Showing papers on "Bicubic interpolation published in 2002"

A new direction adaptive scheme for image interpolation

Abstract: We present a novel image interpolation method based on variational models with both smoothing and orientation constraints. By introducing the orientation constraint, we simplify the nonlinear PDE problem into a series of problems with explicit solutions. In our model, the gradient directions for the interpolated pixels are first estimated using a modified orientation diffusion method. Using these estimated gradient directions adaptive directional interpolation is carried out. An effective numerical implementation of the adaptive directional interpolation is presented for the case of upsampling by factors of two. This implementation had very low complexity and is well suited for real-time applications.

Canny edge based image expansion

Abstract: In this paper, a Canny edge-based image expansion method is introduced. Our proposed expansion method outperforms the pixel replication, the bilinear interpolation and the bicubic interpolation methods. It gives crisp and less zigzag pictures. Our method is applied on the image after it has been expanded using bilinear or bicubic interpolation. The edges of such an expanded image are obtained using the Canny edge detector. The values of pixels around the edges are modified to yield a crisper and less zigzagged picture.

Robust array interpolation using second-order cone programming

Abstract: We study Friedlander's (1993) array interpolation technique, whose main shortcoming in multisource scenarios is that it does not provide sufficient robustness against sources arriving outside specified interpolation sectors. In this letter, we develop a new robust interpolation approach by minimizing the interpolation error inside the sectors of interest while setting multiple "stopband" constraints outside these sectors to prevent performance degradation effects caused by out-of-sector sources. Computationally efficient convex formulations of the robust interpolation matrix design problem using second-order cone programming are derived.

Adaptive interpolation filter for motion compensated prediction

Abstract: Standardized hybrid video coding systems are based on motion compensated prediction with fractional-pel displacement vector resolution. In the recent JVT video coding scheme (MPEG-4 part 10, H.264) displacement vector resolutions of 1/4- or 1/8-pel are applied. In order to estimate and compensate these fractional-pel displacements, interpolation filters are used. So far, these interpolation filters are invariant. The same filter coefficients are applied for all sequences and for all images of a sequence. Therefore it is not possible to consider non-stationary statistical properties of video signals in the interpolation process. In this paper an adaptive interpolation scheme is presented. This interpolation scheme uses filter coefficients that are adapted once per image to the non-stationary statistical properties of the video signal. The filter-coefficients are coded and transmitted. Due to the adaptive interpolation filter a coding gain up to 0.8 dB PSNR is obtained in the JVT coding scheme.

Study of Cubic Splines and Fourier Series as Interpolation Techniques for Filling in Short Periods of Missing Building Energy Use and Weather Data

Abstract: A study of cubic splines and Fourier series as interpolation techniques for filling in missing data in energy and meteorological time series is presented. The followed procedure created artificially missing points (pseudo-gaps) in measured data sets and was based on the local behavior of the data set around those pseudo-gaps. Five variants of the cubic spline technique and 12 variants of Fourier series were tested and compared with linear interpolation, for filling in gaps of 1 to 6 hours of data in 20 samples of energy use and weather data. Each of the samples is at least one year in length. The analysis showed that linear interpolation is superior to the spline and Fourier series techniques for filling in 1–6 hour gaps in time series dry bulb and dew point temperature data. For filling 1–6 hour gaps in building cooling and heating use, the Fourier series approach with 24 data points before and after each gap and six constants was found to be the most suitable. In cases where there are insufficient data points for the application of this approach, simple linear interpolation is recommended.Copyright © 2002 by ASME

Image Interpolation Using PBLP Method on the Eigenspace

Abstract: In this paper the authors propose a method to use interpolation to eliminate characters in only one image with telops or other text through an image interpolation method that uses the eigenspace method. Background scenes and other images have a fractal character, and often the self-correlation in the image can be assumed to be high. The authors focus on this point and represent rules for describing the image based on an eigenspace consisting of only one image that has defects. The eigenspace generated in this manner reflects the features of the image, and by using this eigenspace, image interpolation can be achieved. Although this interpolation method does not restore the original image, the authors confirmed through experimental results that it can provide interpolation without a feeling of oddness for images which have a high level of self-correlation. © 2006 Wiley Periodicals, Inc. Syst Comp Jpn, 38(1): 87– 96, 2007; Published online in Wiley InterScience (). DOI 10.1002sscj.10319.

