Showing papers on "Bicubic interpolation published in 2003"

On marching cubes

Abstract: A characterization and classification of the isosurfaces of trilinear functions is presented. Based upon these results, a new algorithm for computing a triangular mesh approximation to isosurfaces for data given on a 3D rectilinear grid is presented. The original marching cubes algorithm is based upon linear interpolation along edges of the voxels. The asymptotic decider method is based upon bilinear interpolation on faces of the voxels. The algorithm of this paper carries this theme forward to using trilinear interpolation on the interior of voxels. The algorithm described here will produce a triangular mesh surface approximation to an isosurface which preserves the same connectivity/separation of vertices as given by the isosurface of trilinear interpolation.

Method and system for selecting interpolation filter type in video coding

Abstract: A method and system for coding a video sequence based on motion compensated prediction (642), wherein an interpolation filter (640) is used to generate predicted pixel values for picture blocks in the video sequence. The interpolation filter for use in conjunction with a multi-picture type is shorter or having fewer coefficients than the interpolation filter for use in conjunction with a single-picture type. As such, the complexity of the interpolation filter for the multi-picture type can be reduced. Furthermore, the interpolation filter may be changed based on the characteristics of the block, the size and/or the shape of the block.

A note on cubic convolution interpolation

Abstract: We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing.

Smooth geometry images

Abstract: Previous parametric representations of smooth genus-zero surfaces require a collection of abutting patches (e.g. plines, NURBS, recursively subdivided polygons). We introduce a simple construction for these surfaces using a single uniform bi-cubic B-spline. Due to its tensor-product structure, the spline control points are conveniently stored as a geometry image with simple boundary symmetries. The bicubic surface is evaluated using subdivision, and the regular structure of the geometry image makes this computation ideally suited for graphics hardware. Specifically, we let the fragment shader pipeline perform subdivision by applying a sequence of masks (splitting, averaging, limit, and tangent) uniformly to the geometry image. We then extend this scheme to provide smooth level-of-detail transitions from a subsampled base octahedron all the way to a finely subdivided, smooth model. Finally, we show how the framework easily supports scalar displacement mapping.

Higher-order interpolation of regular grid digital elevation models

Abstract: The fundamental aim of a digital elevation model (DEM) is to represent a surface accurately, such that elevations can be estimated for any given location. It is, therefore, necessary to have efficient and precise algorithms for the computation of surface elevations between given points. The hypothesis presented here, is that higher-order interpolation techniques will always be more accurate than the likes of the popular bilinear algorithm. This hypothesis will be evaluated through an assessment of the accuracy with which DEMs can be interpolated to higher spatial resolutions. A variety of interpolation techniques are assessed, ranging from the one-term level plane to the 36-term biquintic polynomial. In general, techniques that take account of the local terrain neighbourhood are more consistent and accurate, reducing the rms. error by up to 20% of the bilinear interpolant.

Approximate bicubic filter

Abstract: Various techniques and tools for approximate bicubic filtering are described. For example, during motion estimation and compensation, a video encoder uses approximate bicubic filtering when computing pixel values at quarter-pixel positions in reference video frames. Or, during motion compensation, a video decoder uses approximate bicubic filtering when computing pixel values at quarter-pixel positions.

A full-disk image standardisation of the synoptic solar observations at the Meudon Observatory

Abstract: Robust techniques are developed to put the Hα and Ca K line full-disk images taken at the Meudon Observatory into a standardised form of a `virtual solar image'. The techniques include limb fitting, removal of geometrical distortion, centre position and size standardisation and intensity normalisation. The limb fitting starts with an initial estimate of the solar centre using raw 12-bit image data and then applies a Canny edge-detection routine. Candidate edge points for the limb are selected using a histogram based method and the chosen points fitted to a quadratic function by minimising the algebraic distance using SVD. The five parameters of the ellipse fitting the limb are extracted from the quadratic function. These parameters are used to define an affine transformation that transforms the image shape into a circle. Transformed images are generated using the nearest neighbour, bilinear or bicubic interpolation. Intensity renormalisation is also required because of a limb darkening and other non-radial intensity variations. It is achieved by fitting a background function in polar coordinates to a set of sample points having the median intensities and by standardising the average brightness. Representative examples of intermediate and final processed results are presented in addition to the algorithms developed. The research was done for the European Grid of Solar Observations (EGSO) project.

