AD concept requires an operational definition that permits the design of an automatic (computerised), quantitative procedure to determine a models AD. An attempt is made to address this need, and methods and criteria for estimating AD through training set interpolation in descriptor space are reviewed. It is proposed that response space should be included in the training set representation. Thus, training set chemicals are points in n-dimensional descriptor space and m-dimensional model response space. Four major approaches for estimating interpolation regions in a multivariate space are reviewed and compared: range, distance, geometrical, and probability density distribution.

Abstract: A cost-effective digital camera uses a single-image sensor, applying alternating patterns of red, green, and blue color filters to each pixel location. A way to reconstruct a full three-color representation of color images by estimating the missing pixel components in each color plane is called a demosaicing algorithm. This paper presents three inherent problems often associated with demosaicing algorithms that incorporate two-dimensional (2-D) directional interpolation: misguidance color artifacts, interpolation color artifacts, and aliasing. The level of misguidance color artifacts present in two images can be compared using metric neighborhood modeling. The proposed demosaicing algorithm estimates missing pixels by interpolating in the direction with fewer color artifacts. The aliasing problem is addressed by applying filterbank techniques to 2-D directional interpolation. The interpolation artifacts are reduced using a nonlinear iterative procedure. Experimental results using digital images confirm the effectiveness of this approach.

Abstract: The estimation of the frequency of a complex exponential is a problem that is relevant to a large number of fields. In this paper, we propose and analyze two new frequency estimators that interpolate on the Fourier coefficients of the received signal samples. The estimators are shown to achieve identical asymptotic performances. They are asymptotically unbiased and normally distributed with a variance that is only 1.0147 times the asymptotic Crame/spl acute/r-Rao bound (ACRB) uniformly over the frequency estimation range.

Abstract: We consider the problem of estimating the covariance of two diffusion processes when they are observed only at discrete times in a non-synchronous manner. The modern, popular approach in the literature, the realized covariance estimator, which is based on (regularly spaced) synchronous data, is problematic because the choice of regular interval size and data interpolation scheme may lead to unreliable estimation. We propose a new estimator which is free of any `synchronization' processing of the original data, hence free of bias or other problems caused by it.

Abstract: We describe algebraic methods for creating implicit surfaces using linear combinations of radial basis interpolants to form complex models from scattered surface points. Shapes with arbitrary topology are easily represented without the usual interpolation or aliasing errors arising from discrete sampling. These methods were first applied to implicit surfaces by Savchenko, et al. and later developed independently by Turk and O'Brien as a means of performing shape interpolation. Earlier approaches were limited as a modeling mechanism because of the order of the computational complexity involved. We explore and extend these implicit interpolating methods to make them suitable for systems of large numbers of scattered surface points by using compactly supported radial basis interpolants. The use of compactly supported elements generates a sparse solution space, reducing the computational complexity and making the technique practical for large models. The local nature of compactly supported radial basis functions permits the use of computational techniques and data structures such as k-d trees for spatial subdivision, promoting fast solvers and methods to divide and conquer many of the subproblems associated with these methods. Moreover, the representation of complex models permits the exploration of diverse surface geometry. This reduction in computational complexity enables the application of these methods to the study of shape properties of large complex shapes.

Abstract: In this work, we focus our interest on blind source camera identification problem by extending our results in the direction of M. Kharrazi et al. (2004). The interpolation in the color surface of an image due to the use of a color filter array (CFA) forms the basis of the paper. We propose to identify the source camera of an image based on traces of the proprietary interpolation algorithm deployed by a digital camera. For this purpose, a set of image characteristics are defined and then used in conjunction with a support vector machine based multi-class classifier to determine the originating digital camera. We also provide initial results on identifying source among two and three digital cameras.

Abstract: The purpose of this paper is to give a local tricubic interpolation scheme in three dimensions that is both C^1 and isotropic. The algorithm is based on a specific 64 × 64 matrix that gives the relationship between the derivatives at the corners of the elements and the coefficients of the tricubic interpolant for this element. In contrast with global interpolation where the interpolated function usually depends on the whole data set, our tricubic local interpolation only uses data in a neighbourhood of an element. We show that the resulting interpolated function and its three first derivatives are continuous if one uses cubic interpolants. The implementation of the interpolator can be downloaded as a static and dynamic library for most platforms. The major difference between this work and current local interpolation schemes is that we do not separate the problem into three one-dimensional problems. This allows for a much easier and accurate computation of higher derivatives of the extrapolated field. Applications to the computation of Lagrangian coherent structures in ocean data are briefly discussed.

