Showing papers on "Bicubic interpolation published in 1992"

Shape-based interpolation

Abstract: Extensions to a shape-based interpolation method in which pixels that share a boundary edge (one inside and the other outside the object) are considered to be at a distance between adjacent pixel centers are proposed. Using such an initialization for distance calculations, a generalization of the chamfer distance calculation is developed. The generalization allows the simultaneous calculation of distances within the object and its background by two consecutive chamfering processes. The performances of a number of variants of the methods are evaluated. It is shown that the shape-based interpolation using a near-optimal 3*3 distance and modified cubic spline between-slice interpolation has superior properties to previously proposed methods for estimating object locations in missing slices in tomographic radiology. >

A two-stage algorithm for discontinuity-preserving surface reconstruction

Abstract: A two-stage algorithm for visual surface reconstruction from scattered data while preserving discontinuities is presented The first stage consists of a robust local approximation algorithm (the moving least median of squares (MLMS) of error) to clean the data and create a grid from the original scattered data points This process is discontinuity preserving The second stage introduces a weighted bicubic spline (WBS) as a surface descriptor The WBS has a factor in the regularizing term that adapts the behavior of the spline across discontinuities The weighted bicubic approximating spline can approximate data with step discontinuities with no discernible distortion in the approximating surface The combination of robust surface fitting and WBSs removes outliers and reduces Gaussian noise Either stage by itself would not effectively remove both kinds of noise Experimental results with the two-stage algorithm are presented >

Multilinear array manifold interpolation

Abstract: Two algorithmic solutions for interpolating between array manifold grid points are presented. The algorithms are for sensor arrays in vector or in scalar wavefields. The algorithms make successful use of the condition that the reciprocal DOA (direction-of-arrival) spectrum is a multilinear function in the small, i.e. over the region of adjacent grid points. Since polarization is a linear parameter subspace, a DOA spectrum can be computed without recourse to the unknown polarizations. Then, vector interpolation is replaced by bivector interpolation to address the radio wavefield case. The approach distinguishes between sensor arrays in scalar wavefields (e.g. acoustic) and those in vector wavefields (e.g. electromagnetic). Since both storage and computational load vary with the reciprocal of the grid spacing or its square, the design relationship between desired accuracy and the required array manifold grid spacing is given. >

Interpolation for upper triangular operators

Abstract: In this paper the classical interpolation problems of Nevanlinna-Pick and Caratheodory-Fejer, as well as mixtures of the two, are solved in the general setting of upper triangular operators. Herein, the “points” at which the interpolation is carried out are themselves (diagonal) operators, and the components of all the intervening operators in their natural matrix representation may be finite or infinite dimensional. Moreover, we consider both contractive and strictly contractive solutions. A number of classical and new interpolation problems emerge as special cases.

Multiquadric interpolation improved

Abstract: Our concern in this paper is the improvement of localization properties of multiquadric interpolation on a multivariate integer grid.

A motion-adaptive de-interlacing method

Abstract: The authors describe an improved motion-adaptive de-interlacing method that incorporates the missing lines of interlaced fields from pixels of the same field or adjacent fields after motion compensation. Some improvements were obtained by suppressing the effect of false motion caused by interpolation error in the searched field, and by interpolation filtering based on the characteristics of moving objects. Experimental data show that the proposed method resulted in smaller interpolation error than conventional de-interlacing methods. >

Method and device for frame interpolation of a moving image

Abstract: A method of forming an interpolated image corresponding to a given temporal distance ratio between a first and a second image comprising, respectively, a first image is described in which the first and second images include a first and a second 3-D shape model of an object having respective shading values and that there is a 3-D motion vector defining the transformation between the first and the second 3-D shape models. The method comprises: a) adjusting the interpolation 3-D motion vector (Vab) to obtain an interpolation 3-D motion vector (Vi); b) forming an interpolation 3-D shape model (Mi) from the interpolation 3-D motion vector (Vi) and either the first or the second 3-D shape model (Ma, Mb); and c) forming an interpolation image from the interpolation 3-D shape model and the image shaping values from the first and second 3-D shape models. The invention aims to provide a method and device for frame interpolation of a moving image which remedies block-shaped distortion in interpolated frames, and which can reproduce smooth movement even when the input image includes movement in 3-dimensional space. Apparatus is also described for carrying out the above method.

