Showing papers on "Bicubic interpolation published in 2013"

Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations

Abstract: High-efficiency and high-accuracy deformation analysis using digital image correlation (DIC) has become increasingly important in recent years, considering the ongoing trend of using higher resolution digital cameras and common requirement of processing a large sequence of images recorded in a dynamic testing. In this work, to eliminate the redundant computations involved in conventional DIC method using forward additive matching strategy and classic Newton–Raphson (FA-NR) algorithm without sacrificing its sub-pixel registration accuracy, we proposed an equivalent but more efficient DIC method by combining inverse compositional matching strategy and Gauss-Newton (IC-GN) algorithm for fast, robust and accurate full-field displacement measurement. To this purpose, first, an efficient IC-GN algorithm, without the need of re-evaluating and inverting Hessian matrix in each iteration, is introduced to optimize the robust zero-mean normalized sum of squared difference (ZNSSD) criterion to determine the desired deformation parameters of each interrogated subset. Then, an improved reliability-guided displacement tracking strategy is employed to achieve further speed advantage by automatically providing accurate and complete initial guess of deformation for the IC-GN algorithm implemented on each calculation point. Finally, an easy-to-implement interpolation coefficient look-up table approach is employed to avoid the repeated calculation of bicubic interpolation at sub-pixel locations. With the above improvements, redundant calculations involved in various procedures (i.e. initial guess of deformation, sub-pixel displacement registration and sub-pixel intensity interpolation) of conventional DIC method are entirely eliminated. The registration accuracy and computational efficiency of the proposed DIC method are carefully tested using numerical experiments and real experimental images. Experimental results verify that the proposed DIC method using IC-GN algorithm and the existing DIC method using classic FA-NR algorithm generate similar results, but the former is about three to five times faster. The proposed reliability-guided IC-GN algorithm is expected to be a new standard full-field displacement tracking algorithm in DIC.

Comparison of Commonly Used Image Interpolation Methods

Abstract: Image magnification algorithms directly affect the quality of image magnification. In this paper, based on the image interpolation algorithm principle, features of the nearest neighbor interpolation, bilinear interpolation, bicubic interpolation and cubic B spline interpolation were analyzed. At the same time, their advantages and disadvantages were compared. In the experiment, image magnification performance of different interpolation algorithms was compared from subjective and objective aspects. The experimental results give the guidance for the user to choose a suitable algorithm to achieve optimum results according to different application. KeywordsImage magnification; Interpolation algorithm; Performance comparison

A Self-Learning Approach to Single Image Super-Resolution

Abstract: Learning-based approaches for image super-resolution (SR) have attracted the attention from researchers in the past few years. In this paper, we present a novel self-learning approach for SR. In our proposed framework, we advance support vector regression (SVR) with image sparse representation, which offers excellent generalization in modeling the relationship between images and their associated SR versions. Unlike most prior SR methods, our proposed framework does not require the collection of training low and high-resolution image data in advance, and we do not assume the reoccurrence (or self-similarity) of image patches within an image or across image scales. With theoretical supports of Bayes decision theory, we verify that our SR framework learns and selects the optimal SVR model when producing an SR image, which results in the minimum SR reconstruction error. We evaluate our method on a variety of images, and obtain very promising SR results. In most cases, our method quantitatively and qualitatively outperforms bicubic interpolation and state-of-the-art learning-based SR approaches.

A constructive approach to cubic Hermite Fractal Interpolation Function and its constrained aspects

Abstract: The theory of splines is a well studied topic, but the kinship of splines with fractals is novel We introduce a simple explicit construction for a Open image in new window-cubic Hermite Fractal Interpolation Function (FIF) Under some suitable hypotheses on the original function, we establish a priori estimates (with respect to the Lp-norm, 1≤p≤∞) for the interpolation error of the Open image in new window-cubic Hermite FIF and its first derivative Treating the first derivatives at the knots as free parameters, we derive suitable values for these parameters so that the resulting cubic FIF enjoys Open image in new window global smoothness Consequently, our method offers an alternative to the standard moment construction of Open image in new window-cubic spline FIFs Furthermore, we identify appropriate values for the scaling factors in each subinterval and the derivatives at the knots so that the graph of the resulting Open image in new window-cubic FIF lies within a prescribed rectangle These parameters include, in particular, conditions for the positivity of the cubic FIF Thus, in the current article, we initiate the study of the shape preserving aspects of fractal interpolation polynomials We also provide numerical examples to corroborate our results

