Abstract: Watermarking embeds information into a digital signal like audio, image, or video. Reversible image watermarking can restore the original image without any distortion after the hidden data is extracted. In this paper, we present a novel reversible watermarking scheme using an interpolation technique, which can embed a large amount of covert data into images with imperceptible modification. Different from previous watermarking schemes, we utilize the interpolation-error, the difference between interpolation value and corresponding pixel value, to embed bit ?1? or ?0? by expanding it additively or leaving it unchanged. Due to the slight modification of pixels, high image quality is preserved. Experimental results also demonstrate that the proposed scheme can provide greater payload capacity and higher image fidelity compared with other state-of-the-art schemes.

Abstract: We extend the basic theory of kriging, as applied to the design and analysis of deterministic computer experiments, to the stochastic simulation setting. Our goal is to provide flexible, interpolation-based metamodels of simulation output performance measures as functions of the controllable design or decision variables, or uncontrollable environmental variables. To accomplish this, we characterize both the intrinsic uncertainty inherent in a stochastic simulation and the extrinsic uncertainty about the unknown response surface. We use tractable examples to demonstrate why it is critical to characterize both types of uncertainty, derive general results for experiment design and analysis, and present a numerical example that illustrates the stochastic kriging method.

Abstract: Purpose: While modern clinical CT scanners under normal circumstances produce high quality images, severe artifacts degrade the image quality and the diagnostic value if metal prostheses or other metal objects are present in the field of measurement. Standard methods for metal artifact reduction (MAR) replace those parts of the projection data that are affected by metal (the so-called metal trace or metal shadow) by interpolation. However, while sinogram interpolation methods efficiently remove metal artifacts, new artifacts are often introduced, as interpolation cannot completely recover the information from the metal trace. The purpose of this work is to introduce a generalized normalization technique for MAR, allowing for efficient reduction of metal artifacts while adding almost no new ones. The method presented is compared to a standard MAR method, as well as MAR using simple length normalization. Methods: In the first step, metal is segmented in the image domain by thresholding. A 3D forward projection identifies the metal trace in the original projections. Before interpolation, the projections are normalized based on a 3D forward projection of a prior image. This prior image is obtained, for example, by a multithreshold segmentation of the initial image. The original rawdata are divided by the projection data of the prior image and, after interpolation, denormalized again. Simulations and measurements are performed to compare normalized metal artifact reduction (NMAR) to standard MAR with linear interpolation and MAR based on simple length normalization. Results: Promising results for clinical spiral cone-beam data are presented in this work. Included are patients with hip prostheses, dental fillings, and spine fixation, which were scanned at pitch values ranging from 0.9 to 3.2. Image quality is improved considerably, particularly for metal implants within bone structures or in their proximity. The improvements are evaluated by comparing profiles through images and sinograms for the different methods and by inspecting ROIs. NMAR outperforms both other methods in all cases. It reduces metal artifacts to a minimum, even close to metal regions. Even for patients with dental fillings, which cause most severe artifacts, satisfactory results are obtained with NMAR. In contrast to other methods, NMAR prevents the usual blurring of structures close to metal implants if the metal artifacts are moderate. Conclusions: NMAR clearly outperforms the other methods for both moderate and severe artifacts. The proposed method reliably reduces metal artifacts from simulated as well as from clinical CT data. Computationally efficient and inexpensive compared to iterative methods, NMAR can be used as an additional step in any conventional sinogram inpainting-based MAR method.

Abstract: Most engineering and scientific phenomena, such as the surface of a landscape or the continuously changing temperature at a location are inherently infinite in space or time or both. We cannot measure all the data. Generally it is possible to record surface elevation values or the temperature only at some specific locations and times.

