Showing papers on "Bicubic interpolation published in 2006"
TL;DR: A new edge-guided nonlinear interpolation technique is proposed through directional filtering and data fusion that can preserve edge sharpness and reduce ringing artifacts in image interpolation algorithms.
Abstract: Preserving edge structures is a challenge to image interpolation algorithms that reconstruct a high-resolution image from a low-resolution counterpart. We propose a new edge-guided nonlinear interpolation technique through directional filtering and data fusion. For a pixel to be interpolated, two observation sets are defined in two orthogonal directions, and each set produces an estimate of the pixel value. These directional estimates, modeled as different noisy measurements of the missing pixel are fused by the linear minimum mean square-error estimation (LMMSE) technique into a more robust estimate, using the statistics of the two observation sets. We also present a simplified version of the LMMSE-based interpolation algorithm to reduce computational cost without sacrificing much the interpolation performance. Experiments show that the new interpolation techniques can preserve edge sharpness and reduce ringing artifacts
971 citations
TL;DR: A new envelope algorithm, the segment power function method, is put forward that is superior to existing algorithms because in most situations it is more flexible than the cubic spline interpolation algorithm and smoother than the Akima interpolation algorithms, and it is less likely to introduce a false frequency when applied to HHT.
106 citations
TL;DR: Quantitative fidelity analyses and visual experiments indicate that these new nonseparable, 2-D cubic-convolution kernels can outperform several popular interpolation methods and establish a practical foundation for adaptive interpolation based on local autocorrelation estimates.
Abstract: Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2,2]/spl times/[-2,2] with constraints for biaxial symmetry, diagonal (or 90/spl deg/ rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-5PCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply.
80 citations
TL;DR: In this paper, a procedure for the construction of smooth fractal functions, with the help of Hermite osculatory polynomials, is described, and a set of interpolating mappings associated to a cubic spline is defined and the density of fractal cubic splines in the real world is proven.
Abstract: Fractal methodology provides a general frame for the understanding of real-world phenomena. In particular, the classical methods of real-data interpolation can be generalized by means of fractal techniques. In this paper, we describe a procedure for the construction of smooth fractal functions, with the help of Hermite osculatory polynomials. As a consequence of the process, we generalize any smooth interpolant by means of a family of fractal functions. In particular, the elements of the class can be defined so that the smoothness of the original is preserved. Under some hypotheses, bounds of the interpolation error for function and derivatives are obtained. A set of interpolating mappings associated to a cubic spline is defined and the density of fractal cubic splines in
is proven.
74 citations
05 Jul 2006
TL;DR: In this article, a method for determining the required angular sampling rate is proposed and the implementation scheme is evaluated for nearest neighbor and cubic interpolation kernels against image quality and number of operations required.
Abstract: An implementation of a fast, factorised, back-projection scheme is presented which is based on interpolation of range-angle sub-aperture data. A method for determining the required angular sampling rate is proposed and the implementation scheme is evaluated for nearest neighbour and cubic interpolation kernels against image quality and number of operations required. A SAR simulator is used for investigation of the performance and to trade the algorithm parameters. The impulse response function, using interpolation kernels at different sampling rates, is evaluated in terms of peak side-lobe levels and compared with a global back projection implementation. The results show that good processing performance is obtained even when high image quality is required when using cubic interpolation and an adequate sampling rate. This approach is thus suitable for challenging microwave SAR processing problems.
61 citations
Patent•
24 Feb 2006
TL;DR: In this paper, an image correction device for use in a pattern inspection apparatus is disclosed, which has automatic adaptability to variations in density of a pattern image of a workpiece being tested.
Abstract: An image correction device for use in a pattern inspection apparatus is disclosed, which has automatic adaptability to variations in density of a pattern image of a workpiece being tested. The device is operable to identify a two-dimensional (2D) linear predictive model parameters from the pattern image of interest and determine the value of a total sum of these identified parameters. This value is then used to switch between a corrected pattern image due to the 2D linear prediction modeling and a corrected image that is interpolated by bicubic interpolation techniques. A pattern inspection method using the image correction technique is also disclosed.
39 citations
TL;DR: Restoring images processed with the new method were visually much closer to high-resolution counterparts than those obtained with common interpolation methods and was relatively insensitive to noise.