Medical image interpolation based on multi-resolution registration

Abstract: We present a novel registration-based image interpolation approach in this paper. The proposed method is divided into two steps: image registration and intensity interpolation. An image registration method is developed to construct a corresponding transformation, which is represented by the bicubic B -spline vector-valued function, between the given images so that the image features are well matched. To match features from coarse to fine, a multi-resolution strategy is applied with different numbers of B -spline control points adopted at various resolution levels. After registration, the intensity values of in-between images are calculated by linear/cubic interpolation along the matching lines. Experimental results demonstrate that our interpolation approach is effective, robust, and capable of producing continuously deformed in-between images with clear shape features.

Contrast-Guided Image Interpolation

Abstract: In this paper a contrast-guided image interpolation method is proposed that incorporates contrast information into the image interpolation process. Given the image under interpolation, four binary contrast-guided decision maps (CDMs) are generated and used to guide the interpolation filtering through two sequential stages: 1) the 45° and 135° CDMs for interpolating the diagonal pixels and 2) the 0° and 90° CDMs for interpolating the row and column pixels. After applying edge detection to the input image, the generation of a CDM lies in evaluating those nearby non-edge pixels of each detected edge for re-classifying them possibly as edge pixels. This decision is realized by solving two generalized diffusion equations over the computed directional variation (DV) fields using a derived numerical approach to diffuse or spread the contrast boundaries or edges, respectively. The amount of diffusion or spreading is proportional to the amount of local contrast measured at each detected edge. The diffused DV fields are then thresholded for yielding the binary CDMs, respectively. Therefore, the decision bands with variable widths will be created on each CDM. The two CDMs generated in each stage will be exploited as the guidance maps to conduct the interpolation process: for each declared edge pixel on the CDM, a 1-D directional filtering will be applied to estimate its associated to-be-interpolated pixel along the direction as indicated by the respective CDM; otherwise, a 2-D directionless or isotropic filtering will be used instead to estimate the associated missing pixels for each declared non-edge pixel. Extensive simulation results have clearly shown that the proposed contrast-guided image interpolation is superior to other state-of-the-art edge-guided image interpolation methods. In addition, the computational complexity is relatively low when compared with existing methods; hence, it is fairly attractive for real-time image applications.

Planar shape interpolation with bounded distortion

Abstract: Planar shape interpolation is widely used in computer graphics applications. Despite a wealth of interpolation methods, there is currently no approach that produces shapes with a bounded amount of distortion with respect to the input. As a result, existing interpolation methods may produce shapes that are significantly different than the input and can suffer from fold-overs and other visual artifacts, making them less useful in many practical scenarios. We introduce a novel shape interpolation scheme designed specifically to produce results with a bounded amount of conformal (angular) distortion. Our method is based on an elegant continuous mathematical formulation and provides several appealing properties such as existence and uniqueness of the solution as well as smoothness in space and time domains. We further present a discretization and an efficient practical algorithm to compute the interpolant and demonstrate its usability and good convergence behavior on a wide variety of input shapes. The method is simple to implement and understand. We compare our method to state-of-the-art interpolation methods and demonstrate its superiority in various cases.

A Review on Different Image Interpolation Techniques for Image Enhancement

Abstract: Image enhancement is an important processing task in image processing field. By applying image enhancement, blur or any type of noise in the image can be removed so that the resultant image quality is better. Image enhancement is used in various fields like medical diagnosis, remote sensing, agriculture, geology, oceanography. There are numbers of techniques for image enhancement. Image interpolation is used to do enhancement of any image. This paper gives overview about different interpolation techniques like nearest neighbor, bilinear, bicubic, new edge-directed interpolation (NEDI), data dependent triangulation (DDT), and iterative curvature-based interpolation (ICBI).

