Showing papers on "Bicubic interpolation published in 1997"

Scattered data interpolation with multilevel B-splines

Abstract: The paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C/sup 2/ continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse to fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high fidelity reconstruction is possible from a selected set of sparse and irregular samples.

Quadratic interpolation for image resampling

Abstract: Nearest-neighbor, linear, and various cubic interpolation functions are frequently used in image resampling. Quadratic functions have been disregarded largely because they have been thought to introduce phase distortions. This is shown not to be the case, and a family of quadratic functions is derived. The interpolating member of this family has visual quality close to that of the Catmull-Rom cubic, yet requires only 60% of the computation time.

Interpolation methods for nonlinear wavelet regression with irregularly spaced design

Abstract: We introduce interpolation methods that enable nonlinear wavelet estimators to be employed with stochastic design, or nondyadic regular design, in problems of nonparametric regression. This approach allows relatively rapid computation, involving dyadic approximations to wavelet-after-interpolation techniques. New types of interpolation are described, enabling first-order variance reduction at the expense of second-order increases in bias. The effect of interpolation on threshold choice is addressed, and appropriate thresholds are suggested for error distributions with as few as four finite moments.

Spherical Methods for Spatial Interpolation: Review and Evaluation

Abstract: Global change research has placed new demands on methods of spatial analysis. In particular, spherical methods for spatial interpolation are required when spatial analyses are performed over large areas of the Earth's surface. In this article, spherical spatial interpolation procedures are reviewed, compared, and evaluated. Three classes of spherical interpolants are evaluated in detail: distance weighting, functional minimization, and tesselation. The strengths and weaknesses of a method from each of these classes—inverse-distance weighting, thin-plate splines, and surfaces fit to triangulated patches—are evaluated using a hypothetical mathematical surface and a global scale representation of topography. For smooth functions, such as the hypothetical mathematical surface, thin-plate splines produce a visually pleasing surface and have low interpolation error. For non-smooth surfaces, such as global topography, inverse-distance weighting, interpolating thin-plate splines, and triangulated C0 patches appea...

Efficient algorithm for discrete sinc interpolation

Abstract: A new computing method for discrete-signal sinc interpolation suitable for use in image and signal processing and the synthesis of holograms is described. It is shown to be superior to the commonly used zero-padding interpolation method in terms of interpolation accuracy, flexibility, and computational complexity.

Regularity-preserving image interpolation

Abstract: Common image interpolation methods assume that the underlying signal is continuous and may require that it possess one or more continuous derivatives. These assumptions are not generally true of natural images, most of which have instantaneous luminance transitions at the boundaries between objects. Continuity requirements on the interpolating function produce interpolated images with oversmoothed edges. To avoid this effect, a wavelet-based interpolation method that imposes no continuity constraints is introduced. The algorithm estimates the regularity of edges by measuring the decay of wavelet transform coefficients across scales and attempts to preserve the underlying regularity by extrapolating a new subband to be used in image resynthesis. The algorithm produces noticeably sharper edges than traditional techniques and exhibits an average PSNR improvement of 2.5 dB over bilinear and bicubic techniques.

Image pickup apparatus having an interpolation function

Abstract: The present invention enables to obtain an image of a high resolution as reasonable costs by using an adaptive interpolation circuit which is supplied by image data R, G, and B which have been subjected to a white balance adjustment in a DSP and an R-G image is combined in an internal memory. The adaptive interpolation circuit calculates correlation degrees in a vertical direction, a horizontal direction, and diagonal directions. If an interpolation is executed according to the R-G image in the direction having the greatest correlation degree, no LPF processing is executed, i.e., no resolution deterioration is caused in a direction which orthogonally intersects the aforementioned direction. That is, the adaptive interpolation circuit enables to enhance a resolution by executing an interpolation according to the correlation of the image data around a portion to be interpolated.

