Showing papers on "Interpolation published in 1993"
1 Sep 1993
TL;DR: In this paper, a view interpolation approach to synthesize 3D scenes has been proposed, which combines interpolation of texture maps and their shape, is applied to computing arbitrary intermediate frames from an array of prestored images.
Abstract: Image-space simplifications have been used to accelerate the calculation of computer graphic images since the dawn of visual simulation. Texture mapping has been used to provide a means by which images may themselves be used as display primitives. The work reported by this paper endeavors to carry this concept to its logical extreme by using interpolated images to portray three-dimensional scenes. The special-effects technique of morphing, which combines interpolation of texture maps and their shape, is applied to computing arbitrary intermediate frames from an array of prestored images. If the images are a structured set of views of a 3D object or scene, intermediate frames derived by morphing can be used to approximate intermediate 3D transformations of the object or scene. Using the view interpolation approach to synthesize 3D scenes has two main advantages. First, the 3D representation of the scene may be replaced with images. Second, the image synthesis time is independent of the scene complexity. The correspondence between images, required for the morphing method, can be predetermined automatically using the range data associated with the images. The method is further accelerated by a quadtree decomposition and a view-independent visible priority. Our experiments have shown that the morphing can be performed at interactive rates on today’s high-end personal computers. Potential applications of the method include virtual holograms, a walkthrough in a virtual environment, image-based primitives and incremental rendering. The method also can be used to greatly accelerate the computation of motion blur and soft shadows cast by area light sources. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism. Additional Keywords: image morphing, interpolation, virtual reality, motion blur, shadow, incremental rendering, real-time display, virtual holography, motion compensation.
1,500 citations
TL;DR: The author describes the fundamental equation for interpolation, proposes a method for control, and outlines the signal-processing characteristics appropriate to an interpolator.
Abstract: Timing adjustment in a digital modem must be performed by interpolation if sampling is not synchronized to the data symbols. The author describes the fundamental equation for interpolation, proposes a method for control, and outlines the signal-processing characteristics appropriate to an interpolator. A review of previous results and a tutorial exposition of the subject are given, along with new results. >
733 citations
TL;DR: The NCO-based control method presented in Part I is shown to be equivalent to a conventional phase locked loop and its operation is verified by simulation, demonstrating that simple interpolators give excellent performance.
Abstract: For pt.I, see ibid., vol.41, no.3, p.502-208 (1993). Properties of a specific class of interpolators that are based upon polynomials are discussed. Several implementations are described, one of which is particularly convenient in practical hardware. Simulations demonstrate that simple interpolators give excellent performance. In many cases, two-point, linear interpolation is adequate. If better performance is needed, classical four-point, third-order polynomials could be used. Better yet, a novel four-point interpolating filter with piecewise-parabolic impulse response can have performance superior to that of the standard cubic interpolator and still be implemented much more simply. The NCO-based control method presented in Part I is shown to be equivalent to a conventional phase locked loop and its operation is verified by simulation. >
676 citations
Patent•
30 Jun 1993
TL;DR: Adaptive interpolation is performed by apparatus operating upon a digitized image signal obtained from an image sensor having color photosites that generate a plurality of color values, but only one color per photosite.
Abstract: Adaptive interpolation is performed by apparatus operating upon a digitized image signal obtained from an image sensor having color photosites that generate a plurality of color values, but only one color per photosite. A digital processor obtains gradient values from the differences between chrominance values in vertical and horizontal image directions. The gradient values are compared with each other in order to select one of the directions as the preferred orientation for the interpolation of additional luminance values. The interpolation is then performed upon values selected to agree with the preferred orientation.
415 citations
TL;DR: A three-state technique for reliable displacement estimation with fractional-pel accuracy is introduced, based on phase correlation, and for motion-compensation with block size of 16 pels*16 pels, 1/4- Pel accuracy appears to be sufficient for broadcast TV signals, whereas for videophone signals,1/2-pel Accuracy is desirable.