Abstract: This paper explores the effects of terrain morphology, sampling density, and interpolation methods for scattered sample data on the accuracy of interpolated heights in grid Digital Elevation Models (DEM). Sampled data were collected with a 2 by 2 meters sampling interval from seven different morphologies, applying digital photogrammetric methods to large scale aerial stereo imagery (1:5000). The experimen- tal design was outlined using a factorial scheme, and an analysis of variance was carried out. This analysis yielded the following main conclusions: DEM accuracy (RMSE) is affected significantly by the variables studied in this paper according to "morphologysampling densityinterpola- tion" method. Multiquadric Radial Basis Function (RBF) was rated as the best interpolation method, although Multilog RBF performed similarly for most morphologies. The rest of RBF interpolants tested (Natural Cubic Splines, Inverse Multiquadric, and Thin Plate Splines) showed numerical instability working with low smoothing factors. Inverse Distance Weighted interpolant performed worse than RBF Multiquadric or RBF Multilog. In addition, it is found that the relationship between the RMSE and the sampling density N is adjusted to a decreasing potential function that may be expressed as RMSE/Sdz � 0.1906(N/M) � 0.5684 (R 2 � 0.8578), being Sdz the standard deviation of the heights of the M check points used for accuracy estimation, and N the number of sampling points used for creating the DEM. The results obtained in this study allow us to observe the possibility of establishing empirical relationships between the RMSE expected in the interpolation of a Grid DEM and such variables as terrain ruggedness, sampling density, and the interpolation method, among others that could be added. Therefore, it would be possible to establish a priori the optimum grid size required to generate or storage a DEM of a particular accuracy, with the economy in computing time and file size that this would signify for the digital flow of the mapping information.

Abstract: Basic Theory.- Linear Interpolation.- Polynomial Interpolation.- Hermite Interpolation.- Spline Interpolation.- Bezier Approximation.- B-Spline Approximation.- Subdivision Methods.- Sweep Surfaces.

Abstract: In this letter, we describe a new method for bidimensional empirical mode decomposition (EMD). This decomposition is based on Delaunay triangulation and on piecewise cubic polynomial interpolation. Particular attention is devoted to boundary conditions that are crucial for the feasibility of the bidimensional EMD. The study of the behavior of the decomposition on a different kind of image shows its efficiency in terms of computational cost, and the decomposition of Gaussian white noises leads to bidimensional selective filter banks.

Abstract: In this paper, we develop a set of data processing algorithms for generating textured facade meshes of cities from a series of vertical 2D surface scans and camera images, obtained by a laser scanner and digital camera while driving on public roads under normal traffic conditions. These processing steps are needed to cope with imperfections and non-idealities inherent in laser scanning systems such as occlusions and reflections from glass surfaces. The data is divided into easy-to-handle quasi-linear segments corresponding to approximately straight driving direction and sequential topological order of vertical laser scans; each segment is then transformed into a depth image. Dominant building structures are detected in the depth images, and points are classified into foreground and background layers. Large holes in the background layer, caused by occlusion from foreground layer objects, are filled in by planar or horizontal interpolation. The depth image is further processed by removing isolated points and filling remaining small holes. The foreground objects also leave holes in the texture of building facades, which are filled by horizontal and vertical interpolation in low frequency regions, or by a copy-paste method otherwise. We apply the above steps to a large set of data of downtown Berkeley with several million 3D points, in order to obtain texture-mapped 3D models.