Efficient radiosity rendering using textures and bicubic reconstruction

Abstract: Wepresenta method to speed up walkthmttghs of static scenes. It involves the cmatiort of acmttimsous C1 radiosity reconstruction for adaptively sampled tegiotts. This mpmaentation is a unitied solution to handle usuestricted quadtrees and T-vertices, and allows for the generation of multiple different levels-of-detail of the radiosity function, which are represented as texture maps. The method also involves the use of hardwase bicublc filtering for the mdiosity shading. Both techniques allow improvenmts in performance and memory usage while preserving visual appearance. CR CMegories and Subject Deaeriptom: L3.3 [Computer Graphics]: Pictusdmage Generation Viewing Algorithm, 1.3.6 [Computer Graphics]: Methodology and Techniques Integration Techniques. Additioatsl

A vision-aided reverse engineering approach to reconstructing free-form surfaces

Abstract: A vision-aided reverse engineering approach (VAREA) has been developed to reconstruct least-square free-form surface models from physical models, with a coordinate measurement machine (CMM) equipped with a touch-triggered probe and a computer vision system. The VAREA integrates computer vision, surface data digitization and surface modelling into a single process. Two main steps are applied in this innovative approach. The initial vision-driven surface triangulation process (IVSTP) generates a triangular patch by using stereo image detection and a constrained Delaunay triangulation method. The adaptive model-based digitizing process is then used to refine the surface reconstruction and to control accuracy to within user-specified tolerances. As a result, a least-squares bicubic B-spline surface model with the controlled accuracy of digitization can be obtained for further application in product design and manufacturing processes. More than 85% reduction has been achieved in the time required to construct free-form surfaces using this approach, as compared with traditional manual methods with CMM. Therefore, product design lead time can be significantly reduced.

Interpolation processing method and apparatus for image signals having improved image edge differentiation

Abstract: A judgment is made as to whether an interpolation point in an original image is or is not located at an image edge portion. The judgment is made by using a threshold value having been set such that, as a desired level of sharpness of an interpolation image obtained from interpolation processing becomes low, the threshold value may become large. When an interpolation point is judged as being located at an image edge portion, an interpolated image signal component corresponding to the interpolation point is calculated with interpolation processing capable of keeping the image edge portion sharp. When an interpolation point is judged as not being located at an image edge portion, an interpolated image signal component corresponding to the interpolation point is calculated with the interpolation processing, which is carried out by combining interpolation processing for obtaining an interpolation image, which has a comparatively high sharpness, and interpolation processing for obtaining an interpolation image, which has a low sharpness.

Improvements to Image Magnification

Abstract: The main limitation of current magnifying techniques is that they do not introduce any new information into the original image. This lack of information is responsible for the perceived degradation of the enlarged image. The idea underlying this work is to estimate missing frequencies from the original low resolution image and to synthesize them. Sub-pixel edge estimation and a polynomial interpolation step are the key techniques of the proposed method. Furthermore, a new extension to color images is presented. Results are encouraging even if they suggest that further effort should be spent in improving edge localization accuracy.

Interpolation method for binary image

Abstract: An improved interpolation method in which a threshold value used for determining a pixel value of a pixel generated by interpolation according to a context (state value of adjacent pixels). In the interpolation method, the ambiguity between the interpolation value and the threshold value is removed by using the context (state value of the reference pixels around the interpolated pixel), thereby reducing the blocking and smoothing phenomena in the restored binary image.

An approximation for discrete B-splines in time domain

Abstract: A simple discrete version of B-splines defined as a multifold discrete convolution of sampled rectangles is proposed in the analogy of B-splines being multifold convolution integrals of rectangular functions. Then it is proven that its staircase interpolation tends to the B-spline when the sampling interval goes to zero. This version can be regarded as an approximation for the discrete B-splines established in the literature, and it is faster in numerical evaluation.

Method of interpolation in an n-dimensional colour space

Abstract: The present invention pertains to a method for interpolating colour values with a view to converting an initial colour space into an output colour space. The initial colour space is divided into a multidimensional network. For the reseau points converted components of the output colour space are prescribed as interpolation nodes; the converted components, located between the reseau points, are obtained by interpolating said nodes. For the purpose of interpolation, the components of an initial colour to be interpolated are broken down in a multiple of the reseau point spacing and a remainder, and the remaining values are classified by order of magnitude. At the reseau points of a sub-space comprising the initial colour to be interpolated, the interpolation nodes are selected in a series determined by the classification of the remaining values, and the initial colour is interpolated based on the selection of interpolation nodes. The inventive method can be used without significantly increasing the calculation work for the initial colour space and the output colour space with any number of dimensions.

Slice interpolation using the distance transform and morphing

Abstract: Shape-based interpolation is an important technique in the area of three dimensional reconstruction from cross-sectional images. A shape-based interpolation technique using the distance transform and morphological concept is presented. Experimental results of interpolation and 3D reconstructed surfaces for synthetic, CT and MRI slice images are given.