Abstract: The effect of fractional-pel accuracy on the efficiency of motion-compensating predictors is studied using various spatial prediction/interpolation filters. In model calculations, the power spectral density of the prediction error is related to the probability density function of the displacement error. Prediction can be improved both by higher accuracy of motion-compensation and by spatial Wiener filtering in the predictor. Beyond a critical accuracy, the possibility of further improving prediction by more accurate motion-compensation is small. Experiments with videophone signals and with broadcast TV signals confirm these model calculations. Sinc-interpolation, bilinear interpolation, and Wiener filtering are compared at integer-pel, 1/2-pel, 1/4-pel, and 1/8-pel accuracies. A three-state technique for reliable displacement estimation with fractional-pel accuracy is introduced. It is based on phase correlation. For motion-compensation with block size of 16 pels*16 pels, 1/4-pel accuracy appears to be sufficient for broadcast TV signals, whereas for videophone signals, 1/2-pel accuracy is desirable. >
353 citations
TL;DR: In this article, a wavefront (WF) construction approach is proposed to estimate a new WF from the old one by using ray tracing, which is defined as a curve (in 2D) of constant traveltime from the source.
Abstract: We have developed and implemented a new method for estimating traveltimes and amplitudes in a general smooth two‐dimensional (2-D) model. The basic idea of this wavefront (WF) construction approach is to use ray tracing to estimate a new WF from the old one. The WF is defined as a curve (in 2-D) of constant traveltime from the source. The ray direction and amplitude will then be a function of s, the distance along the front. To maintain a sufficiently small sampling distance along the WF, it is scanned at every time step and new rays are interpolated whenever the distance between two rays becomes larger than a predefined limit. As the wavefronts are constructed, the data (i.e. traveltimes, amplitude coefficients, etc.) are transferred to the receivers by interpolation within the ray cells. Advantages of the WF construction method are its flexibility, robustness, and accuracy. First, second, and later arrivals may be found at any point in the model. Any shape of the initial wavefront is possible. The drawb...
311 citations
TL;DR: The Joint Photographic Experts Group (JPEG) and Motion Picture Experts group (MPEG) algorithms for image and video compression are modified to incorporate block interleaving in the spatial domain and DCT coefficient segmentation in the frequency domain to conceal the errors due to packet loss.
Abstract: The applications of discrete cosine transform (DCT)-based image- and video-coding methods in the asynchronous transfer mode (ATM) environment are considered. Coding and reconstruction mechanisms are jointly designed to achieve a good compromise among compression gain, system complexity, processing delay, error-concealment capability, and reconstruction quality. The Joint Photographic Experts Group (JPEG) and Motion Picture Experts Group (MPEG) algorithms for image and video compression are modified to incorporate block interleaving in the spatial domain and DCT coefficient segmentation in the frequency domain to conceal the errors due to packet loss. A new algorithm is developed that recovers the damaged regions by adaptive interpolation in the spatial, temporal, and frequency domains. The weights used for spatial and temporal interpolations are varied according to the motion content and loss patterns of the damaged regions. When combined with proper layered transmission, the proposed coding and reconstruction methods can handle very high packet-loss rates at only a slight cost in compression gain, system complexity, and processing delay. >
303 citations
1 Jan 1993
TL;DR: This second volume includes contributions from leading researchers in the field on such topics as Gabor's signal expansion, sampling in optical image formation, linear prediction theory, polar and spiral sampling theory, interpolation from non-uniform samples, and applications of sampling theory to optics and to time-frequency representations.
Abstract: "Advanced Topics in Shannon Sampling and Interpolation Theory" is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images. Sampling and reconstruction are fundamental problems in any field that deals with real-time signals or images, including communication engineering, image processing, seismology, speech recognition, and digital signal processing. This second volume includes contributions from leading researchers in the field on such topics as Gabor's signal expansion, sampling in optical image formation, linear prediction theory, polar and spiral sampling theory, interpolation from non-uniform samples, an extension of Papoulis' generalized sampling expansion to higher dimensions, and applications of sampling theory to optics and to time-frequency representations.