Abstract: Many medical images suffer from the partial volume effect where a boundary between two structures of interest falls in the midst of a voxel giving a signal value that is a mixture of the two. We propose a method to restore the ideal boundary by splitting a voxel into subvoxels and reapportioning the signal into the subvoxels. Each voxel is divided by nearest neighbor interpolation. The gray level of each subvoxel is considered as "material" able to move between subvoxels but not between voxels. A partial differential equation is written to allow the material to flow towards the highest gradient direction, creating a "reverse" diffusion process. Flow is subject to constraints that tend to create step edges. Material is conserved in the process thereby conserving signal. The method proceeds until the flow decreases to a low value. To test the method, synthetic images were downsampled to simulate the partial volume artifact and restored. Corrected images were remarkably closer both visually and quantitatively to the original images than those obtained from common interpolation methods: on simulated data standard deviation of the errors were 3.8%, 6.6%, and 7.1% of the dynamic range for the proposed method, bicubic, and bilinear interpolation, respectively. The method was relatively insensitive to noise. On gray level, scanned text, MRI physical phantom, and brain images, restored images processed with the new method were visually much closer to high-resolution counterparts than those obtained with common interpolation methods.
38 citations
TL;DR: A method for quantifying the quality of interpolation methods is given and it is demonstrated that a method using bicubic spatial interpolation together with third-order Lagrange polynomials in time gives excellent accuracy at very modest computational expense compared to other methods.
34 citations
30 Aug 2006
TL;DR: An adaptive interpolation algorithm is presented based on the Newton polynomial to improve the limitation of the traditional algorithm for image resizing and has a lower complexity than the bicubic interpolation in visual effect.
Abstract: In this paper, an adaptive interpolation algorithm is presented based on the Newton Polynomial to improve the limitation of the traditional algorithm for image resizing The second-order difference of adjacent pixels gray values shows the relativity among the pixels Accordingly, the adaptive function for image interpolation is deduced according to both this relativity and the classical Newton polynomial Then the efficiency of our method is compared with that of the traditional algorithm for image resizing in Matlab Furthermore, the implementation circuit architecture is devised by three stage paralleling pipelines for the adaptive image resizing algorithm and is verified in FPGA (field programmable gate array) The experimental results show that our proposed algorithm excels the bicubic interpolation in visual effect, and has a lower complexity Therefore, the algorithm adapts to real-time image resizing
31 citations
TL;DR: A method for preserving the contours or edges based on adaptive osculatory rational interpolation kernel function, which is built up by approximating the ideal interpolating kernel function by continued fractions is presented.
29 citations
TL;DR: The unified scheme allows piece-wise smooth, continuous and boundary preservation interpolation of DTI data, so that smooth fiber tracts can be tracked in a continuous manner and confined within the boundaries of the targeted structure.
01 Jan 2006
TL;DR: In this paper, free parameters are constrained in the description of rational cubic functions to preserve the shape of data that lies above the straight line, and a local positivity preserving scheme is developed for positive data by making constraints on free parameters in the descriptions of rational bicubic partially blended patches.
Abstract: In this paper, first free parameters are constrained in the description of rational cubic function (6) to preserve the shape of data that lies above the straight line. Then, rational cubic function is extended to rational bicubic partially blended function (Coons patches). A local positivity preserving scheme is developed for positive data by making constraints on free parameters in the description of rational bicubic partially blended patches. We also develop at the end the constraints for visualizing a data that lie above the plane.
TL;DR: The bounded property and the point control method of the interpolating surface are proved and the interpolation surface may be modified for the given interpolation data when needed in practical design.
Abstract: A bivariate rational interpolation method with parameters was created in an earlier work which was based on function values only. This paper will deal with the bounded property and the point control method of the interpolating surface. It is proved that the values of the interpolating function in the interpolation region are bounded no matter what the parameters might be; this is called the bounded property of the interpolation. Also, the approximation expressions of the interpolation are derived; they do not depend on the parameters. More important is that the value of the interpolating function at any point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting suitable parameters, so the interpolation surface may be modified for the given interpolation data when needed in practical design. In the special case, the ''Central Point-Mean Value'' control is studied, and an example is given to show the control.
01 Oct 2006
TL;DR: A novel method for interpolating images and the concept of non-local interpolation is introduced, which exploits the repetitive character of the image and its superiority at very large magnifications to other interpolation methods.