Abstract: Given any scheme in conservation form and an appropriate uniform grid for the numerical solution of the initial value problem for one-dimensional hyperbolic conservation laws we describe a multiresolution algorithm that approximates this numerical solution to a prescribed tolerance in an efficient manner. To do so we consider the grid-averages of the numerical solution for a hierarchy of nested diadic grids in which the given grid is the finest, and introduce an equivalent multiresolution representation. The multiresolution representation of the numerical solution consists of its grid-averages for the coarsest grid and the set of errors in predicting the grid-averages of each level of resolution in this hierarchy from those of the next coarser one. Once the numerical solution is resolved to our satisfaction in a certain locality of some grid, then the prediction errors there are small for this particular grid and all finer ones; this enables us to compress data by setting to zero small components of the representation which fall below a prescribed tolerance. Therefore instead of computing the time-evolution of the numerical solution on the given grid we compute the time-evolution of its compressed multiresolution representation. Algorithmically this amounts to computing the numerical fluxes of the given scheme at the points of the given grid by a hierarchical algorithm which starts with the computation of these numerical fluxes at the points of the coarsest grid and then proceeds through diadic refinements to the given grid. At each step of refinement we add the values of the numerical flux at the center of the coarser cells. The information in the multiresolution representation of the numerical solution is used to determine whether the solution is locally well-resolved. When this is the case we replace the costly exact value of the numerical flux with an accurate enough approximate value which is obtained by an inexpensive interpolation from the coarser grid. The computational efficiency of this multiresolution algorithm is proportional to the rate of data compression (for a prescribed level of tolerance) that can be achieved for the numerical solution of the given scheme.

Abstract: We study the influence of station network density on the distributions and trends in indices of area-average daily precipitation and temperature in the E-OBS high resolution gridded dataset of daily climate over Europe, which was produced with the primary purpose of Regional Climate Model evaluation. Area averages can only be determined with reasonable accuracy from a sufficiently large number of stations within a grid-box. However, the station network on which E-OBS is based comprises only 2,316 stations, spread unevenly across approximately 18,000 0.22° grid-boxes. Consequently, grid-box data in E-OBS are derived through interpolation of stations up to 500 km distant, with the distance of stations that contribute significantly to any grid-box value increasing in areas with lower station density. Since more dispersed stations have less shared variance, the resultant interpolated values are likely to be over-smoothed, and extreme daily values even more so. We perform an experiment over five E-OBS grid boxes for precipitation and temperature that have a sufficiently dense local station network to enable a reasonable estimate of the area-average. We then create a series of randomly selected station sub-networks ranging in size from four to all stations within the E-OBS interpolation search radii. For each sub-network realisation, we estimate the grid-box average applying the same interpolation methodology as used for E-OBS, and then evaluate the effect of network density on the distribution of daily values, as well as trends in extremes indices. The results show that when fewer stations have been used for the interpolation, both precipitation and temperature are over-smoothed, leading to a strong tendency for interpolated daily values to be reduced relative to the “true” area-average. The smoothing is greatest for higher percentiles, and therefore has a disproportionate effect on extremes and any derived extremes indices. For many regions of the E-OBS dataset, the station density is sufficiently low to expect this smoothing effect to be significant and this should be borne in mind by any users of the E-OBS dataset.

Abstract: A system and machine-implemented method are described for performing precoding interpolation in a DIDO system which employs orthogonal frequency-division multiplexing (OFDM) and DIDO precoding to communicate with a plurality of distributed-input-distributed-output (DIDO) clients. For example, a system according to one embodiment of the invention comprises: selecting a first subset of ODFM tones to determine a first subset of precoding weights; deriving a second subset of precoding weights for a second subset of ODFM tones by interpolating between the first subset of precoding weights; and using a combination of the first subset of precoding weights and the second subset of precoding weights to precode a data stream prior to transmitting the data stream to a DIDO client.