297 citations
TL;DR: A direction finding technique which uses the outputs of a virtual array, computed from the real array using a linear interpolation procedure over a given sector, which was found to equal the performance of the MUSIC algorithm applied to the realarray.
276 citations
1 Aug 1993
TL;DR: In this article, an edge classifier analyzes the values of pels in the blocks surrounding the missing block and determines which edge directions cut through the missing blocks, and interpolations are performed on a local pel neighborhood along the directions specified by the edge classifiers.
Abstract: An algorithm using multidirectional interpolation is presented for error concealment. In the algorithm, an edge classifier analyzes the values of pels in the blocks surrounding the missing block and determines which edge directions cut through the missing block. Interpolations are performed on a local pel neighborhood along the directions specified by the edge classifier. Then a mixing operation is used to restore the missing block by extracting the features obtained from the different directional interpolations and combining them together. The method of multidirectional interpolation and image mixing has demonstrated very good results when a sufficiently large neighborhood of correlated pels exists. This method of spatial interpolation can be combined with temporal interpolation to provide for a powerful error concealment technique for compressed video signal transmission. >
230 citations
Patent•
30 Jun 1993
TL;DR: Adaptive interpolation is performed by apparatus operating upon a digitized image signal obtained from an image sensor having color photosites that generate a plurality of color values, but only one color per photosite as discussed by the authors.
Abstract: Adaptive interpolation is performed by apparatus operating upon a digitized image signal obtained from an image sensor having color photosites that generate a plurality of color values, but only one color per photosite. A digital processor obtains gradient values from the differences between luminance values in vertical and horizontal image directions. The gradient values are compared to a programmable threshold in order to select one of the directions as the preferred orientation for the interpolation of additional luminance values. The interpolation is then performed upon values selected to agree with the preferred orientation.
TL;DR: A shift-invariant multiresolution representation of signals or images using dilations and translations of the autocorrelation functions of compactly supported wavelets, which reduces the reconstruction problem to that of solving a system of linear algebraic equations.
Abstract: Proposes a shift-invariant multiresolution representation of signals or images using dilations and translations of the autocorrelation functions of compactly supported wavelets. Although these functions do not form an orthonormal basis, their properties make them useful for signal and image analysis. Unlike wavelet-based orthonormal representations, the present representation has (1) symmetric analyzing functions, (2) shift-invariance, (3) associated iterative interpolation schemes, and (4) a simple algorithm for finding the locations of the multiscale edges as zero-crossings. The authors also develop a noniterative method for reconstructing signals from their zero-crossings (and slopes at these zero-crossings) in their representation. This method reduces the reconstruction problem to that of solving a system of linear algebraic equations. >
TL;DR: In this paper, a postprocessing technique is developed for determining first-order derivatives (fluxes, stresses) at nodal points based on derivatives in superconvergent points.
Abstract: In this paper a postprocessing technique is developed for determining first-order derivatives (fluxes, stresses) at nodal points based on derivatives in superconvergent points. It is an extension of the superconvergent patch recovery technique presented by Zienkiewicz and Zhu. In contrast to that technique all flux or stress components are interpolated at the same time, coupled by equilibrium equations at the superconvergent points. The equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries.
TL;DR: A new direction-finding algorithm for multiple wideband signals received by an arbitrary array and its performance is derived using an interpolation technique and special attention is given to correlated and coherent signals.
Abstract: The authors derive a new direction-finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance. Using an interpolation technique, they generate a set of virtual arrays, each for a different frequency band, having the same array manifold. The convergence matrices of these arrays are added to produce a composite covariance matrix. Direction-of-arrival (DOA) estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband MUSIC algorithm or its variants. Closed-form expressions for the asymptotic covariance matrix of the DOA estimation errors are derived using a perturbation analysis, evaluated for specific cases, and compared with the Cramer-Rao lower bound. Special attention is given to correlated and coherent signals. The formulas for the error covariance are quite general and can be modified to provide results for other wideband DOA estimation algorithms. >
TL;DR: The resulting Multi-Band Resynthesis Pitch Synchronous OverLap Add (MBR-PSOLA) synthesis algorithm supports spectral interpolation between voiced parts of segments, with virtually no increase in complexity.