Smart interpolation by anisotropic diffusion

Abstract: To enlarge a digital image from a single frame preserving the perceptive cues is a relevant research issue. The best known algorithms take into account the presence of edges in the luminance channel, to interpolate correctly the samples/pixels of the original image. This approach allows the production of pictures where the interpolated artifacts (aliasing blurring effect,...) are limited but where high frequencies are not properly preserved. The zooming algorithm proposed in this paper on the other hand reduces the noise and enhances the contrast to the borders/edges of the enlarged picture using classical anisotropic diffusion improved by a smart heuristic strategy. The method requires limited computational resources and it works on gray-level images, RGB color pictures and Bayer data. Our experiments show that this algorithm outperforms in quality and efficiency the classical interpolation methods (replication, bilinear, bicubic).

On the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines

Abstract: This paper proves convergence rates for local scattered data interpolation by polyharmonic splines. To this end, it is shown that the Lagrange basis functions of polyharmonic spline interpolation are invariant under uniform scalings. Consequences of this important result for the numerical stability of the local interpolation scheme are discussed. A stable algorithm for the evaluation of polyharmonic spline interpolants is proposed.

Progressive scan method used in display using adaptive edge dependent interpolation

Abstract: Provided is a progressive scan method used in a display using adaptive edge interpolation. According to the progressive scan method, a final edge direction that satisfies a first edge-determination condition and a second edge-determination condition is detected by performing interpolation for 7×3 pixel windows, using code determination and a comparison of a standard deviation based on differences between luminances of pixel data divided by an edge boundary. As a result, directional edge interpolation is carried out in a region of a low gradient below 45° and to 27° at the minimum, and simple intra-field linear interpolation can be performed in a high-frequency texture region. Subsequently, it is possible to remove high-frequency noise introduced in edge dependent interpolation or unnatural screen display due to zigzagged edges, thereby improving the quality of a display.

Reduced multicubic database interpolation method for optical measurement of diffractive microstructures

Abstract: A reduced multicubic database interpolation method is provided. The interpolation method is designed to map a function and its associated argument into an interpolated value using a database of points. The database is searched to locate an interpolation cell that includes the function argument. The interpolation cell is used to transform the function argument to reflect translation of the interpolation cell to a unit cell. The interpolated value is then generated as a cubic function using the data points that correspond to vertices of the unit cell. All of the derivatives in the cubic function are simple and the interpolation accuracy order is higher than first-order.

Boundary effect free and adaptive discrete signal sinc-interpolation algorithms for signal and image resampling.

Abstract: The problem of digital signal and image resampling with discrete sinc interpolation is addressed. Discrete sinc interpolation is theoretically the best one among the digital convolution-based signal resampling methods because it does not distort the signal as defined by its samples and is completely reversible. However, sinc interpolation is frequently not considered in applications because it suffers from boundary effects, tends to produce signal oscillations at the image edges, and has relatively high computational complexity when irregular signal resampling is required. A solution that enables the elimination of these limitations of the discrete sinc interpolation is suggested. Two flexible and computationally efficient algorithms for boundary effects free and adaptive discrete sinc interpolation are presented: frame-wise (global) sinc interpolation in the discrete cosine transform (DCT) domain and local adaptive sinc interpolation in the DCT domain of a sliding window. The latter offers options not available with other interpolation methods: interpolation with simultaneous signal restoration/enhancement and adaptive interpolation with super resolution.

Deinterlacing apparatus and method thereof

Abstract: An apparatus for and a method of deinterlacing an interlaced image signal. A weight value is calculated after detecting degree of a motion between a pixel of a previous field and a pixel of a next field relative to a pixel of the current field to be interpolated. An inter-field interpolation value is calculated based on pixels in previous and next fields corresponding to the pixel to be interpolated. An intra-field interpolation value is calculated based adjacent pixels in the same field as the pixel to be interpolated. A final interpolation value is calculated based on the on the inter-field interpolation value, the intra-field interpolation value and the weight value.