Image resampling between orthogonal and hexagonal lattices

Abstract: Resampling techniques are commonly required in digital image processing systems. Many times the classical interpolation functions are used, i.e., nearest-neighbour interpolation and bilinear interpolation, which are prone to the introduction of undesirable artifacts due to aliasing such as moire patterns. This paper presents a novel approach which minimizes the loss of information, in a least-squares sense, while resampling between orthogonal and hexagonal lattices. Making use of an extension of 2D splines to hexagonal lattices, the proper reconstruction function is derived. Experimental results for a printing application demonstrate the feasibility of the proposed method and are compared against the classical techniques.

Image interpolation method and apparatus thereof

Abstract: Disclosed is an image interpolation method and apparatus thereof. The present invention includes the steps of searching an edge direction to be used for interpolation by a pixel matching using input pixels and generating a pixel to be substantially interpolated by referring to pixels located on the searched edge direction. The present invention includes the steps of carrying out a first interpolation on input pixels using linear interpolation and finding weighted value coefficients in accordance with a relationship between the first interpolated pixel and the adjacent input pixels to be used for interpolation and preparing a pixel to be substantially interpolated by adaptive weighted interpolation applying the found weighted value coefficient to the adjacent input pixels. Accordingly, the present invention minimizes the blurring and is free of geometrical distortion.

Notes on EEG Resampling by Natural Cubic Spline Interpolation

Abstract: Resampling of digitized electroencephalographic data allows changing the sampling rate with minimal distortion of the signal. Useful applications of the procedure include compatibility among diverse hardware and software and the customization of data analysis. The natural cubic spline interpolation procedure is introduced in a discursive fashion. A formal presentation is provided in the appendix.

Subdivision of Box-Splines

Abstract: The two original refinement algorithms for defining subdivision surfaces were based on the biquadratic and bicubic tensor-product B-splines. At about the same time the use of box-splines as a more inclusive extension of B-splines to multivariate interpolation and approximation was being developed, and fairly soon a refinement algorithm over triangulations based on a box-spline was published.

Fast signal sinc-interpolation methods for signal and image resampling

Abstract: Digital signal resampling is required in many digital signal and image processing applications. Among the digital convolution based signal resampling methods, sinc-interpolation is theoretically the best one since it does not distort the signal defined by its samples. Discrete sinc-interpolation is most frequently implemented by the 'signal spectrum zero padding method.' However, this method is very inefficient and inflexible. Sinc-interpolation badly suffers also from boundary effects. In the paper, a flexible and computationally efficient methods for boundary effects free discrete sinc-interpolation are presented in two modifications: frame (global) sinc-interpolation in DCT domain and sinc-interpolation in sliding widow (local). In sliding window interpolation, interpolation kernel is a windowed sinc-function. Windowed sinc-interpolation offers options not available with other interpolation methods: interpolation with simultaneous local adaptive signal denoising and adaptive interpolation with super resolution. The methods outperform other existing discrete signal interpolation methods in terms of the interpolation accuracy and flexibility of the interpolation kernel design. Their computational complexity is O[log(Size of the frame)] per output sample for frame interpolation and O(Window Size) per output sample for sliding window interpolation.

Isophote estimation by cubic-spline interpolation

Abstract: We apply the cubic-spline interpolation to estimate isophotes from sparsely sampled digital images. For any non-pixel, we interpolate it by cubic spline, and by solving the yielding cubic function analytically, we find positions of pixels with the same intensity value. Experiment results are given and discussed. This spreads some important light on the nature of interpolation in images and why the well-known zigzag effects are obtained when images are interpolated.

