Showing papers on "Bicubic interpolation published in 1991"

Seismic trace interpolation in the F-X domain

Abstract: Interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing. A major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated. In this respect, a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events, nor estimation of these directions.The method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly, regardless of the original spatial interval, without any attempt to determine their true dips. The predictability of linear events in the f-x domain allows the missing traces to be expressed as the output of a linear system, the input of which consists of the recorded traces. The interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces.Synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations. Assessment of the method with a real data set shows that the interpolation yields an improved migrated section.

Optimal interpolation of radiated fields over a sphere

Abstract: An optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples. Using the concept of the field equivalent (spatial) bandwidth, a central interpolation scheme is developed to compute the field in theta , phi coordinates, starting from its samples. The maximum allowable sample spacing and error upper bounds are also rigorously derived. Several simulated examples of pattern reconstruction are presented, for both the cases of field and power pattern interpolation. The interpolation error, as a function of the retained sample number, has been also evaluated and compared with the theoretical upper bounds. The algorithm stability versus randomly distributed errors added to the exact samples is demonstrated. >

Digital image interpolator using a plurality of interpolation kernals

Abstract: An interpolator for enlarging or reducing a digital image includes an interpolation coefficient memory containing interpolation coefficients representing a one dimension interpolation kernel. A row interpolator receives image pixel values, retrieves interpolation coefficients from the memory, and produces interpolated pixel values by interpolating in a row direction. A column interpolator receives multiple rows of interpolated pixel values from the row interpolator, retrieves interpolation coefficients from the memory, and produces rows of interpolated pixel values by interpolating in a column direction.

A method for intersecting algebraic surfaces with rational polynomial patches in presented

Abstract: The paper presents a hybrid algorithm for the computation of the intersection of an algebraic surface and a rational polynomial parametric surface patch. This algorithm is based on analytic representation of the intersection as an algebraic curve expressed in the Bernstein basis; automatic computation of the significant points of the curve using numerical techniques, subdivision and convexity properties of the Bernstein basis; partitioning of the intersection domain at these points; and tracing of the resulting monotonic intersection segments using coarse subdivision and faceting methods coupled with Newton techniques. The algorithm described in the paper treats intersections of arbitrary order algebraic surfaces with rational biquadratic and bicubic patches and introduces efficiency enhancements in the partitioning and tracing parts of the solution process. The algorithm has been tested with up to degree four algebraics and bicubic patches.

Closed surfaces defined from biquadratic splines

Abstract: In order to construct closed surfaces with continuous unit normal, this paper studies certain spaces of spline functions on meshes of four-sided faces. The functions restricted to the faces are biquadratic polynomials or, in certain special cases, bicubic polynomials. A basis is constructed of positive functions with “small” support which sum to 1 and reduce to tensor-product biquadratic B-splines away from certain “singular” vertices. It is also shown that the space is suitable for interpolating data at the midpoints of the faces.

Motion/pattern adaptive interpolation of interlaced video sequences

Abstract: A hybrid motion/pattern adaptive scheme for the conversion of interlaced video sequences to the progressive format is presented. It normally operates in the temporal interpolation model and switches to spatial interpolation when motion is detected. The filter for spatial interpolation is adapted according to the local image pattern. Directional filters are designed for oriented features based on their representation by oriented polynomials. Although the proposed scheme has only been applied to the interpolation of interlaced signals, its principle is applicable to other problems in video signal resolution enhancement. >

Method for interpolating between two regions of a display

Abstract: A method of forming three dimensional displays (100) from a series of two dimensional sections (102) by interpolation using image algebraic operations or distance measurements on the two dimensional sections to generate interpolation sections (104) The interpolating region between two regions in successive sections is generated automatically Multiple interpolation regions connecting the original two regions may be included

Closed smooth piecewise bicubic surfaces

Abstract: Two classes of closed piecewiee bicubic surfaces are considered. These surfaces are geometrically smooth about each extraordinary point and, for a large mesh and a large control polyhedron, they are parametrically smooth away from the extraordinary points. Furthermore, free parameters are available for manipulating the shape of the surface without changing the control polyhedron. The control is local for a large control polyhedron.

