Abstract: We present a new method for digitally interpolating images to higher resolution. It consists of two phases: rendering and correction. The rendering phase is edge-directed. From the low resolution image data, we generate a high resolution edge map by first filtering with a rectangular center-on-surround-off filter and then performing piecewise linear interpolation between the zero crossings in the filter output. The rendering phase is based on bilinear interpolation modified to prevent interpolation across edges, as determined from the estimated high resolution edge map. During the correction phase, we modify the mesh values on which the rendering is based to account for the disparity between the true low resolution data, and that predicted by a sensor model operating on the high resolution output of the rendering phase. The overall process is repeated iteratively. We show experimental results which demonstrate the efficacy of our interpolation method.

Abstract: 1. Introduction 2. Introduction to spectral methods via orthogonal functions 3. Introduction to PS methods via finite differences 4. Key properties of PS approximations 5. PS variations/enhancements 6. PS methods in polar and spherical geometries 7. Comparisons of computational cost - FD vs. PS methods 8. Some application areas for spectral methods Appendices.

Abstract: : This is a preliminary paper in which the authors discuss a general framework for the treatment of pattern-recognition problems. They make precise the notion of a 'fuzzy' set. Then they show how this may be employed in a sequential experimental procedure to ascertain whether a symbol is a member of a particular set or not. The close relation between the problem of pattern recognition and interpolation is stressed. (Author)

Abstract: This paper discusses quasi-interpolation and interpolation with Gaussians. Estimates are obtained showing a high-order approximation up to some saturation error negligible in numerical applications. The construction of local high-order quasi-interpolation formulas is given.

Abstract: In this paper, a new algorithm (LOLIMOT) for nonlinear dynamic system identification with local linear models is proposed. The input space is partitioned by a tree-construction algorithm. The local models are interpolated by overlapping local basis functions. The resulting structure is equivalent to a Sugeno-Takagi fuzzy system and a local model network and can therefore be interpreted correspondingly. The LOLIMOT algorithm is very simple, easy to implement, and fast. Moreover, this approach has the following appealing properties: it does not underlie the "curse of dimensionality", it reveals irrelevant inputs, it detects inputs that influence the output mainly in a linear way, and it applies robust local linear estimation schemes. The drawbacks are that only orthogonal cuts are performed and that the local estimation approach may lead to interpolation errors.

Abstract: We consider elastic registration of medical image data based on thin-plate splines using a set of corresponding anatomical point landmarks. Previous work on this topic has concentrated on using interpolation schemes. Such schemes force the corresponding landmarks to exactly match each other and assume that the landmark positions are known exactly. However, in real applications the localization of landmarks is always prone to some error. Therefore, to take into account these localization errors, we have investigated the application of an approximation scheme which is based on regularization theory. This approach generally leads to a more accurate and robust registration result. In particular, outliers do not disturb the registration result as much as is the case with an interpolation scheme. Also, it is possible to individually weight the landmarks according to their localization uncertainty. In addition to this study, we report on investigations into semi-automatic extraction of anatomical point landmarks.

Abstract: A frame interpolation algorithm for frame rate up-conversion of progressive image sequences is proposed. The algorithm is based on simple motion compensation and linear interpolation. A motion vector is searched for each pixel in the interpolated image and the resulting motion field is median filtered to remove inconsistent vectors. Averaging along the motion trajectory is used to produce the interpolated pixel values. The main novelty of the proposed method is the motion compensation algorithm which has been designed with low computational complexity as an important criterion. Subsampled blocks are used in block matching and the vector search range is constrained to the most likely motion vectors. Simulation results show that good visual quality has been obtained with moderate complexity. The algorithm has been designed mainly for 50 Hz to 75 Hz frame rate up-conversion with applications in a multimedia environment, but it can also be used in advanced television receivers to remove artifacts due to low scan rate.

Abstract: A novel scheme for edge-preserving image interpolation is introduced, which is based on the use of a simple nonlinear filter which accurately reconstructs sharp edges. Simulation results show the superior performances of the proposed approach with respect to other interpolation techniques.

Abstract: This paper explores the use of multivariate interpolation techniques in the context of methods for unconstrained optimization that do not require derivative of the objective function. A new algorithm is proposed that uses quadratic models in a trust region framework. The algorithm is constructed to require few evaluations of the objective function and is designed to be relatively insensitive to noise in the objective function values. Its performance is analyzed on a set of 20 examples, both with and without noise.

Abstract: For functions tabulated at Chebyshev nodes on an interval, spectral interpolation and indefinite integration can be performed stably and efficiently via the fast Fourier transform. For many other sets of nodes (such as the Gaussian nodes on an interval) the classical interpolation and indefinite integration schemes are stable but slow, requiring $O(N^2 )$ arithmetic operations with N the number of nodes in the discretization of the interval. In this paper, a group of algorithms is presented for the efficient evaluation of Lagrange polynomial interpolants at multiple points on the line and for the rapid indefinite integration and differentiation of functions tabulated at nodes other than Chebyshev. The interpolation scheme requires $O(N \cdot \log ({1 / \varepsilon }))$arithmetic operations, and $O(N \cdot \log N + N \cdot \log ({1 / \varepsilon }))$ operations are required for the integration and differentiation schemes, where $\varepsilon $ is the precision of computations and N is the number of nodes (t...

Abstract: If the sampling of the received signal is not synchronized to the incoming data symbols, timing adjustment must be done after sampling using interpolation. If the impulse response of the interpolation filter is a polynomial or piecewise polynomial, it can be implemented efficiently using a Farrow structure. The remaining problem is that there exist no good design methods for polynomial-based filters. In this paper we present a new synthesis technique which allows to design polynomial-based interpolation filters with an arbitrary frequency response. This means that we are able to design interpolation filters in the same manner as normal FIR filters. There can be many passbands and stopbands, and for every band we can set the desired amplitude and weight.