Abstract: A common motion interpolation technique for realistic human animation is to blend similar motion samples with weighting functions whose parameters are embedded in an abstract space. Existing methods, however, are insensitive to statistical properties, such as correlations between motions. In addition, they lack the capability to quantitatively evaluate the reliability of synthesized motions. This paper proposes a method that treats motion interpolations as statistical predictions of missing data in an arbitrarily definable parametric space. A practical technique of geostatistics, called universal kriging, is then introduced for statistically estimating the correlations between the dissimilarity of motions and the distance in the parametric space. Our method statistically optimizes interpolation kernels for given parameters at each frame, using a pose distance metric to efficiently analyze the correlation. Motions are accurately predicted for the spatial constraints represented in the parametric space, and they therefore have few undesirable artifacts, if any. This property alleviates the problem of spatial inconsistencies, such as foot-sliding, that are associated with many existing methods. Moreover, numerical estimates for the reliability of predictions enable motions to be adaptively sampled. Since the interpolation kernels are computed with a linear system in real-time, motions can be interactively edited using various spatial controls.

Abstract: A novel algorithm is introduced that can detect the presence of interpolation in images prior to compression as well as estimate the interpolation factor. The interpolation detection algorithm exploits a periodicity in the second derivative signal of interpolated images. The algorithm performs well for a wide variety of interpolation factors, both integer factors and non-integer factors. The algorithm performance is noted with respect to a digital camera's "digital zoom" feature. Overall the algorithm has demonstrated robust results and might prove to be useful for situations where an original resolution of the image determines the action of an image processing chain.

Abstract: A meshfree radial point interpolation method (RPIM) is developed for stress analysis of three-dimensional (3D) solids, based on the Galerkin weak form formulation using 3D meshfree shape functions constructed using radial basis functions (RBFs). As the RPIM shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite element method (FEM). Numerical examples of 3D solids are presented to verify validity and accuracy of the present RPIM method, and intensive numerical study has been conducted to investigate the effects of some important parameters. It is demonstrated that the present meshfree RPIM is robust, stable, and reliable for stress analysis of 3D solids.

Abstract: With airborne laser scanning points are measured on the terrain surface, and on other objects as buildings and vegetation. With socalled filtering methods a classification of the points into terrain and object points is performed. In the literature two approaches – i.e. a general strategies for solving the problem – for filtering can be identified. The first work directly on the measured points and geometric criteria are used for the decision, if a point is on the ground or an object point. The methods from the second approach first segment the data and then make a classification based on segments. In this paper we present a new approach for filtering. It is a combination of both approaches, specifically exploiting their strengths. A filter method following this new approach is developed and demonstrated by examples.

Abstract: An efficient depth image based rendering with edge dependent depth filter and interpolation is proposed. The proposed method can solve the hole-filling problem in DIBR system efficiently with high quality. The PSNR of the proposed method is better than the previous work by 6 dB and the subjective view shows the quality is better. In addition to that, the number of instruction cycles is 3.7 percent compared with the previous work

Abstract: The Model Coupling Toolkit (MCT) is a software library for constructing parallel coupled models from individual parallel models. MCT was created to address the challenges of creating a parallel coupler for the Community Climate System Model (CCSM). Each of the submodels that make up CCSM is a separate parallel application with its own domain decomposition, running on its own set of processors. This application contains multiple instances of the MXN problem, the problem of transferring data between two parallel programs running on disjoint sets of processors. CCSM also requires efficient data transfer to facilitate its interpolation algorithms. MCT was created as a generalized solution to handle these and other common functions in parallel coupled models. Here we describe MCT's implementation of the data transfer infrastructure needed for a parallel coupled model. The performance of MCT scales satisfactorily as processors are added to the system. However, the types of decompositions used in the submodels can affect performance. MCT's infrastructure provides a flexible and high-performing set of tools for enabling interoperability between parallel applications.

Abstract: By use of matrix-based techniques it is shown how the space–bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.

Abstract: REPRODUCING KERNEL HILBERT SPACES Baver Okutmustur M.S. in Mathematics Supervisor: Assist. Prof. Dr. Aurelian Gheondea August, 2005 In this thesis we make a survey of the theory of reproducing kernel Hilbert spaces associated with positive definite kernels and we illustrate their applications for interpolation problems of Nevanlinna-Pick type. Firstly we focus on the properties of reproducing kernel Hilbert spaces, generation of new spaces and relationships between their kernels and some theorems on extensions of functions and kernels. One of the most useful reproducing kernel Hilbert spaces, the Bergman space, is studied in details in chapter 3. After giving a brief definition of Hardy spaces, we dedicate the last part for applications of interpolation problems of NevanlinnaPick type with three main theorems: interpolation with a finite number of points, interpolation with an infinite number of points and interpolation with points on the boundary. Finally we include an Appendix that contains a brief recall of the main results from functional analysis and operator theory.