TL;DR: A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented and further insight is gained into the structure of the optimal solution.
Abstract: A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented. By formulating the interpolation conditions in a concise and natural way, the general theory is developed in simpler terms and with a minimum number of assumptions. In addition, further insight is gained into the structure of the optimal solution, and different classes of multiblock problems are distinguished. This leads to a conceptually attractive, iterative method for finding approximate solutions. >
TL;DR: In this paper, the incompressible Navier-Stokes equations are discretized by stabilized finite element methods, which are applicable to various combinations of interpolation functions, including the simplest equal-order linear and bilinear elements.
1 Mar 1993
TL;DR: Methods that identify the spatial variation in elevation model accuracy and highlight relative variation are proposed to identify the accuracy preserved in interpolation digital contour data to produce elevation models.
Abstract: Methods that identify the spatial variation in elevation model accuracy and highlight relative variation are proposed. Visualization within the geographic resources analysis support system (GRASS) is used to identify the accuracy preserved in interpolation digital contour data to produce elevation models. The interpolation routines are inverse distance weighting, contour flood filling, simultaneous over-relaxation, and one-dimensional spline fitting. The results of the interpolation process are presented as colored contours, shaded relief maps, aspect maps, and products of Laplacian filtering, profile and plan convexity, and visualizing root mean square error methods. >
TL;DR: In this article, the authors relax the monotonicity constraint in a geometric framework in which the median function plays a crucial role, and present algorithms for piecewise cubic interpolants, which preserve monoticity as well as uniform third and fourth-order accuracy.
Abstract: Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.
Book•
1 Jan 1993TL;DR: I. Engineering Problem Solving, II.
Abstract: I. FUNDAMENTAL ENGINEERING COMPUTING. 1. Engineering Problem Solving. 2. MATLAB Environment. 3. MATLAB Functions. 4. Linear Algebra and Matrices. II. NUMERICAL TECHNIQUES. 5. Solutions to Systems of Linear Equations. 6. Interpolation and Curve Fitting. 7. Numerical Integration and Differentiation. 8. Ordinary Differential Equations. III. SPECIAL TOPICS. 9. Symbolic Mathematics. 10. Signal Processing. 11. Control Systems. Appendix A: MATLAB Function Summary. Complete Solutions to Practice! Problems. Index.
TL;DR: This article contains tables of 95th percentile eigenvalues from random data that can be used when the sample size is between 50 and 500 and when the number of variables is between 5 and 50.
Abstract: Selecting the "correct" number of components to retain in principal components analysis is crucial. Parallel analysis, which requires a comparison of eigenvalues from observed and random data, is a highly promising strategy for making this decision. This paper focuses on linear interpolation, which has been shown to be an accurate method of implementing parallel analysis. Specifically, this article contains tables of 95th percentile eigenvalues from random data that can be used when the sample size is between 50 and 500 and when the number of variables is between 5 and 50. An empirical example is provided illustrating linear interpolation, direct computation, and regression methods for obtaining 95th percentile eigenvalues from random data. The tables of eigenvalues given in this report will hopefully enable more researchers to use parallel analysis because interpolation is an accurate and simple method of obviating the Monte Carlo requirements of parallel analysis.
TL;DR: In this paper, an Eulerian procedure that avoids both interpolation and iteration is proposed for determining the departure points of trajectories, which is applicable to semi-Lagrangian models formulated either on the plane or on the sphere.
Abstract: An Eulerian procedure that avoids both interpolation and iteration is proposed for determining the departure points of trajectories. It is applicable to semi-Lagrangian models formulated either on the plane or on the sphere. The technique can achieve a high degree of accuracy; it is also simpler and more economical than other schemes, especially when applied on the sphere. The technique is applied to the cone advection test on the plane, as well as to a “Gaussian hill” problem on a rotating sphere.