Abstract: Elastography uses estimates of the time delay (obtained by cross-correlation) to compute strain estimates in tissue due to quasistatic compression. Because the time delay estimates do not generally occur at the sampling intervals, the location of the cross-correlation peak does not give and accurate estimate of the time delay. Sampling errors in the time-delay estimate are reduced using signal interpolation techniques to obtain subsample time-delay estimates. Distortions of the echo signals due to tissue compression introduce correlation artifacts in the elastogram. These artifacts are reduced by a combination of small compressions and temporal stretching of the postcompression signal. Random noise effects in the resulting elastograms are reduced by averaging several elastograms, obtained from successive small compressions (assuming that the errors are uncorrelated). Multicompression averaging with temporal stretching is shown to increase the signal-to-noise ratio in the elastogram by an order of magnitude, without sacrificing sensitivity, resolution or dynamic range. The strain filter concept is extended in this article to theoretically characterize the performance of multicompression averaging with temporal stretching.

Abstract: An original image signal, which represents an original image and are composed of original image signal components representing a plurality of sampling points, that are arrayed at predetermined intervals and in a lattice-like form, is obtained. A judgment is made as to whether an interpolation point belongs to an image edge portion, at which the change in the original image signal is sharp, or belongs to a flat portion, at which the change in the original image signal is unsharp. Interpolating operation processes, one of which is to be employed for the interpolation point, is changed over to each other in accordance with the results of the judgment. Interpolated image signal components corresponding to interpolation points are thereby obtained from the interpolating operation processes such that a visible image, in which a character pattern and an image edge portion are free from any step-like pattern and are sharp and a flat portion has an appropriate level of sharpness, can be reproduced from the interpolated image signal components.

Abstract: A technique is presented for elastic alignment applicable to human brains. The transformation which minimizes the distance measure D(u) between template and reference is determined, thereby simultaneously satisfying smoothness constraints derived from an elastic potential known from the theory of kontinuum mechanics. The resulting partial differential equations, with up to 3·220 unknowns are directly solved for each voxel, that is, without interpolation, by an adapted full multigrid-method (FMG) providing a perfect alignment. For further increases of resolution, the full advantages of the FMG are maintained, that is, parallelization and linear effort with O(N), N being the number of grid-points.

Abstract: A new 3D wavefield modelling approach based on dynamic ray tracing is presented. This approach is called wavefront construction, and it can be used in 3D models with constant or smoothly varying material properties (S- and P-velocity and density) separated by smooth interfaces. Wavefronts consisting of rays arranged in a triangular network are propagated stepwise through the model. At each time step, the differences in a number of parameters are checked between each pair of rays on the wavefront. New rays are interpolated whenever this difference between pairs of rays exceeds some predefined maximum value. A controlled sampling of the wavefront at all time steps is thus obtained. Receivers are given multiple-event values by interpolation when the wavefronts pass them. The strength of the wavefront construction method is that it is robust and efficient.

Abstract: Gradient information is used in volume rendering to classify and color samples along a ray. In this paper, we present an analysis of the theoretically ideal gradient estimator and compare it to some commonly used gradient estimators. A new method is presented to calculate the gradient at arbitrary sample positions, using the derivative of the interpolation filter as the basis for the new gradient filter. As an example, we will discuss the use of the derivative of the cubic spline. Comparisons with several other methods are demonstrated. Computational efficiency can be realized since parts of the interpolation computation can be leveraged in the gradient estimation.

Abstract: A new technical theory and associated finite element model is introduced for thick laminated and sandwich beams. The theory can be cast as a layerwise theory with high-order zig-zag sublaminate approximations, thus greatly reducing the number of degrees of freedom required to accurately describe the bending and transverse shear kinematics in thick laminates. Furthermore, the theory is adaptable, allowing the user to choose the number of sublaminate approximations to achieve the desired accuracy. Based on this theory, a simple, efficient, and robust finite element model is developed that has the nodal topology of a four-noded planar element yet has the advantages of beam-type kinematics and a special interpolation scheme that obviates locking. The element contains a single zig-zag sublaminate approximation. If desired, multiple elements can be used through the thickness of a laminate to increase accuracy.

Abstract: Method and apparatus are disclosed for deinterlacing of an interlaced video frame sequence using interpolation estimations, such as spatial and temporal interpolations. Interpolations requiring a less accurate estimation of missing pixel values in the frames being deinterlaced, such that an interpolation may be performed with a minimum of error, are performed before interpolations which require a more accurate estimation of missing pixel values for performing an interpolation, such that estimates of missing pixel values are obtained with a minimum of error. Interpolation estimations are weighted in combination for computing approximations of missing pixel values in accordance with the errors associated with the respective interpolations.

Abstract: The efficiency of the orthogonal least squares (OLS) method for training approximation networks is examined using the criterion of energy compaction. We show that the selection of basis vectors produced by the procedure is not the most compact when the approximation is performed using a nonorthogonal basis. Hence, the algorithm does not produce the smallest possible networks for a given approximation error. Specific examples are given using the Gaussian radial basis functions type of approximation networks.

Abstract: An adaptive technique for scanning rate conversion and interpolation is proposed. This technique performs better than the edge-based line average algorithm, especially for an image with more horizontal edges. Moreover, it is easy to implement and a simple VLSI architecture is proposed. Computer simulation shows that a 37.0 dB image can be obtained via our proposed technique, while edge-based line average algorithm only achieves 35.2 dB.