Improved pre-warping for wide angle, head mounted displays

Abstract: High-quality head mounted displays are becoming available in the consumer space. These displays provide an immersive gaming experience by filling the wearer's field of view. To achieve immersion with low cost, a commodity display panel is placed a short distance in front of each eye, and wide-angle optics are used to bring the image into focus. However, these optics introduce spatial and chromatic distortion into the image seen by the viewer. As a result, the images to be displayed must be pre-warped to cancel this distortion. This correction can be performed by warping the image in a post-processing step, by warping the scene geometry before rendering, or by modeling corrective optics in the virtual camera.Here, we examine the image quality and performance of several correction methods. Though image warping with a bilinear filter is common [Antonov et al. 2013], we find that bicubic filtering yields improved image quality with minimal performance impact. We also propose a new method for correcting chromatic distortion by warping the image using distortion meshes, and we propose a method for correcting spatial and chromatic distortion accurately in-camera.

Performance comparison of bilinear interpolation, bicubic interpolation, and B-spline interpolation in parallel phase-shifting digital holography

Abstract: To improve the quality of reconstructed images, we apply bicubic interpolation and B-spline interpolation to parallel phase-shifting digital holography for the first time. The effectiveness of bilinear interpolation, bicubic interpolation, and B-spline interpolation in parallel phase-shifting digital holography is shown by a numerical simulation. In the simulation result, the application of bicubic interpolation and B-spline interpolation succeeded in decreasing the rootmean- square error of the reconstructed image by 12.6 and 11.9%, respectively.

Computing Relational Fixed Points using Interpolation

Abstract: We present a interpolation-based method for symbolically computing relational post-fixed points. The method can be used to solve for unknown predicates in the verification conditions of programs. Thus, it has a variety of applications, including including model checking of recursive and threaded programs. The method is implemented in tool called Duality, which we evaluate using device driver verification benchmarks.

Positivity-preserving C2 rational cubic spline interpolation

Abstract: This work addresses the shape preserving interpolation problem for visualization of positive data. A piecewise rational function in cubic/quadratic form involving three shape parameters is presented. Simple data dependent conditions for a single shape parameter are derived to preserve the inherited shape feature (positivity) of data. The remaining two shape parameters are left free for the designer to modify the shape of positive curves as per industrial needs. The interpolant is not only C, local, computationally economical, but it is also a visually pleasant and smooth in comparison with existing schemes. Several numerical examples are supplied to illustrate the proposed interpolant.

Statistical torsion angle potential energy functions for protein structure modeling: A bicubic interpolation approach

Abstract: A set of grid type knowledge-based energy functions is introduced for ϕ-χ₁ , ψ-χ₁ , ϕ-ψ, and χ₁ -χ₂ torsion angle combinations. Boltzmann distribution is assumed for the torsion angle populations from protein X-ray structures, and the functions are named as statistical torsion angle potential energy functions. The grid points around periodic boundaries are duplicated to force periodicity, and the remedy relieves the derivative discontinuity problem. The devised functions rapidly improve the quality of model structures. The potential bias in the functions and the usefulness of additional secondary structure information are also investigated. The proposed guiding functions are expected to facilitate protein structure modeling, such as protein structure prediction, protein design, and structure refinement.

Image resolution enhancement by using interpolation followed by iterative back projection

Abstract: In this paper, we propose a new super resolution technique based on the interpolation followed by registering them using iterative back projection (IBP). Low resolution images are being interpolated and then the interpolated images are being registered in order to generate a sharper high resolution image. The proposed technique has been tested on Lena, Elaine, Pepper, and Baboon. The quantitative peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) results as well as the visual results show the superiority of the proposed technique over the conventional and state-of-art image super resolution techniques. For Lena's image, the PSNR is 6.52 dB higher than the bicubic interpolation.