Abstract: In this letter, a satellite image resolution enhancement technique based on interpolation of the high-frequency subband images obtained by dual-tree complex wavelet transform (DT-CWT) is proposed. DT-CWT is used to decompose an input low-resolution satellite image into different subbands. Then, the high-frequency subband images and the input image are interpolated, followed by combining all these images to generate a new high-resolution image by using inverse DT-CWT. The resolution enhancement is achieved by using directional selectivity provided by the CWT, where the high-frequency subbands in six different directions contribute to the sharpness of the high-frequency details such as edges. The quantitative peak signal-to-noise ratio (PSNR) and visual results show the superiority of the proposed technique over the conventional bicubic interpolation, wavelet zero padding, and Irani and Peleg based image resolution enhancement techniques.

Abstract: 1. Surface Reconstruction and Interpolation Marietta E. Cameron, Kenneth R. Sloan, and Ying Sun: Reconstruction from Unorganized Point Sets using Gamma Shapes Ingrid Hotz and Hans Hagen: Isometric embedding for a discrete metric David Levin: Mesh-Independent Surface Interpolation Robert Mencl and Heinrich Mueller: Empirical Analysis of Surface Interpolation by Spatial Environment Graphs 2. Surface Interrogation and Modeling Georges-Pierre Bonneau and Stefanie Hahmann: Smooth Polylines on Polygon Meshes Mark A. Duchaineau and Kenneth I. Joy: Progressive Precision Surface Design Helwig Hauser, Thomas Theussl, Andreas Koenig, and Eduard Groeller: Smart Surface Interrogation for Advanced Visualization Techniques Yootai Kim, Raghu Machiraju, and David Thompson: Modeling Rough Surfaces Georgios Stylianou: A Feature Based Method for Rigid Registration of Anatomical Surfaces 3. Wavelets and Compression on Surfaces Martin Bertram: Lifting Biorthogonal B-spline Wavelets Ioannis Ivrissimtzis, Christian Roessl, and Hans-Peter Seidel: Tree-based Data Structures for Triangle Mesh Connectivity Encoding Andrei Khodakovsky and Igor Guskov: Compression of Normal Meshes Gabriel Taubin: New Results in Signal Processing and Compression of Polygon Meshes 4. Topology, Distance Fields and Solid Modeling Jian Huang and Roger Crawfis: Adaptively Refined Complete Distance Fields of Polygonal Models Marcelo Kallmann, Hanspeter Bieri, and Daniel Thalmann: Fully Dynamic Constrained Delaunay Triangulations Jorge Rodriguez, Dolors Ayala, and Antonio Aguilera: EVM: A Complete Solid Model for Surface Rendering Xavier Tricoche and Gerik Scheuermann: Topology Simplification of Symmetric, Second-Order 2D Tensor

Abstract: Several georeferenced measurements of electric field were done in a pilot area of Caracas, Venezuela, to verify that the magnitude of radio frequency electromagnetic fields is below the human exposure limits, recommended by the International Commission on Non-Ionizing Radiation Protection. The collected data were analyzed using geographical information systems, with the objective of using interpolation techniques to estimate the average electromagnetic field magnitude, to obtain a continuous dataset that could be represented over a map of the entire pilot area. This paper reviews the three methods of interpolation used: SPLINE, Inverse Distance Weighting (IDW) and KRIGING. A statistical assessment of the resultant continuous surfaces indicates that there is substantial difference between the estimating ability of the three interpolation methods and IDW performing better overall.

Abstract: In this paper, we propose a reduced-rank space-time adaptive processing (STAP) technique for airborne phased array radar applications. The proposed STAP method performs dimensionality reduction by using a reduced-rank switched joint interpolation, decimation and filtering algorithm (RR-SJIDF). In this scheme, a multiple-processing-branch (MPB) framework, which contains a set of jointly optimized interpolation, decimation and filtering units, is proposed to adaptively process the observations and suppress jammers and clutter. The output is switched to the branch with the best performance according to the minimum variance criterion. In order to design the decimation unit, we present an optimal decimation scheme and a low-complexity decimation scheme. We also develop two adaptive implementations for the proposed scheme, one based on a recursive least squares (RLS) algorithm and the other on a constrained conjugate gradient (CCG) algorithm. The proposed adaptive algorithms are tested with simulated radar data. The simulation results show that the proposed RR-SJIDF STAP schemes with both the RLS and the CCG algorithms converge at a very fast speed and provide a considerable SINR improvement over the state-of-the-art reduced-rank schemes.