Method and device for varying interpolation factors

Abstract: A method and device for varying interpolation factor of at least one position-dependent, periodic signal in a position measurement system. The method and device allows switching between one of a specified number of different interpolation factors at a switching time point at which the interpolated measurement signal has an identical signal form for every possible interpolation factor.

Interpolation by Bivariate Splines on Crosscut Partitions

Abstract: We give a survey of recent methods to construct Lagrange interpolation points for splines of arbitrary smoothness r and degree q on general crosscut partitions in ℝ2. For certain regular types of partitions, also results on Hermite interpolation sets and on the approximation order of the corresponding interpolating splines are given.

A neural implementation of interpolation with a family of kernels

Abstract: A paradigm for interpolating images based on a family of kernels is presented. Each kernel is "tuned" to specific image characteristics and contains the information responsible for the local creation of missing detail. This interpolation process (1) exploits the correlation that exists in the local structure of images via a self-organizing feature map (SOFM) and (2) establishes an optimal set of linear associative memories (LAMs) from the homologous neighborhoods of a set of low and high resolution image counterparts. Each LAM creates members of the family of interpolation kernels. We compare the performance of this technique with the commonly used bilinear and spline interpolation methods and demonstrate its ability to generalize well.

Shape-based calculation and visualisation of general cross-sections through biological data

Abstract: The paper reports a solution to the problem of image interpolation for generating, with high precision, an arbitrary cross-section from a series of slices. Shape-based interpolation as proposed allows the interpolation process to be influenced by the shape of the object. It is accomplished first by creating reconstructed shapes of the objects from a series of slices. Correspondence vectors distributed along the object surface are then generated from the reconstructed shapes. These vectors ensure the correct image interpolation on the boundaries of objects. Next, the correspondence vectors are interpolated to every image point within the new cross-section in process, and the image points at the start and end of a vector are linearly interpolated. Places where the correspondence vectors cannot be (branching or holes in the object shape) are treated separately. Results are presented from biological data obtained using an optical microscope. The data indicate that the proposed method produces more accurate results than commonly used interpolation methods, although at the cost of increased computation.

Tetrahedral and pruned tetrahedral interpolation

Abstract: New interpolation techniques allow improved efficiency and speed in performing color space conversions A radial interpolation technique accomplishes an interpolation by generating successive subcubes A value of a vertex of the final subcube generated is used as the result of the interpolation Subcubes are generated by averaging a selected vertex value with the vertex values of each of the remaining vertices A pruned radial interpolation technique employs a subset of the vertex values of the initially selected cube to generate the result of the interpolation, thereby improving upon the efficiency of the radial interpolation A tetrahedral interpolation technique accomplishes an interpolation by generating successive subcubes A value of a vertex of the final subcube generated is used as the result of the interpolation Subcubes are generated by applying a mathematical relationship which allows computation of subcube vertex values through a series of logical AND, logical OR and averaging operations A pruned tetrahedral interpolation technique employs a subset of the vertex values of the initially selected cube to generate the result of the interpolation, thereby improving upon the efficiency of the tetrahedral interpolation A common hardware implementation of pruned radial interpolation and pruned tetrahedral interpolation uses the common hardware structure of the two techniques with multiplexing of the input vertex values to allow performance of either a pruned radial interpolation or a pruned tetrahedral interpolation Non-symmetric pruned radial and Non-symmetric pruned tetrahedral interpolation permit interpolation using interpolation data values distributed throughout the color space with a resolution that varies according to characteristics of the color space Multiplexing of the interpolation data values to the non-symmetric pruned radial interpolation hardware and to the non-symmetric pruned tetrahedral interpolation hardware allows for a common hardware implementation

Radial Basis Functions Viewed From Cubic Splines

Abstract: In the context of radial basis function interpolation, the construction of native spaces and the techniques for proving error bounds deserve some further clarification and improvement. This can be described by applying the general theory to the special case of cubic splines. It shows the prevailing gaps in the general theory and yields a simple approach to local error bounds for cubic spline interpolation.