TL;DR: The algorithm for segmentation and interpolation of the MRI data gives an isotropic binary representation of both gray and white matter which are available for 3-D surface rendering and the power and practicality of this method favorably compares to a manual one.
Abstract: The authors propose a method for the 3-D reconstruction of the brain from anisotropic magnetic resonance imaging (MRI) brain data. The method essentially consists in two original algorithms both for segmentation and for interpolation of the MRI data. The segmentation process is performed in three steps. A gray level thresholding of the white and gray matter tissue is performed on the brain MR raw data. A global white matter segmentation is automatically performed with a global 3-D connectivity algorithm which takes into account the anisotropy of the MRI voxel. The gray matter is segmented with a local 3-D connectivity algorithm. Mathematical morphology tools are used to interpolate slices. The whole process gives an isotropic binary representation of both gray and white matter which are available for 3-D surface rendering. The power and practicality of this method have been tested on four brain datasets. The segmentation algorithm favorably compares to a manual one. The interpolation algorithm was compared to the shaped-based method both quantitatively and qualitatively. >
TL;DR: The authors present the solution of the (continuous-time) polynomial-exponential time series modeling problem and shows, in particular, that recursive modeling corresponds to updating by means of a cascade inter-connection of systems.
Abstract: The behavioral approach to system theory provides a parameter-free framework for the study of the general problem of linear exact modeling and recursive modeling. The authors present the solution of the (continuous-time) polynomial-exponential time series modeling problem. Both recursive and nonrecursive solutions are provided and classified according to properties like complexity and controllability. It is shown, in particular, that recursive modeling corresponds to updating by means of a cascade inter-connection of systems. As a special case, the solution of several other problems, such as rational interpolation, realization, and modeling of arbitrary discrete-time time series, is obtained. >
TL;DR: In this paper, a linear traveltime interpolation (LTI) method is proposed to calculate traveltimes and raypaths in a 2D velocity structure more rapidly and accurately than other conventional methods.
Abstract: A new ray-tracing method called linear traveltime interpolation (LTI) is proposed. This method computes traveltimes and raypaths in a 2D velocity structure more rapidly and accurately than other conventional methods. The LTI method is formulated for a 2D cell model, and calculations of traveltimes and raypaths are carried out only on cell boundaries. Therefore a raypath is considered to be always straight in a cell with uniform velocity. This approach is suitable to tomography analysis. The algorithm of LTI consists of two separate steps: step 1 calculates traveltimes on all cell boundaries; step 2 traces raypaths for all pairs of receivers and the shot. A traveltime at an arbitrary point on a cell boundary is assumed to be linearly interpolated between traveltimes at the adjacent discrete points at which we calculate traveltimes. Fermat's principle is used as the criterion for choosing the correct traveltimes and raypaths from several candidates routinely. The LTI method has been compared numerically with the shooting method and the finite-difference method (FDM) of the eikonal equation. The results show that the LTI method has great advantages of high speed and high accuracy in the calculation of both traveltimes and raypaths. The LTI method can be regarded as an advanced version of the conventional FDM of the eikonal equation because the formulae of FDM are independently derived from LTI. In the process of derivation, it is shown theoretically that LTI is more accurate than FDM. Moreover in the LTI method, we can avoid the numerical instability that occurs in Vidale's method where the velocity changes abruptly.
TL;DR: Two different techniques, convolution with an adaptive Gaussian window (AGW), and a two-dimensional thin-shell spline (STS), have been compared and contrasted for interpolating irregularly spaced data onto a regular grid and the importance of matching the interpolation technique to the characteristics of the original data is stressed.
Abstract: Although it is common for automated image processing techniques to claim subpixel accuracy in the identification of particles, or centroids of displacements of groups of particles, additional errors are inevitably introduced when and if these data are reinterpolated back onto a grid mesh whose nodes lie at different locations from the original data. Moreover, these errors can be large compared to the errors introduced in the original image processing step.
TL;DR: Two methods for shape-based interpolation that offer an improvement to linear interpolation are presented and tests with 3-D images of the coronary arterial tree demonstrate the efficacy of the methods.