Abstract: In this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal-dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher-order interpolation as well. The study builds on previous work by the authors for two-dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi-smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis.

Abstract: Wedescribe aweighted-average approach for incorporating varioustypes of data (observed peak ground motions and intensities and estimates from ground- motion prediction equations) into theShakeMap ground motion and intensity mapping framework.ThisapproachrepresentsafundamentalrevisionofourexistingShakeMap methodology. In addition, the increased availability of near-real-time macroseismic intensitydata,thedevelopmentofnewrelationshipsbetweenintensityandpeakground motions, and new relationships to directly predict intensity from earthquake source information have facilitated the inclusion of intensity measurements directly into ShakeMap computations. Our approach allows for the combination of (1) direct observations (ground-motion measurements or reported intensities), (2) observations converted from intensity to ground motion (or vice versa), and (3) estimated ground motionsandintensities frompredictionequationsornumerical models.Critically,each oftheaforementioneddatatypesmustincludeanestimateofitsuncertainties,including those caused by scaling the influence of observations to surrounding grid points and those associated with estimates given an unknown fault geometry. The ShakeMap ground-motion and intensity estimates are an uncertainty-weighted combination of these various data and estimates. A natural by-product of this interpolation process is an estimate of total uncertainty at each point on the map, which can be vital for comprehensive inventory loss calculations. We perform a number of tests to validate this new methodology and find that it produces a substantial improvement in the accuracy of ground-motion predictions over empirical prediction equations alone.

Abstract: We realized graphics processing unit (GPU) based real-time 4D (3D+time) signal processing and visualization on a regular Fourier-domain optical coherence tomography (FD-OCT) system with a nonlinear k-space spectrometer. An ultra-high speed linear spline interpolation (LSI) method for lambda-to-k spectral re-sampling is implemented in the GPU architecture, which gives average interpolation speeds of >3,000,000 line/s for 1024-pixel OCT (1024-OCT) and >1,400,000 line/s for 2048-pixel OCT (2048-OCT). The complete FD-OCT signal processing including lambda-to-k spectral re-sampling, fast Fourier transform (FFT) and post-FFT processing have all been implemented on a GPU. The maximum complete A-scan processing speeds are investigated to be 680,000 line/s for 1024-OCT and 320,000 line/s for 2048-OCT, which correspond to 1GByte processing bandwidth. In our experiment, a 2048-pixel CMOS camera running up to 70 kHz is used as an acquisition device. Therefore the actual imaging speed is camera- limited to 128,000 line/s for 1024-OCT or 70,000 line/s for 2048-OCT. 3D Data sets are continuously acquired in real time at 1024-OCT mode, immediately processed and visualized as high as 10 volumes/second (12,500 A-scans/volume) by either en face slice extraction or ray-casting based volume rendering from 3D texture mapped in graphics memory. For standard FD-OCT systems, a GPU is the only additional hardware needed to realize this improvement and no optical modification is needed. This technique is highly cost-effective and can be easily integrated into most ultrahigh speed FD-OCT systems to overcome the 3D data processing and visualization bottlenecks.

Abstract: Spatial interpolation methods are frequently used to estimate values of physical or chemical constituents in locations where they are not measured. Very little research has been conducted, however, to investigate the relative performance of different interpolation methods in surface waters. The study reported here uses archived water quality data from the Chesapeake Bay to compare three spatial interpolation methods: inverse distance weighting, ordinary kriging, and a universal kriging method that incorporates output from a process-based water quality model. Interpolations were performed on salinity, water temperature, and dissolved oxygen "snap shots" cruise-based data sets taken between 1985 and 1994 at 21 different depths for multiple locations in the mainstem Bay, using data compiled by the prototypical Chesapeake Bay Environmental Observatory. The kriging methods generally outperform inverse distance weighting for all parameters and depths. Incorporating output from the water quality model through universal kriging appears to improve some of the interpolations by specifically accounting for some physical and biogeochemical features of the estuary. Such integration of process-based information with statistical interpolation warrants further study.