Sparse implicitization by interpolation: Characterizing non-exactness and an application to computing discriminants

Abstract: We revisit implicitization by interpolation in order to examine its properties in the context of sparse elimination theory. Based on the computation of a superset of the implicit support, implicitization is reduced to computing the nullspace of a numeric matrix. The approach is applicable to polynomial and rational parameterizations of curves and (hyper)surfaces of any dimension, including the case of parameterizations with base points. Our support prediction is based on sparse (or toric) resultant theory, in order to exploit the sparsity of the input and the output. Our method may yield a multiple of the implicit equation: we characterize and quantify this situation by relating the nullspace dimension to the predicted support and its geometry. In this case, we obtain more than one multiple of the implicit equation; the latter can be obtained via multivariate polynomial GCD (or factoring). All of the above techniques extend to the case of approximate computation, thus yielding a method of sparse approximate implicitization, which is important in tackling larger problems. We discuss our publicly available Maple implementation through several examples, including the benchmark of a bicubic surface. For a novel application, we focus on computing the discriminant of a multivariate polynomial, which characterizes the existence of multiple roots and generalizes the resultant of a polynomial system. This yields an efficient, output-sensitive algorithm for computing the discriminant polynomial.

Image Interpolation Using Kriging Technique for Spatial Data

Abstract: Image interpolation has been used spaciously by customary interpolation techniques. Recently, Kriging technique has been widely implemented in simulation area and geostatistics for prediction. In this article, Kriging technique was used instead of the classical interpolation methods to predict the unknown points in the digital image array. The efficiency of the proposed technique was proven using the PSNR and compared with the traditional interpolation techniques. The results showed that Kriging technique is almost accurate as cubic interpolation and in some images Kriging has higher accuracy. A miscellaneous test images have been used to consolidate the proposed technique. 1

Directional Bicubic Interpolation — A New Method of Image Super-Resolution

Abstract: Bicubic interpolation is a standard method in image interpolation field because of its low complexity and relatively good results. But as it only interpolates in horizontal and vertical directions, edges easily suffer from artifacts such as blocking, blurring and ringing. This paper proposed a new method of image super-resolution which is named directional bicubic interpolation. According to local strength and directions, different ways are used to interpolate missing pixels. Compared with bicubic interpolation, the proposed method can preserve sharp edges and details better. Experiment results show that the proposed method is better than existing edge-directed interpolations in terms of subjective and objective measures, and its computation complexity is low.

Radial basis function interpolation of unstructured, three-dimensional, volumetric particle tracking velocimetry data

Abstract: Unstructured three-dimensional fluid velocity data were interpolated using Gaussian radial basis function (RBF) interpolation Data were generated to imitate the spatial resolution and experimental uncertainty of a typical implementation of defocusing digital particle image velocimetry The velocity field associated with a steadily rotating infinite plate was simulated to provide a bounded, fully three-dimensional analytical solution of the Navier–Stokes equations, allowing for robust analysis of the interpolation accuracy The spatial resolution of the data (ie particle density) and the number of RBFs were varied in order to assess the requirements for accurate interpolation Interpolation constraints, including boundary conditions and continuity, were included in the error metric used for the least-squares minimization that determines the interpolation parameters to explore methods for improving RBF interpolation results Even spacing and logarithmic spacing of RBF locations were also investigated Interpolation accuracy was assessed using the velocity field, divergence of the velocity field, and viscous torque on the rotating boundary The results suggest that for the present implementation, RBF spacing of 028 times the boundary layer thickness is sufficient for accurate interpolation, though theoretical error analysis suggests that improved RBF positioning may yield more accurate results All RBF interpolation results were compared to standard Gaussian weighting and Taylor expansion interpolation methods Results showed that RBF interpolation improves interpolation results compared to the Taylor expansion method by 60% to 90% based on the average squared velocity error and provides comparable velocity results to Gaussian weighted interpolation in terms of velocity error RMS accuracy of the flow field divergence was one to two orders of magnitude better for the RBF interpolation compared to the other two methods RBF interpolation that was applied to vortex identification in experimental data showed reduced noise and reliable calculation of vortex ring geometry