Abstract: Image deformation methods in particle image velocimetry are becoming more and more accepted by the scientific community but some aspects have not been thoroughly investigated neither theoretically nor with the aid of simulations. A fundamental step in this type of algorithm is reconstruction of the deformed images that requires the use of an interpolation scheme. The aim of this paper is to examine the influence of this aspect on the accuracy of the PIV algorithm. The performance assessment has been conducted using synthetic images and the results show that both the systematic and total errors are strongly influenced by the interpolation scheme used in the reconstruction of the deformed images. Time performances and the influence of particle diameter are also analysed.

Abstract: We present a new method for numerically reconstructing digital holograms on tilted planes. The method is based on the angular spectrum of plane waves. Fast Fourier transform algorithm is used twice and coordinate rotation in the Fourier domain enables to reconstruct the object field on the tilted planes. Correction of the anamorphism resulting from the coordinate transformation is performed by suitable interpolation of the spectral data. Experimental results are presented to demonstrate the method for a singleaxis rotation. The algorithm is especially useful for tomographic image reconstruction.

Abstract: Natural head motion is important to realistic facial animation and engaging human–computer interactions. In this paper, we present a novel data-driven approach to synthesize appropriate head motion by sampling from trained hidden markov models (HMMs). First, while an actress recited a corpus specifically designed to elicit various emotions, her 3D head motion was captured and further processed to construct a head motion database that included synchronized speech information. Then, an HMM for each discrete head motion representation (derived directly from data using vector quantization) was created by using acoustic prosodic features derived from speech. Finally, first-order Markov models and interpolation techniques were used to smooth the synthesized sequence. Our comparison experiments and novel synthesis results show that synthesized head motions follow the temporal dynamic behavior of real human subjects. Copyright © 2005 John Wiley & Sons, Ltd.

Abstract: Data processing for the spatial analysis of small-area social, demographic, and economic data often requires the combination of data spatially aggregated to two or more incompatible zone systems in a region, such as a set of enumeration districts that changes over time. Such situations can be addressed by areal interpolation—the transfer of data between zonal systems according to spatial algorithms. The authors test a technique of areal interpolation using geographic information systems (GIS) that employs a digital map layer representing streets and roads to derive varying density weights for small areas within aggregation zones. The technique reduces errors in estimation compared with estimates derived using the commonly applied area-weighting technique, with its assumption of uniform density. The street-weighting technique is much easier to use than other interpolation techniques that have also been shown to reduce error compared with area-based weighting.

Abstract: Video stabilization is an important video enhancement technology which aims at removing annoying shaky motion from videos. We propose a practical and robust approach of video stabilization that produces full-frame stabilized videos with good visual quality. While most previous methods end up with producing low resolution stabilized videos, our completion method can produce full-frame videos by naturally filling in missing image parts by locally aligning image data of neighboring frames. To achieve this, motion inpainting is proposed to enforce spatial and temporal consistency of the completion in both static and dynamic image areas. In addition, image quality in the stabilized video is enhanced with a new practical deblurring algorithm. Instead of estimating point spread functions, our method transfers and interpolates sharper image pixels of neighbouring frames to increase the sharpness of the frame. The proposed video completion and deblurring methods enabled us to develop a complete video stabilizer which can naturally keep the original image quality in the stabilized videos. The effectiveness of our method is confirmed by extensive experiments over a wide variety of videos.

Abstract: The goal of this paper is to construct data-independent optimal point sets for interpolation by radial basis functions. The interpolation points are chosen to be uniformly good for all functions from the associated native Hilbert space. To this end we collect various results on the power function, which we use to show that good interpolation points are always uniformly distributed in a certain sense. We also prove convergence of two different greedy algorithms for the construction of near-optimal sets which lead to stable interpolation. Finally, we provide several examples.