Fast hybrid interpolation methods

Abstract: Hybrid interpolation methods are provided that employ more than one interpolation algorithm and choose the most appropriate interpolation algorithm that provides high quality images with a minimum processing time. Prediction means is first applied to predict which interpolation is most appropriate for a given pixel in terms of complexity and performance. Then, a simple interpolation algorithm is used for pixels for which the simple interpolation algorithm provides acceptable performances and a complex interpolation algorithm is used for pixels for which the complex interpolation algorithm, which requires a larger number of operations, significantly outperforms the simple interpolation algorithm. Consequently, it is possible to obtain high quality images without significantly increasing the processing time.

Interpolated Mth-band filters for image size conversion

Abstract: Image/video size conversion at variable rates requires that a large set of interpolation filters should be stored in a table. We present the interpolated Mth-band filters as the interpolation filters, which are obtained from the cubic spline interpolation of a prototype M/sub p/th-band eigenfilter. The proposed filter can be calculated in real time, eliminating the need for a large on-chip memory. Scaled images using the proposed filters show superb image quality.

Scattered data interpolation using data dependant optimization techniques

Abstract: Interpolation of scattered data has many applications in different areas. Recently, this problem has gained a lot of interest for CAD applications, in combination with the process of reverse engineering, i.e., the construction of CAD models for existing objects. Until now, no method for scattered data interpolation with a bivariate function has produced surface formats that can be directly integrated into a CAD system. Additionally many of the existing interpolation schemes exhibit undesirable curvature distribution of the reconstructed surface. In this paper we present a method for scattered data interpolation producing tensor-product B-splines with high quality curvature distribution. This method first determines the knot vectors in a way that guarantees the existence of an interpolating B-spline. In a second step the degrees of freedom not specified by the interpolation constraints are automatically set using a data dependent optimization technique. Examples demonstrate the quality of the resulting interpolants w.r.t. curvature distribution and approximation of known surfaces.

Edge oriented interpolation of video data

Abstract: The invention relates to a method for error reduction during interpolation of pixels in a video image along edges. By combining the output of two interpolation methods (4, 6) and by calculating a mix factor (k) using only the output of one interpolation method, the interpolation results may be improved. When applying the estimation error of edge-dependent interpolation in direction of a pixel obtained with a second interpolation method, the output is improved.

Method and program for interpolation processing, recording medium with the same recorded thereon, image processor and image forming device provided with the same

Abstract: PROBLEM TO BE SOLVED: To provide an interpolation processing method for minimizing the occurrence of an interpolation error and synthesizing a high quality image, an interpolation processing program and a recording medium with the interpolation processing program recorded thereon and further to provide an image processor for using the interpolation processing method to process an image and an image forming device provided with the image processor. SOLUTION: A plurality of kinds of interpolation directions with an interpolation pixel as an origin are defined (a4), and a block pair consisting of two blocks respectively located at both interpolation direction destinations and having a position relation of being point symmetrical to each other with respect to the interpolation pixel as a symmetrical point is extracted for each of the interpolation directions (a5). A correlation between two blocks is calculated for each extracted pair of blocks (a6), and at least one interpolation direction is selected on the basis of the correlation (a7). Pixel data of the interpolation pixel is generated on the basis of the selected interpolation direction (a8). COPYRIGHT: (C)2004,JPO

Min-max interpolators and Lagrange interpolation formula

Abstract: For oversampled band-limited signals, min-max optimal interpolators have been proposed under assumptions upon either the signal to be interpolated itself (e.g. finite energy) or its Fourier transform. In this paper, we consider the case where the signal is assumed to be bounded. For band-limited signals this is a more realistic assumption that is weaker than those previously considered. We propose an approximate solution that leads to closed form expressions for the interpolator coefficients. It relies upon an extension of the Lagrange interpolation formula.