Abstract: In this paper we present a novel method for interpolating images and we introduce the concept of non-local interpolation. Unlike other conventional interpolation methods, the estimation of the unknown pixel values is not only based on its local surrounding neighbourhood, but on the whole image (non-locally). In particularly, we exploit the repetitive character of the image. A great advantage of our proposed approach is that we have more information at our disposal, which leads to better estimates of the unknown pixel values. Results show the effectiveness of non-local interpolation and its superiority at very large magnifications to other interpolation methods.
TL;DR: This work presents an optimization of interpolation parameters of the3-D direct Fourier method with Fourier reprojection (3D-FRP) for fully 3-D positron emission tomography data with incomplete oblique projections, and confirms that for the optimal interpolations parameters a very good image accuracy can be achieved even without any extra spectral oversampling.
Abstract: Fourier-based approaches for three-dimensional (3-D) reconstruction are based on the relationship between the 3-D Fourier transform (FT) of the volume and the two-dimensional (2-D) FT of a parallel-ray projection of the volume. The critical step in the Fourier-based methods is the estimation of the samples of the 3-D transform of the image from the samples of the 2-D transforms of the projections on the planes through the origin of Fourier space, and vice versa for forward-projection (reprojection). The Fourier-based approaches have the potential for very fast reconstruction, but their straightforward implementation might lead to unsatisfactory results if careful attention is not paid to interpolation and weighting functions. In our previous work, we have investigated optimal interpolation parameters for the Fourier-based forward and back-projectors for iterative image reconstruction. The optimized interpolation kernels were shown to provide excellent quality comparable to the ideal sinc interpolator. This work presents an optimization of interpolation parameters of the 3-D direct Fourier method with Fourier reprojection (3D-FRP) for fully 3-D positron emission tomography (PET) data with incomplete oblique projections. The reprojection step is needed for the estimation (from an initial image) of the missing portions of the oblique data. In the 3D-FRP implementation, we use the gridding interpolation strategy, combined with proper weighting approaches in the transform and image domains. We have found that while the 3-D reprojection step requires similar optimal interpolation parameters as found in our previous studies on Fourier-based iterative approaches, the optimal interpolation parameters for the main 3D-FRP reconstruction stage are quite different. Our experimental results confirm that for the optimal interpolation parameters a very good image accuracy can be achieved even without any extra spectral oversampling, which is a common practice to decrease errors caused by interpolation in Fourier reconstruction
05 Oct 2006
TL;DR: An interesting up-sampling algorithm using 9/7 bi-orthogonal Spline filters based Discrete Wavelet Transform (DWT) that preserves much of the sharp edge features in the image, and lessens the amount of color artifacts.
Abstract: Image up-sampling is found to be a very effective technique useful in today’s digital image processing applications or rendering devices. In image upsampling, an image is enhanced from a lower resolution to a higher resolution with the degree of enhancement depending upon application requirements. It is known that the traditional interpolation based approaches for up-sampling, such as Bilinear or Bicubic interpolation, blur the resultant images [1, 2]. Furthermore; in color imagery, these interpolation based up-sampling methods may have color infringing artifacts in the areas where the images contain sharp edges and fine textures. In this paper, we present an interesting up-sampling algorithm using 9/7 bi-orthogonal Spline filters based Discrete Wavelet Transform (DWT). The proposed method preserves much of the sharp edge features in the image, and lessens the amount of color artifacts. Effectiveness of the proposed algorithm has been demonstrated based on evaluation of PSNR and * ab E ' quality metrics of the original image and the reconstructed image.
09 Jul 2006
TL;DR: Experiments show that the proposed techniques can effectively improve the image qualities than bilinear or bicubic interpolation alone, and outperforms other recently developed algorithms both in perceptual quality and in objective quality in terms of PSNR.
Abstract: By analyzing the deterministic relationship between the lower-resolution and the corresponding higher resolution images, we propose two core techniques namely MLF (modified Laplacian filter) and IC (intensity correction) for image resolution enhancement, by which the image size can be increased revealing better details of the image contents. The simple 3times3 MLF is designed for properly restoring the frequency components attenuated in the averaging and down-sampling degradation process. The IC process iteratively refines the image quality for any resolution enhanced (enlarged) image. Experiments show that the proposed techniques can effectively improve the image qualities than bilinear or bicubic interpolation alone. It outperforms other recently developed algorithms both in perceptual quality (especially in the texture areas) and in objective quality in terms of PSNR. Both MLF and IC are simple in computations, which is quite desirable in many time sensitive applications
01 Oct 2006
TL;DR: An adaptable interpolation approach that can adjust edge sharpness and texture intensity to reconstruct a high quality image according to user's taste in picture quality is presented.