A Comparison of Three‐Dimensional Interpolation Techniques for Plume Characterization

Abstract: Interpolation of contaminant data can present a significant challenge due to sample clustering and sharp gradients in concentration. The research presented in this paper represents a study of commonly used interpolation schemes applied to three-dimensional plume characterization. Kriging, natural neighbor, and inverse distance weighted interpolation were tested on four actual data sets. The accuracy of each scheme was gauged using the cross-validation approach. Each scheme was compared to the other schemes and the effect of various interpolation parameters was studied. The kriging approach resulted in the lowest error at three of the four sites. The simpler and quicker inverse distance weighted approach resulted in a lower interpolation error on the other site and performed well overall. The natural neighbor method had the highest average error at all four sites in spite of the fact that it has been shown to perform well with clustered data. Another unexpected result was that the computationally expensive high order nodal functions resulted in reduced accuracy for the inverse distance weighted and natural neighbor approaches.

A new approach to array interpolation by generation of artificial shift invariances: interpolated ESPRIT

Abstract: We address the problem of data independent robust array interpolation over large angular sectors. Previous interpolation methods apply the root-MUSIC principle to interpolation data of a predefined virtual ULA manifold. These methods either suffer from severely biased direction-of-arrival estimates due to interpolation errors or rely on data dependent interpolation matrix design. In this paper a new interpolation approach is proposed. Instead of transforming the original array geometry to the rather restrictive ULA structure, here interpolation is performed with the objective to create a virtual array manifold which is a shifted version of the real array manifold. This artificial shift-invariance can be exploited by the well-known ESPRIT algorithm. A joint design of virtual array geometry and interpolation matrix yields additional degrees of freedom which reduce interpolation errors and allow us to increase the interpolation sector. The new algorithm enjoys both simple design procedure and fast implementation and offers reliable DOA estimation for a wide range of different scenarios.

Method and apparatus for image interpolation based on adaptive polyphase filters

Abstract: An interpolation system interpolates image positions in an original image to produce an interpolated output image, wherein the original image is represented by digital input pixel data. A first filter with a sharp interpolation characteristic, that interpolates a selected image position in the image to generate a sharp interpolation output value. A second filter having a smooth interpolation characteristic, that interpolates the selected image position in the image to generate a smooth interpolation output value. A controller that calculates a weighting coefficient for the output of each filter. And, a combiner selectively combines the output values from the filters as a function of the weighting coefficients, to generate an interpolation output value for the selected image position of an interpolated output image.

Adaptive image interpolation based on local activity levels

Abstract: In this paper, an adaptive warped distance method is suggested for image interpolation. This method depends on modifying the warped distance technique for image interpolation taking into consideration the level of activity in local regions of the image. This is performed by weighting the pixels used in the interpolation process with different adaptive weights. The adaptation can be extended to different traditional interpolation techniques such as bilinear, bicubic and cubic spline techniques as well as to the warped distance technique. Results show that the adaptive weighting of pixels in interpolation gives better results than that obtained using traditional interpolation methods only or by using the warped distance technique.

Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization

Abstract: We present a segmentation approach to scientific visualization that combines the definition of higher-level data, the efficient extraction of meaningful derived feature-like data from defined properties, and the effective visual representation of the extracted data. Our framework is aimed at multi-valued time-varying data sets, where, for example, grid vertices might have a multitude of associated scalar, vector and tensor quantities. This "segmentation" approach to massive data set exploration allows the user to focus upon regions, and interactively explore these regions efficiently. The challenge is to generate this segmented data from existing multi-valued data sets, store this data in an efficient scheme, generate the boundaries of each region, and display these boundaries to the user. We present an integrated scheme that allows a common representation for segmentation, allows it to be applied to a number of data types, and allows derived representations to be calculated. We illustrate this framework with examples from scalar-and vector-field visualization.

Differential coding of interpolation filters

Abstract: A video coding system for coding a sequence of video frames each having an array of pixel values is provided. The system includes an interpolation filter to reconstruct sub-pixel values for use in the inter-frame prediction process. The coefficients of an interpolation filter are obtained differentially with respect to a predefined base filter in order to provide a set of difference values. As the base filter coefficients are known to both encoder and decoder and they are statistically close to the actual filters used in the video sequence, the decoder can reconstruct the pixel values based on the set of difference values.