Abstract: Many three-dimensional (3-D) medical images have lower resolution in the z direction than in the x or y directions. Before extracting and displaying objects in such images, an interpolated 3-D gray-scale image is usually generated via a technique such as linear interpolation to fill in the missing slices. Unfortunately, when objects are extracted and displayed from the interpolated image, they often exhibit a blocky and generally unsatisfactory appearance, a problem that is particularly acute for thin treelike structures such as the coronary arteries. Two methods for shape-based interpolation that offer an improvement to linear interpolation are presented. In shape-based interpolation, the object of interest is first segmented (extracted) from the initial 3-D image to produce a low-z-resolution binary-valued image, and the segmented image is interpolated to produce a high-resolution binary-valued 3-D image. The first method incorporates geometrical constraints and takes as input a segmented version of the original 3-D image. The second method builds on the first in that it also uses the original gray-scale image as a second input. Tests with 3-D images of the coronary arterial tree demonstrate the efficacy of the methods. >
TL;DR: A new method for coherent wide-band direction finding of far-field sources impinging on a two-dimensional array with a known arbitrary geometry, based on linear interpolation of the array manifold at a given frequency, f.
Abstract: We present a new method for coherent wide-band direction finding of far-field sources impinging on a two-dimensional array with a known arbitrary geometry. This method, termed array manifold interpolation (AMI), is based on obtaining the array manifold at a desired frequency f0, by linear interpolation of the array manifold at a given frequency, f. We use a separable representation of the array manifold vector, which separates the array geometry and the frequency from the direction θ, in order to derive the required array manifold interpolation matrix. The AMI method is practical, computationally efficient, and robust. For the special case of a uniform circular array, we present a fast implementation of the AMI method, which utilizes the FFT algorithm.
TL;DR: In this article, a simple empirical analysis system based on Bratseth's method of successive corrections applied to detrended field data, which approximates an optimal interpolation of fields with a spatially variable mean sampled within a limited domain by scattered observations, is described.
Abstract: This paper describes a simple empirical analysis system based on Bratseth's method of successive corrections applied to detrended field data, which approximates an optimal interpolation of fields with a spatially variable mean sampled within a limited domain by scattered observations. As in other empirical interpolation schemes, the influence function that determines the weights applied to increment variables is chosen such that unresolvable scales tend to be strongly damped, even if the contribution from observation error is not represented in a formally equivalent correlation model for observed increment variables. Unlike most empirical successive correction schemes, the number of iterations is not necessarily considered as a prescribed analysis parameter. Instead, the number of iterations can be chosen on a judgemental, posterior basis such that the analysis approximates the observed field to within some acceptable limit. The analysis generated by this form of successive corrections can be rep...
Patent•
17 Aug 1993TL;DR: Barycentric coordinates are determined using data readily available in computer graphics systems and defining polygons in world space so as to interpolate such polygons with regard to pixels selected by scan conversion as discussed by the authors.
Abstract: Barycentric coordinates are determined using data readily available in computer graphics systems and defining polygons in world space so as to interpolate such polygons with regard to pixels selected by scan conversion. The barycentric coordinates are employed to interpolate the polygons, for example to accomplish smooth shading or texture mapping. The process of the system involves defining primitive data (e.g. polygons) in a space not subject to nonlinear distortion (e.g. world space), transforming select primitive data to a space that is subject to nonlinear distortion, calculating in the space subject to nonlinear distortion (e.g. screen space) a set of areas (e.g. pixels) within a defined primitive (e.g. polygon) using data transformed to space subject to nonlinear distortion, transforming the set of areas to the space not subject to nonlinear distortion, determining at least one differential value (rate of change) of a variable for the primitive, calculating display data that is not subject to nonlinear distortion and using the differential to provide display data. For example, at a pixel, the rate of change in coordinate value (differential) is determined and utilized in texture mapping to facilitate the selection of levels of fuzziness with regard to picture detail for the pixel. Specifically, the differentials are in the coordinates of the texture du land dv.