Constructing Cl Surfaces of Arbitrary Topology Using Biquadratic and Bicubic Splines

Abstract: Given a bivariate mesh of points, a C 1 surface of corresponding genus and connectedness is constructed. Most of the surface is parametrized by a biquadratic spline whose control points are obtained by refining the input mesh via corner cutting. The remaining mesh regions are parametrized by bicubic patches in Bernstein-Bezier form. The construction can be extended to rational patches and to interpolate at the vertices of the input mesh. t Department of Computer Science, Purdue University, W-Lafayette IN 47907 Supported by NSF grant CCR-9211322

An edge-restricted spatial interpolation algorithm

Abstract: This study addresses how to generate high spatial resolution image data from a low spatial resolution imaging source. An edge-restricted spatial interpolation algorithm is developed to increase the image resolution and at the same time to enhance the sharp edges and details from the original imaging source. The algorithm is based on a cubic spline-under-tension interpolation kernel. The weights of the interpolation kernel can be adjusted adaptively according to the edge information in the neighborhood of the interpolated pixels. The algorithm can be applied to a relatively low spatial resolution image source, such as video, to generate highresolution image data for high-quality printing devices.

Comparative study of several nonlinear image interpolation schemes

Abstract: Image interpolation using non-linear approaches is investigated in this paper. We shall study this problem by concentrating on two sub-sampling schemes that are most commonly adopted in practice: (1) quincunx lattice and (2) every other row and every other column (EORC) lattice. For each sub-sampling lattice, we propose four interpolation structures and compare them by considering the computational complexity and testing with both natural and synthetic images. Comparisons of the proposed non-linear interpolators with some linear approaches are also presented. With the results obtained in this paper, we can come out with a general conclusion that the non-linear interpolation should be preferred to in practice.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Contour compensation method for numerically controlled machines

Abstract: When the movement of a machine element is guided by a multi-axial, numerically controlled machine through the selection of interpolation points which are calculated and stored off-line, a tool-radius correction is rendered possible. This occurs because correction interpolation points are calculated on the basis of interpolation points and thus, with the least possible expenditure of time, a new trajectory curve can be generated, with which the radius changes are considered. In addition, a change in feedrate can be achieved through the selection of override values by placing fine interpolation points between two interpolation points at a time.

Space scale analysis for image sampling and interpolation

Abstract: In image processing operations involving changes in the sampling grid, including increases or decreases in resolution, care must be taken to preserve image structure. Structure includes regions of high contrast, such as edges, streaks, or corners, all indicated by large gradients. The authors consider the use of local spatial analysis for both sampling and interpolation. Anisotropic diffusion is considered as a directional smoothing technique that preserves structure. This is used in conjunction with a method of directional interpolation, which is also based on structure analysis. >

Local motion-adaptive interpolation technique based on block matching algorithms

Abstract: Interpolation techniques based on block-by-block motion compensation algorithms are studied for the video conference/video telephone signals. In this paper, we propose the local motion-adaptive interpolation technique, which can be used in the codec using a motion compensated coding-block matching algorithm (MCC-BMA). Computer simulation results at 2:1 subsampling rate of the proposed local motion-adaptive interpolation techniques combined with the conventional three-step search algorithm and the fast BMA using integral projections are given.

A method of smooth bivariate interpolation for data given on a generalized curvilinear grid

Abstract: A method of locally bicubic interpolation is presented for data given at the nodes of a two-dimensional generalized curvilinear grid. The physical domain is transformed to a computational domain in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. The metrics of the transformation are obtained by finite differences in the computational domain. Metric derivatives are determined by repeated application of the chain rule for partial differentiation. Given the metrics and the metric derivatives, the partial derivatives required to determine a locally bicubic interpolant can be estimated at each data point using finite differences in the computational domain. A bilinear transformation is used to analytically transform the individual quadrilateral cells in the physical domain into unit squares, thus allowing the use of simple formulas for bicubic interpolation.