Abstract: This paper presents an adaptable interpolation approach that can adjust edge sharpness and texture intensity to reconstruct a high quality image according to user's taste in picture quality. Our interpolation approach first resolves an input image I into its skeleton image U and its texture generator V and its residual image D such that I = U·V + D, and then interpolates each of the three components independently with a proper interpolation method suitable to each. The skeleton image is a bounded-variation function meaning a cartoon approximation of I, and interpolated with a super-resolution deblurring-oversampling method that interpolates sharp edges without producing ringing artifacts. The texture generator is an oscillatory function representing regular distinct textures, and interpolated with a standard linear interpolation algorithm. The residual image is a function with some randomness, and interpolated with a statistical re-sampling interpolation algorithm.
18 Sep 2006
TL;DR: In this article, the unknown pixel value is not estimated based on its local surrounding neighbourhood, but on the whole image, which leads to a better reconstruction of the interpolated image.
Abstract: In this paper we present a novel method for interpolating images with repetitive structures. Unlike other conventional interpolation methods, the unknown pixel value is not estimated based on its local surrounding neighbourhood, but on the whole image. In particularly, we exploit the repetitive character of the image. A great advantage of our proposed approach is that we have more information at our disposal, which leads to a better reconstruction of the interpolated image. Results show the effectiveness of our proposed method and its superiority at very large magnifications to other traditional interpolation methods.
Patent•
24 Feb 2006
TL;DR: In this article, an image correction device for use in a pattern inspection apparatus is disclosed, which has automatic adaptability to variations in density of a pattern image of a workpiece being tested.
Abstract: An image correction device for use in a pattern inspection apparatus is disclosed, which has automatic adaptability to variations in density of a pattern image of a workpiece being tested. The device is operable to identify a two-dimensional (2D) linear predictive model from the pattern image of interest and determine the amount of eccentricity of a centroid position of this model. This amount is then used to switch between a corrected pattern image due to the 2D linear prediction modeling and a corrected image that is interpolated by bicubic interpolation techniques. A pattern inspection method using the image correction technique is also disclosed.
01 Oct 2006
TL;DR: In this article, a causality-constrained interpolation procedure is introduced, with the aim of reconstructing missing samples in the data, like e.g. the DC point, via a sound numerical procedure that does not compromise the self-consistency and the causality of the entire dataset.
Abstract: We apply a recently developed formulation of the generalized Hilbert transform to the processing of tabulated and finite-bandwidth frequency responses. A causality-constrained interpolation procedure is introduced, with the aim of reconstructing missing samples in the data, like e.g. the DC point, via a sound numerical procedure that does not compromise the self-consistency and the causality of the entire dataset
01 Jul 2006
TL;DR: Experimental results demonstrate that the partial volume interpolation shows much more smoothness of the mutual information function than nearest neighbor and bilinear interpolations and is much more robust to improve the accuracy than the other two interpolations.
Abstract: The image registration inevitably involves interpolation problems to estimate gray values of the image at positions other than the grid points. In this paper interpolation induced effects on the accuracy of registered results are investigated by using a mutual information measure. Three interpolation techniques, namely nearest neighbor interpolation, bilinear interpolation and partial volume interpolation, are investigated under some elaborately designed experiments. The rigid transformation is limited and the simplex search strategy is adopted. The effects of histogram bin numbers and the subsampling rates are also investigated. Experimental results demonstrate that the partial volume interpolation shows much more smoothness of the mutual information function than nearest neighbor and bilinear interpolations. It is much more robust to improve the accuracy than the other two interpolations. The suitable decrease of histogram bin numbers can further smooth the mutual information function and increase the accuracy of the registration results. The decrease of the subsampling rates greatly saves the computation time, and it results in little losses of the accuracy of the final registered results, when using the partial volume interpolation.
Patent•
06 Nov 2006TL;DR: In this article, a directional interpolation method for video encoder/decoder is presented, which includes selecting one of a plurality of directional interpolations for a predetermined-size block based on the characteristics of input image data.
Abstract: A directional interpolation method and a video encoding/decoding apparatus and method using the directional interpolation method. The directional interpolation method includes selecting one of a plurality of directional interpolation modes for a predetermined-size block based on the characteristics of input image data, performing directional interpolation on the predetermined-size block based on the selected directional interpolation mode, and generating mode information indicating the selected directional interpolation mode.