Smooth Shape-Based Interpolation using the Conjugate Gradient Method

Abstract: In this paper a novel technique for smooth shapebased interpolation of volume data is introduced. Previously simple linear interpolation of signed distance maps has been used in practice. As it will be shown, this approach results in artifacts, since sharp edges appear along the original slices. In order to obtain a smooth 3D implicit function generated by interpolating 2D distance maps, we use a global interpolation method instead of a higher order local technique. The global curvature of the implicit function representing an isosurface is minimized using an iterative conjugate gradient method. Because of the iterative approach the user can easily control the trade-off between the smoothness of the isosurface and the computational cost of the refinement. As opposed to previous techniques, like variational interpolation, our method can generate a reasonably good approximation of the idealsolution in a significantly shorter time.

Optimal face reconstruction using training

Abstract: In previous work Muresan and Parks (see ICIP 2001, Greece, 2001) considered the problem of image interpolation from an adaptive optimal recovery point of view. They showed how a training set S determines a quadratic signal class and how to use this signal class to perform image interpolation. In that work the training set S was taken from the low resolution version of the image they were interpolating. In this paper we continue our discussion of the method presented previously by looking more closely at the training set S. In particular, we show how a training set of high resolution images can give very good interpolation results through the use of the method.

Noise equalization in resampling of images

Abstract: Changing resolution of images is a common operation. Typical applications use linear interpolation or piecewise cubic interpolation. Enlarging an image by a factor of (L/M), is represented by first interpolating the image on a grid L times finer than the original sampling grid, and then resampling it every M grid points. An equivalent but more efficient implementation is to use L interpolation kernels, which are decimated versions of the original interpolation kernel. The appropriate kernel is applied according to the desired position of the output pixel. When enlarging an image by a factor of (L/M), every L samples of the output signal are produced "from" M input samples (and their neighborhood) using different kernels. This pattern of resampling repeats itself every L output samples. Since the frequency responses of these kernels are totally different, the resampling cause "modulation", with a period of L samples, to high frequencies, e.g., the sampling circuit noise. This paper describes a simple procedure for equalization of this noise modulation. The procedure is based on handling each of the L interpolation kernels separately. We discuss separable interpolation and so the analysis is conducted for the one-dimensional case.

Generalized Interpolation for Super-Resolution

Abstract: In this chapter, we present a generalized interpolation scheme for image expansion and generation of super-resolution images. The underlying idea is to decompose the image into appropriate subspaces, to interpolate each of the subspacs individually and finally, to transform the interpolated values back to the image domain. This method is shown to presere various optical and structural properties of the image, such as 3-D shape of an object, regional homogeneity, local variations in scene reflectivity, etc. The motivation for doing so has also been explained theoretically. The generalized interpolation scheme is also shown to be useful in perceptually based high resolution representation of images where interpolation is done on individual groups as per the perceptual necessity. Further, this scheme is also applied to generation of highresolution transparencies from low resolution transparencies.

The Research Progress of Areal Interpolation

Abstract: In a broad sense, spatial interpolation includes point interpolation and areal interpolation. In this article these two types of interpolation methods were reviewed and the areal interpolation which was not very popular to major people was especially introduced according to whether the interpolation methods use ancillary data or not. In the areal interpolation methods without using ancillary data, the algorithm and its characteristic of the following methods were introduced: point-based areal interpolation, areal-weighted interpolation, areal-weighted interpolation using control zones and pycnophylactic method. In the areal interpolation methods using ancillary data, the EM algorithm and the method using remote sensing data as ancillary data were introduced. And the special case of areal interpolation - statistics variables spatialization-was also introduced. In the end, these two types of interpolation methods were compared and the main research trend of areal interpolation was foreseen.

Cubic splines with minimal norm

Abstract: Natural cubic interpolatory splines are known to have a minimal L2-norm of its second derivative on the C2 (or W22) class of interpolants. We consider cubic splines which minimize some other norms (or functionals) on the class of interpolatory cubic splines only. The cases of classical cubic splines with defect one (interpolation of function values) and of Hermite C1 splines (interpolation of function values and first derivatives) with spline knots different from the points of interpolation are discussed.