Procedural interpolation with geometrically continuous cubic splines

Abstract: A local interpolation method for curves in R2 or R3 offering G1 continuity is described. A curve is represented as a union of geometrically continuous cubic Bezier segments between each pair of adjacent vertices. At each interpolation point, the procedure determines a tangent direction and two derivative magnitudes on either side of the vertex. The method uses an intuitive geometric, rule-based approach to find a ‘good’ default solution that produces pleasing-looking results even for highly irregular sets of data Various spline properties and their relevance to the method are also discussed.

Multi-Resolution Surface Approximation for Animation

Abstract: This paper considers the problem of approximating a digitized surface in R3 with a hierarchical bicubic B-spline to produce a manipulatable surface for further modeling or animation. The 3D data''s original mapping from R3 (multiple rows of cylindrical scans) is mapped into the parametric domain of the B-splice (also in R3) using a modified chord-length parameterization. This mapping is used to produce a gridded sampling of the surface, and a modified full multi-grid (FMG) technique is employed to obtain a high-resolution B-spline approximation. The intermediate results of the FMG calculations generate the component overlays of a hierarchical spline surface reconstruction. Storage requirements of the hierarchical representation are reduced by eliminating offsets wherever their removal will not increase the error in the approximation by more than a given amount. The resulting hierarchical spline surface is interactively modifiable (modulo the size of the dataset and computing power) using the editing capabilities of the hierarchical surface representation allowing either local or global changes to surface shape while retaining details of the scanned data.

Randomized interpolation and approximation of sparse polynomials stPreliminary version

Abstract: We present a randomized algorithm that interpolates a sparse polynomial in polynomial time in the bit complexity model. The algorithm can be also applied to approximate polynomials that can be approximated by sparse polynomials (the approximation is in the L2 norm).

Interpolation using Hartley transform

Abstract: The revised interpolation method for a 1-D signal via the fast Hartley transform (FHT) is presented and a new interpolation algorithm for a 2-D signal by using the 1-D FHT is suggested. Results show that the proposed algorithm is superior to the FFT method both in accuracy and in computational time for interpolating discrete bandlimited 2-D signals.

Method for image interpolation based on a novel multirate filter bank structure and properties of the human visual system

Abstract: Image interpolation systems are used to render a high resolution version of an image from a lower resolution representation. Conventional interpolation systems such as bilinear interpolation and nearest neighbor interpolation often perform poorly (in a subjective sense) when acting on a spatial region of an image which has an oriented structure such as an edge, line, or corner. Recently, systems based on directional interpolation have been presented which yield improved performance on these oriented structures. However, separate models are used for the detection of edges, lines, and corners. In this work, we combine simple building blocks (a Sobel edge detector, directional interpolation, and the directional filter bank) to form a system which exploits the orientational tuning and the spatial-frequency variant sensitivity of the human visual system. The new system handles all of the oriented features in the same manner. First, the image to be processed is split into its directional components. These directional components are then individually interpolated using the directional interpolation system. Since orthogonal (or nearly orthogonal components) are contained in different directional components, corners do not exist in the directional components. Furthermore, since the directional filter bank is an exactly reconstructing structure, the representation of the image in terms of its directional components is complete and thereby an invertible decomposition. In the absence of an oriented component, the directional interpolation system reverts to bilinear interpolation (though any other interpolant could be used).© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Local cardinal spline interpolation and its application to image processing

Abstract: This paper presents an image interpolation algorithm using the recently developed local cardinal interpolatory spline (LCIS). The procedures for constructing the LCIS basis are described for both univariate and bivariate cases. This new LCIS algorithm is very efficient and can be implemented easily. Without the need of a mapping procedure, this method is faster than any other polynomial interpolation approach. The C2 property of the LCIS also allows the gradient operator to be constructed for edge detection. Both image interpolation and edge detection algorithms are compared with existing methods in two different examples.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A method for removing the singularities from Gregory surfaces

Abstract: The bicubic Gregory patch is mathematically equivalent to the bicubic Coons patch with Gregory's square. A method to convert a family of Gregory patches to rational Bezier surfaces which have no singularity is described. The method is mathematically an approximation of Gregory patches based on an approximation of the rational blending function by a rational Bezier function which has an implanted minute error.