Journal Article•
TL;DR: In this paper, the capacity of non-uniform sampling rate conversion techniques, involving different interpolation methods, aimed at defect reduction, is examined, and the performance of an artificially distorted audio signal, restored using nonuniform resampling, is evaluated on the basis of standard audio defect measurement criteria.
Abstract: In this paper the capacity of non-uniform sampling rate conversion techniques, involving different interpolation methods, aimed at wow defect reduction, is examined. Involved are: linear interpolation, four polynomial-based interpolation methods and the windowed sincbased method. The examined polynomial methods are: Lagrange interpolation, polynomial fitting with additional noise reduction, Hermitan and Spline. The performance of an artificially distorted audio signal, restored using non-uniform resampling, is evaluated on the basis of standard audio defect measurement criteria and compared for all of the aforementioned interpolation methods. The chosen defect descriptors are: total harmonic distortion, total harmonic distortion plus noise and signal to noise ratio.
TL;DR: In this paper, the problem of interpolation on a semi-plane grid from a space of box-splines on the three-direction mesh was considered and the solution was obtained as a Lagrange series with suitable localization and polynomial reproduction properties.
01 Aug 2006
TL;DR: A Kriging interpolation based scan conversion algorithm is proposed to distinguish detail regions and smooth regions with asymmetry operator and experiment results indicate the effectiveness of the proposed algorithm.
Abstract: Digital scan conversion was employed in ultrasound image devices to display scanned vector data in Cartesian coordinate that were acquired with polar coordinate. So interpolation was applied to estimate unsampled pixels gray values. Most interpolation algorithms enhanced all the detail and smooth regions. A Kriging interpolation based scan conversion algorithm is proposed to distinguish detail regions and smooth regions with asymmetry operator. Detail regions are interpolated with adaptive cubic interpolation and other smooth regions with Kriging interpolation. This algorithm preserves smooth regions and enhances detail regions in result ultrasound images. Experiment results indicate the effectiveness of the proposed algorithm.
TL;DR: Texture analysis of ultrasonic plaques should be performed under standardised resolution settings; otherwise a resolution normalisation algorithm should be applied.
Abstract: Unstable carotid plaques on subjective, visual, assessment using B-mode ultrasound scanning appear as echolucent and heterogeneous. Although previous studies on computer assisted plaque characterisation have standardised B-mode images for brightness, improving the objective assessment of echolucency, little progress has been made towards standardisation of texture analysis methods, which assess plaque heterogeneity. The aim of the present study was to investigate the influence of image zooming during ultrasound scanning on textural features and to test whether or not resolution standardisation decreases the variability introduced. Eighteen still B-mode images of carotid plaques were zoomed during carotid scanning (zoom factor 1.3) and both images were transferred to a PC and normalised. Using bilinear and bicubic interpolation, the original images were interpolated in a process of simulating off-line zoom using the same interpolation factor. With the aid of the colour-coded image, carotid plaques of the original, zoomed and two resampled images for each case were outlined and histogram, first order and second order statistics were subsequently calculated. Most second order statistics (21/25, 84%) were significantly (p < 0.05) sensitive to image zooming during scanning, in contrast to histogram and first order statistics (4/25, 16%, p < 0.001, Fisher's exact test). Median (interquartile range) change of those features sensitive to zooming was 18.14% (4.94–28.43). Image interpolation restored these changes, the bicubic interpolation being superior compared to bilinear interpolation (p = 0.036). Texture analysis of ultrasonic plaques should be performed under standardised resolution settings; otherwise a resolution normalisation algorithm should be applied.
14 May 2006
TL;DR: Both the theoretical and numerical results show that the regularity-based scheme allows to obtain good quality interpolated images.
Abstract: We consider the problem of interpolating a signal in IRdknown at a given resolution. In our approach, the signal is assumed to belong to a given (large) class of signals. This class is characterized by local regularity constraints, that can be described by a certain inter-scale behaviour of their wavelet coefficients. These constraints allow to predict the scale n coefficients from the ones at lower scales. We investigate some properties of this interpolation scheme. In particular, we give the Holder regularity of the refined signal, and present some asymptotic properties of the method. Finally, numerical experiments are presented. Both the theoretical and numerical results show that our regularity-based scheme allows to obtain good quality interpolated images.