Non-symmetric radial and non-symmetric pruned radial interpolation

Abstract: New interpolation techniques allow improved efficiency and speed in performing color space conversions. A radial interpolation technique accomplishes an interpolation by generating successive subcubes. A value of a vertex of the final subcube generated is used as the result of the interpolation. Subcubes are generated by averaging a selected vertex value with the vertex values of each of the remaining vertices. A pruned radial interpolation technique employs a subset of the vertex values of the initially selected cube to generate the result of the interpolation, thereby improving upon the efficiency of the radial interpolation. A tetrahedral interpolation technique accomplishes an interpolation by generating successive subcubes. A value of a vertex of the final subcube generated is used as the result of the interpolation. Subcubes are generated by applying a mathmatical relationship which allows computation of subcube vertex values through a series of logical AND, logical OR and averaging operations. A pruned tetrahedral interpolation technique employs a subset of the vertex values of the initially selected cube to generate the result of the interpolation, thereby improving upon the efficiency of the tetrahedral interpolation. A common hardware implementation of pruned radial interpolation and pruned tetrahedral interpolation uses the common hardware structure of the two techniques with multiplexing of the input vertex values to allow performance of either a pruned radial interpolation or a pruned tetrahedral interpolation. Non-symmetric pruned radial and Non-symmetric pruned tetrahedral interpolation permit interpolation using interpolation data values distributed throughout the color space with a resolution that varies according to characteristics of the color space. Multiplexing of the interpolation data values to the non-symmetric pruned radial interpolation hardware and to the non-symmetric pruned tetrahedral interpolation hardware allows for a common hardware implementation.

Common non-symmetric pruned radial and non-symmetric pruned tetrahedral interpolation hardware implementation

Abstract: New interpolation techniques allow improved efficiency and speed in performing color space conversions. A radial interpolation technique accomplishes an interpolation by generating successive sub-cubes. A value of a vertex of the final sub-cube generated is used as the result of the interpolation. Subcubes are generated by averaging a selected vertex value with the vertex values of each of the remaining vertices. A pruned radial interpolation technique employs a subset of the vertex values of the initially selected cube to generate the result of the interpolation, thereby improving upon the efficiency of the radial interpolation. A tetrahedral interpolation technique accomplishes an interpolation by generating successive subcubes. A value of a vertex of the final sub-cube generated is used as the result of the interpolation. Subcubes are generated by applying a mathematical relationship which allows computation of sub-cube vertex values through a series of logical AND, logical OR and averaging operations. A pruned tetrahedral interpolation technique employs a subset of the vertex values of the initially selected cube to generate the result of the interpolation, thereby improving upon the efficiency of the tetrahedral interpolation. A common hardware implementation of pruned radial interpolation and pruned tetrahedral interpolation uses the common hardware structure of the two techniques with multiplexing of the input vertex values to allow performance of either a pruned radial interpolation or a pruned tetrahedral interpolation. Non-symmetric pruned radial and Non-symmetric pruned tetrahedral interpolation permit interpolation using interpolation data values distributed throughout the color space with a resolution that varies according to characteristics of the color space. Multiplexing of the interpolation data values to the non-symmetric pruned radial interpolation hardware and to the non-symmetric pruned tetrahedral interpolation hardware allows for a common hardware implementation.

Neural Network Methods for NURBS Curve and Surface Interpolation

Abstract: New algorithms based on artificial neural network models are presented for cubic NURBS curve and surface interpolation. When all the knot spans are identical, the NURBS curve interpolation procedure degenerates into that of uniform rational B-spline curves. If all the weights of data points are identical, then the NURBS curve interpolation procedure degenerates into the integral B-spline curve interpolation.

3D shape modelling using a multi-scale surface model

Abstract: This paper presents a method for extracting the 3D shape of objects from 3D gray level images. The object surface is assumed to be described by a bicubic B-spline surface. The detection of the object shape is achieved using a hierarchical approach in which the object surface is successively estimated using the spline model at increased scales. At each scale, the model is iteratively fitted to a set of measurement points which are believed to be on the object surface. The measurement points are detected by searching for voxels with the strongest edge response along the direction normal to the model surface. Searching for the measurement points is controlled within a search radius determined based on the edge strength at the points on the current model surface. The result is a parametric surface approximating the object surface to be detected.

Interpolation by Translates of a Basis Function

Abstract: Interpolation using radial basis functions has become an established and useful technique in multi-dimensional data fitting. It is a special case of interpolation by translates of a basis function. All the methods used in practice have a strong connection with a variational principle. In this paper we provide a straightforward approach to the variational principle, and make some useful practical deductions from the theory.