Efficient performance function interpolation scheme and its application to statistical circuit design

Abstract: A concept of ‘maximally’ flat polynomial interpolation of circuit responses (or performance functions) is proposed, developed and exploited. This kind of simple approximation of circuit behaviour proves extremely useful for Monte Carlo statistical yield estimation and optimization. Application of the resulting interpolating polynomials may substantially reduce the number of actual, time-consuming circuit analyses. Results of all available circuit analyses can be utilized to construct the interpolating polynomials, even if their number is not sufficient for a full unique quadratic or higher-order interpolation. This is accomplished by selecting the maximally flat interpolation in which all higher-order-term coefficients are minimized in the least squares sense. More importantly, a low-cost updating of the interpolating polynomials is developed in order to accommodate the results of additional circuit simulations as they become available. Examples of this approximation of circuit responses as well as its application to yield estimation and optimization are shown.

Paper: Systolic algorithm for polynomial interpolation and related problems

Abstract: This paper describes a systolic algorithm for interpolation and evaluation of polynomials over any field using a linear array of processors. The periods of these algorithms are O(n) for interpolatin and O(1) for evaluation. This algorithm is readily adapted for Chinese remaindering, easily generalized for the multivariable interpolation and can be extended for rational interpolation to produce Pade approximants. The instruction systolic array implementation of the algorithm is presented here.

Interpolation signal producing circuit with improved amplitude interpolation

Abstract: In an interpolation signal producing circuit, amplitudes of a plurality of proximate pixel signals are compared and the order of magnitudes of such pixel signals is determined, whereupon an interpolation signal is derived which is intermediate the largest and smallest amplitudes, for example, next to the largest or smallest amplitudes or an average thereof. The interpolation signal thus derived may be advantageously employed for sub-sampling, that is, doubling the number of pixels in each horizontal scanning line of a displayed video picture, for doubling the horizontal scanning lines in a field, or in compensating for drop-out and the like.

Shape-Based Interpolation Using a Chamfer Distance

Abstract: Shape-based interpolation is a methodology to estimate the locations of the picture elements (pixels) which would be contained in an organ of interest in non-existent slices through the human body from the locations of the pixels in the organ in slices that have been obtained by a tomographic imager. In this paper we motivate the need for shape-based interpolation and report on some quantitative experiments which were done to evaluate the relative performance of a number of interpolation methods for tomographic imaging of the human body. In particular, we introduce the new notion of shape-based interpolation using a chamfer distance and show that a statistically extremely significant improvement over previously proposed methods is achieved by this newly proposed interpolation method.

Reduced-order distillation model using collocation method with cubic splines

Abstract: A simple and compact form of reduced-order distillation model especially suitable for real-time applications is proposed. For this purpose, a modular collocation approach with the cubic spline interpolation function is developed and applied to an underlying distillation model which is constructed based on the McCabe and Thiele assumptions plus constant tray holdups. To evaluate the performance of the model, numerical simulations are carried out for the case of dynamics as well as steady states. As a consequence, it is found that the proposed reduced-order model gives better approximation than those obtained by the conventional reduced-order model with the Lagrange interpolation function.

Shape-preserving interpolation by parametric piecewise cubic polynomials

Abstract: Smooth piecewise parametric cubic planar curves can be used effectively to perform shape-preserving interpolation for both single-valued and multivalued data. An algorithm that controls shape by automatically adjusting certain free parameters is studied. Both mathematical (monotonicity, convexity, positivity, minimal-oscillation) and heuristic (visual-pleasantness) criteria are considered.

Trend Surface Analysis and Splines for Pattern Determination in Plant Communities

Abstract: Some approximation and interpolation approaches to mapping ecological and vegetation variables on a surface are presented. In this connection trend surface analysis based on polynomial regression is shown to be a promising technique. It is reviewed and typical applications are presented. Basic features of the mathematical background for bicubic and triangular splines are discussed. ‘Splines’ is a family of powerful interpolation techniques for mapping of ecological and vegetational variables both on regular and irregular grids.