Sectioned implementation of regularized image interpolation

Abstract: This paper presents a noniterative regularized inverse solution to the image interpolation problem The suggested solution is based on the segmentation of the image to be interpolated to overlapping blocks and interpolating each block separately The purpose of the overlapping of blocks is to avoid edge effects A global regularization parameter is used in interpolating each block In this suggested implementation, a single matrix inversion process of moderate dimensions is required in the whole interpolation process The suggested solution avoids the large computational complexity due to the matrices of large dimensions involved in the interpolation process The performance of this suggested image interpolation algorithm is compared to the standard iterative regularized interpolation scheme and to polynomial interpolation schemes such as the cubic spline image interpolation algorithm

Surface parameterization in volumetric images for curvature-based feature classification

Abstract: Curvature-based surface features are well suited for use in multimodal medical image registration. The accuracy of such feature-based registration techniques is dependent upon the reliability of the feature computation. The computation of curvature features requires second derivative information that is best obtained from a parametric surface representation. We present a method of explicitly parameterizing surfaces from volumetric data. Surfaces are extracted, without a global thresholding, using active contour models. A monge/spl acute/ basis for each surface patch is estimated and used to transform the patch into local, or parametric, coordinates. Surface patches are fit to a bicubic polynomial in local coordinates using least squares solved by singular value decomposition. We tested our method by reconstructing surfaces from the surface model and analytically computing Gaussian and mean curvatures. The model was tested on analytical and medical data.

Trajectory-planning through interpolation by overlapping cubic arcs and cubic splines

Abstract: A new path-planning interpolation methodology is presented with which the user may analytically specify the desired path to be followed by any planar industrial robot. The user prescribes a set of nodal points along a general curve to be followed by the chosen working point on the end-effector of the mechanism. Given these specified points along the path and additional prescribed kinematical requirements, Overlapping Cubic Arcs are fitted in the Cartesian domain and a cubic Spline interpolation curve is fitted in the time-domain. Further user-specified information is used to determine how the end-effector orientation angle should vary along the specified curve. The proposed trajectory-planning methodology is embodied in a computer-algorithm (OCAS), which outputs continuous graphs for positions, velocities and accelerations in the time-domain. If a varying end-effector orientation angle is specified, the OCAS-algorithm also generates continuous orientation angle, orientation angular velocity and orientation angular acceleration curves in the time-domain. The trajectory-planning capabilities of the OCAS-algorithm are tested for cases where the prescribed nodal points lie along curves defined by analytically known non-linear functions, as well as for nodal points specified along a non-analytical (free-form) test-curve. The proposed trajectory-planner may be implemented as part of kinematic and kinetic simulation software, and it also has the potential application for controlling machine tools in cutting along free-form curves. Copyright © 2003 John Wiley & Sons, Ltd.

Comparisons of Interpolation Methods In the Presence of Aliased Events

Abstract: The need for a process that interpolates beyond aliasing is illustrated by comparing the input in Figure 1 and the simple zero-padded FK interpolation in Figure 2. While the unaliased horizontal event is handled well, the badly aliased dipping event is interpolated poorly. Much of our recorded data contains aliased energy, and simple adjustments, such as NMO, do not always unalias data with overlapping signals such as primaries and multiples, which are often aliased with respect to each other. The methods considered here assume linear events; we will not attempt to consider interpolations that involve parabolic or hyperbolic paths.

A contour-preserving image interpolation method

Abstract: We introduce a novel image interpolation method, which focuses on providing artifact-free contours. In our method, the image contours are divided into edges and ridges, and we estimate the orientation of them differently and apply directional interpolations on them. Our method gives visually pleasing and natural-looking images. Experiment results are shown and compared with other interpolations methods.