Procedural interpolation with curvature-continuous cubic splines

Abstract: A local G2 curve interpolation method in R 2 is described. The method offers a free choice of a tangent direction, two derivatives, and a curvature at each interpolation point. This flexibility can be achieved by constructing two cubic segments for each adjacent pair of vertices. The method is also compared with other local schemes for curve construction.

On interpolation of bilinear operators with a real method

Abstract: This article considers functors of the real method for interpolation of bilinear operators. A description is obtained for them in the case of exponential characteristic functions.

Picture interpolation method

Abstract: PURPOSE:To make it possible to simultaneously perform a proper interpolation processing and a sharpness processing when an expansion processing is performed for a picture by using plural interpolation functions whose frequency characteristics are different. CONSTITUTION:By using first, second and third interpolation functions h1 (x), h2 (x) and h3 (x) whose frequency characteristics are different, the interpolation of a picture is performed by an interpolation function h (x) to be h (x)=h1 (x), +k1. (h1 (x)-h2 (x)), +k2. (h1 (x)-h3(x)), +k3. (h2 (x)-h3 (x)). The k1, k2, k3 show prescribed factors and the x shows the interpolation location of the picture. Namely, by performing the interpolation of the picture by using the interpolation function h (x) obtained by synthesizing the interpolation functions h1 (x), h2 (x) and h3 (x) whose frequency characteristics are different in accordance with the picture by a prescribed ratio, a proper expansion processing can be performed and the degradation of the frequency characteristics in the vicinity of Nyquist frequency can be improved.

Statistically optimal interslice value interpolation in 3D medical imaging: theory and implementation

Abstract: Describes a technique for statistically optimal interslice interpolation of scalar values for use in three-dimensional medical image rendering. The interpolation technique is based upon kriging, which is known to be the best linear unbiased estimation technique for spatially distributed data. The authors present the results obtained using kriging in the object space preprocessing operation of slice interpolation by slice-value interpolation. As a byproduct of the technique, kriging calculates the estimation error for the interslice values. This makes it possible to quantify the interpolation error in slices computed by the estimation technique. >

Interpolation by bivariate quadratic splines on a four-directional mesh

Abstract: We give sufficient conditions which guarantee that a set of points admits unique Lagrange interpolation by quadratic splines on a four-directional mesh. The poisedness of these sets will be proved by reducing one bivariate problem to a finite sequence of univariate problems.

Image interpolation based on image statistics: a case study

Abstract: Two novel approaches to image interpolation aimed at video service interworking, layered image coding, and image zooming are discussed. Compared to conventional interpolation filters used for image interpolation, the schemes proposed take advantage of prior knowledge of image statistics to enhance their performance. Both methods, inverse Wiener filtering (IWF) and vector interpolation (VI), use image training sequences to estimate optimal interpolation parameters. While IWF has online capabilities for parameter estimation, VI parameters need to be designed in computer intense offline optimization procedures. Both IWF and VI methods achieve superior performance compared to standard linear interpolation filters in terms of signal-to-noise ratio of the interpolated images, as well as entropy of the residual errors. >

Infinite dimensional kolmogorov width and optimal interpolation on sobolev-wiener space

Abstract: In this paper, we introduce a kind of Sobolev-Wiener spaces defined on the whole real axis and discuss their infinite dimensional width and optimal interpolation problems. We give the exact values (of strong asymptotics) of the infinite dimensional Kolmogorov width and linear width of W_(∞,p)~r(R) in the metric L_p(R). Meanwhile, we also solve its optimal interpolation problem.