A Bivariate Interpolation Algorithm for Data that are Monotone in One Variable

Abstract: This paper describes an algorithm for interpolating data on a rectangular mesh by piecewise bicubic functions. In [SIAM J. Numer. Anal., 26 (1989), pp. 1–9] the authors presented a monotonicity-preserving algorithm for data that are monotone in both variables. The present paper shows how the algorithm can be modified to treat data that are monotone in only one variable.

Fractal Description And Classification Of Breast Tumors

Abstract: In this paper we present an approach to classify breast tumors with different sizes by using the Bezier bicubic interpolation and fractal feature vector and to describe small tumors by using texture analysis, local fractal dimension, fractal interpolation and fractal feature vector. The basic theory and applications of these techniques are discussed and the results of classification and description of breast tumors by fractals are presented

Interpolation techniques for noisy spectral data

Abstract: A technique for interpolating noisy frequency domain data is presented. It is based on rational function interpolation with the least square error method. Compared to traditional Lagrange interpolation, the method is shown to be more robust. Results for simulated data with additive white Gaussian noise and measured data are presented to demonstrate the validity of the interpolation technique. >

Spatial and temporal surface interpolation using wavelet bases

Abstract: Efficient solutions to spatial interpolation problems (e.g., regularization) and spatio-temporal interpolation problems (e.g., regularization plus Kalman filtering) can be obtained by using wavelet bases either for problem discretization or for preconditioning. Good approximate solutions can be obtained in only O(n) operations and O(n) storage locations, so that rear-real- time implementations are possible on standard microprocessors.

Sequences for DFT interpolation

Abstract: The interpolation sequences needed for cascade structures are considered. First, the optimal sequences based on half-band filters are examined. The sequences with integer coefficients are then studied. The interpolation algorithm is reviewed, and the required number of multiplications is determined for half-band filters and compared with pruning and perfect interpolation techniques. >

Modeling bivariable-dependeiut material properties using an explicit bicubic spline

Abstract: A compact and efficient algorithm is developed for generating and evaluating a bicubic spline interpolating function. The method is useful for the numerical solution of heat transfer and fluid flow problems when the properties are a function of two variables. The explicit formulation allows a one-time calculation of sets of bicubic coefficients, which provide an interpolation of the dependent property over the domain of the independent variables. The method provides continuous first and second derivatives in both variables far the iterative solution of nonlinear problems.

Integrated Computer Aided Surface Modeling and BEM Analysis

Abstract: An integration of Computer aided free form surface modelling and Boundary Element Analysis in the design process of mechanical systems is presented using an new non conforming boundary element. A periodic bicubic B-spline patches representation is introduced to define the surface bounding the parts to be designed. For BEM analysis of mixed elastostatic problems we use a new element having geometric shape functions different from the usual Lagrangian interpolation functions used in isoparametric formulation, and which satisfy CAD requirements. Elements nodes are automatically generated and depend on geometric design criteria.

Lagrange interpolation by quadratic splines on a quadrilateral domain of 2

Abstract: The aim of this paper is to solve a Lagrange interpolation problem by quadratic splines on a triangular partition of a quadrilateral domain of ℝ 2 . Some results concerning the norm of the interpolation operator and error estimates are given for a square domain. For more details see [7].

Low Sensitivity Interpolation Using Feed-Forward Neural Networks With One Hidden Layer

Abstract: : It is possible to assign directly the weights of a feed-forward neural net with one hidden layer so that the network interpolates through a given set of input-output points exactly and in such a way that the sensitivity to noise at the points of interpolation is as small as desired. This is demonstrated with a constructive proof. The weight assignment for exact interpolation requires the inversion of a nonsingular matrix. If the exact interpolation requirement is relaxed, then the inversion of that matrix can be avoided. It is possible to determine weights so that the network approximately interpolates through the set of points with any desired degree of accuracy and with a sensitivity as small as desired. Both the accuracy of interpolation and the sensitivity to noise are controlled by the size of the weights in the first layer of weights. Estimates on how large these weights have to be to achieve a desired interpolation accuracy and noise sensitivity are derived. An algorithm for approximate interpolation with low sensitivity is presented and illustrated with simple examples. weight assignment, exact/approximate interpolation, low sensitivity, total derivative.