FlowField and beyond: applying pressure-sensitive multi-point touchpad interaction

Abstract: In this paper, we discuss a new hand-gesture-based application, FIowField, which explores the use of pressure-sensitive multi-point touchpad (multi-touch) interaction. FIowField allows participants to interact using their whole hand with a flow of circulating particles, providing visual and auditory feedback. Limitations of the raw data mapping used in FIowField motivated work on applying interpolation techniques to improve the data representation. Thus far, bicubic interpolation provides the most effective method for initial processing. We observed two factors limiting the quality of the representation: the spacing of the sensors, and the pressure-distributing property of the touchpad surface.

Analysis and Characterization of Super-Resolution Reconstruction Methods

Abstract: Reconstruction techniques exploit a first building process using Low-resolution (LR) images to obtain a "draft" High Resolution (HR) image and then update the estimated HR by back-projection error reduction. This paper presents different HR draft image construction techniques and shows methods providing the best solution in terms of final perceived/measured quality. The following algorithms have been analysed: a proprietary Resolution Enhancement method (RE-ST); a Locally Adaptive Zooming Algorithm (LAZA); a Smart Interpolation by Anisotropic Diffusion (SIAD); a Directional Adaptive Edge-Interpolation (DAEI); a classical Bicubic interpolation and a Nearest Neighbour algorithm. The resulting HR images are obtained by merging the zoomed LR-pictures using two different strategies: average or median. To improve the corresponding HR images two adaptive error reduction techniques are applied in the last step: auto-iterative and uncertainty-reduction.

On the comparison of interpolation techniques for robotic position compensation

Abstract: This paper describes a novel technique for the position error compensations of the robot and manipulator calibration process based on a fuzzy error interpolation method. Traditional robots calibration implements model and modeless methods. Bilinear and cubic splines are the two popular techniques for the compensation of position error in modeless method. By using the fuzzy error interpolation technique provided in this paper, the accuracy of the position error compensation can be greatly improved. The comparison between the two popular traditional interpolation methods and this fuzzy error interpolation technique is made via simulation for three commonly used error models. The simulation results show that more accurate compensation result can be achieved using the fuzzy error interpolation technique compared with the bilinear and cubic spline interpolation methods.

Image interpolation using wavelet-based contour estimation

Abstract: Successful image interpolation requires proper enhancement of high frequency content of image pixels around edges. In this paper, we introduce a simple edge model to estimate high resolution edge profiles from lower resolution values. Pixels around edges are viewed as samples taken from one dimensional (1-D) continuous edge profiles according to 1-D smooth edge contours defining the sampling instants. The image is highpass filtered by wavelets and subpixel edge locations are estimated by minimizing the modeling error in the wavelet domain. Interpolation is carried out by applying the model, wherever applicable, together with a baseline interpolator (here, bilinear) in order to make edges look sharper without introducing artifacts. The results are compared to bilinear interpolation, and significant improvement in terms of SNR, edge sharpness and contour smoothness is observed.

Improvement of a nonlinear image interpolation method based on heat diffusion equation

Abstract: Recently many nonlinear interpolation schemes for images have produced images of higher resolution than those produced by linear techniques But smoothness still exists, especially on edges The smoothing process can be described as a traditional heat diffusion equation In this paper, this equation is combined with an improved edge-directed interpolation method to improve visual quality in terms of sharpened edges Experimental results indicate that the combination of the two methods is capable of achieving images with noticeably sharper edges

DFT and DCT based discrete sinc-interpolation methods for direct Fourier tomographic reconstruction

Abstract: The paper describes the implementation and use of recently developed DFT and DCT based discrete sinc-interpolation algorithms for the direct Fourier method of reconstructing images from projections. DFT based discrete sinc-interpolation is the only completely reversible discrete interpolation technique. DCT based discrete sinc-interpolation algorithm implements the same interpolation kernel that of the DFT based method and allows to avoid its boundary affect artifacts. It is also computationally more efficient. Two modifications of the DCT based interpolation for tomographic reconstruction are suggested: interpolation by global zooming of 1-D DFT spectra of projections and interpolation with variable zooming factor along the angle coordinate. The latter allows to substantially reduce the computational complexity without compromising interpolation accuracy. Results of comparative numerical simulation of suggested algorithms show a good image reconstruction quality with a reduced level of artifacts.