Abstract: Climate research relies heavily on good quality instrumental data; for modeling efforts gridded data are needed. So far, relatively little effort has been made to create gridded climate data for China. This is especially true for high-resolution daily data. This work, focuses on identifying an accurate method to produce gridded daily precipitation in China based on the observed data at 753 stations for the period 1951-2005. Five interpolation methods, including ordinary nearest neighbor, local polynomial, radial basis function, inverse distance weighting, and ordinary kriging, have been used and compared. Cross-validation shows that the ordinary kriging based on seasonal semi-variograms gives the best performance, closely followed by the inverse distance weighting with a power of 2. Finally the ordinary kriging is chosen to interpolate the station data to a 18 kmx 18 km grid system covering the whole country. Precipitation for each 0.5A degrees x 0.5A degrees latitude-longitude block is then obtained by averaging the values at the grid nodes within the block. Owing to the higher station density in the eastern part of the country, the interpolation errors are much smaller than those in the west (west of 100A degrees E). Excluding 145 stations in the western region, the daily, monthly, and annual relative mean absolute errors of the interpolation for the remaining 608 stations are 74%, 29%, and 16%, respectively. The interpolated daily precipitation has been made available on the internet for the scientific community.

Abstract: This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships In addition to providing a classical introduction to the main issues involving approximation and interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties This also includes the new burgeoning theory of superfractals and superfractal functions The theory of splines is well-established but the relationship to fractal functions is novel Throughout the book, connections between these two apparently different areas will be exposed and presented In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling Numerous examples, figures, and exercises accompany the material

Abstract: In Magnetic Resonance Imaging typical clinical settings, both low- and high-resolution images of different types are routinarily acquired. In some cases, the acquired low-resolution images have to be upsampled to match with other high-resolution images for posterior analysis or postprocessing such as registration or multimodal segmentation. However, classical interpolation techniques are not able to recover the high-frequency information lost during the acquisition process. In the present paper, a new superresolution method is proposed to reconstruct high-resolution images from the low-resolution ones using information from coplanar high resolution images acquired of the same subject. Furthermore, the reconstruction process is constrained to be physically plausible with the MR acquisition model that allows a meaningful interpretation of the results. Experiments on synthetic and real data are supplied to show the effectiveness of the proposed approach. A comparison with classical state-of-the-art interpolation techniques is presented to demonstrate the improved performance of the proposed methodology.

Abstract: This paper proposes an efficient, blind, and robust data hiding scheme which is resilient to both geometric distortion and the general print-scan process, based on a near uniform log-polar mapping (ULPM). In contrast to performing inverse log-polar mapping (a mapping from the log-polar system to the Cartesian system) to the watermark signal or its index as done in the prior works, we apply ULPM to the frequency index (u, v) in the Cartesian system to obtain the discrete log-polar coordinate (l 1, l 2), then embed one watermark bit w(l 1 ,l 2 ) in the corresponding discrete Fourier transform coefficient c(u,v). This mapping of index from the Cartesian system to the log-polar system but embedding the corresponding watermark directly in the Cartesian domain not only completely removes the interpolation distortion and the interference distortion introduced to the watermark signal as observed in some prior works, but also largely expands the cardinality of watermark in the log-polar mapping domain. Both theoretical analysis and experimental results show that the proposed watermarking scheme achieves excellent robustness to geometric distortion, normal signal processing, and the general print-scan process. Compared to existing watermarking schemes, our algorithm offers significant improvement in terms of robustness against general print-scan, receiver operating characteristic (ROC) performance, and efficiency of blind resynchronization.