A priori convergence of the Generalized Empirical Interpolation Method

Abstract: In an effort to extend the classical lagrangian interpolation tools, new interpolating methods that use general interpolating functions are explored. The Generalized Empirical Interpolation Method (GEIM) belongs to this class of new techniques. It generalizes the plain Empirical Interpolation Method by replacing the evaluation at interpolating points by application of a class of interpolating linear functions. Since its efficiency depends critically on the choice of the interpolating functions (that are chosen by a Greedy selection procedure), the purpose of this paper is therefore to provide a priori convergence rates for the Greedy algorithm that is used to build the GEIM interpolating spaces.

Edge curve scaling and smoothing with cubic spline interpolation for image upscaling

Abstract: In this paper, we propose an edge map up-scaling method. We propose an edge curve scaling method with cubic spline interpolation to up-scale an edge map. If an edge curve is directly applied to the cubic spline interpolation function for edge curve up-scaling, the edge curve scaling results have zigzag artifacts. We also propose a simple smoothing function to avoid the zigzag problems and maintain the contour shape of images. By predicting edge regions of the up-scaled image, we can recover high frequency components of edge regions of the up-scaled image to improve the sharpness and reduce ringing artifacts.

FPGA implementation of bilinear interpolation algorithm for CFA demosaicing

Abstract: Color Filter Array (CFA) is a mosaic of tiny color filters placed over the pixels of an image sensor to capture information. The most common filter is Bayer's filter. A Bayer filter arranges RGB color filters on a square grid of photo sensors. The color filters is used in single chip image sensors which is used in digital cameras, camcorders and scanners to create a color image. Digital still cameras (DSC) are widely used nowadays and it has a single chip CCD image sensor in order to reduce the cost. These single chip cameras use CF A to obtain different color information. Since only one component is available (Either R or G or B) at each pixel, the other two missing color components have to be estimated from the neighboring pixels. The process is called as CFA demosaicing. Demosaicing is a digital image process used to reconstruct full color image from the incomplete color samples. Various types of demosaicing algorithms are linear and bilinear interpolation, bicubic interpolation cubic spline interpolation, homogeneity directed demosaicing algorithm, higher order interpolation and higher order extrapolation etc. Bilinear interpolation algorithm for a 64*64 image is simulated in Xilinx.

Comparison of linear and cubic spline methods of interpolating lake water column profiles

Abstract: Two commonly used methods of interpolating lake water column profiles—two-point linear interpolation and cubic spline interpolation—were compared, and their relative performance assessed using “leave-k-out” cross-validation. Artificial “pseudo-gaps” of various sizes were created in measured water column profiles of four representative variables (water temperature, oxygen concentration, total phosphorus concentration, and chloride concentration) from the Lake of Zurich by removing measured data from the profiles. The pseudo-gaps were then filled using each of the two interpolation methods. The performance of each interpolation method was assessed based on the root mean square error, mean bias error, and maximum absolute bias error of the interpolated values in relation to the original measured values. The performance of the interpolation methods varied with depth, season, and profile shape. When the profiles were homogeneous both methods performed well, but when the profiles were heterogeneous, linear interpolation generally performed better than cubic spline interpolation. Although the data generated by cubic spline interpolation were less biased than those generated by linear interpolation, there were more instances of extreme errors. The results of this study suggest that linear interpolation is generally preferable to cubic spline interpolation for filling data gaps in measured lake water column profiles.

Iterative back projection based image resolution enhancement

Abstract: In this paper, we propose a new super resolution technique based on the interpolation followed by registering them using iterative back projection (IBP). Firstly the low resolution image is interpolated and then decimate it to four lower low resolution images. The four low resolution images are interpolated and registered by using IBP in order to generate a sharper high resolution image. The proposed method has been tested on Lena, Elaine, Pepper, and Baboon. The quantitative peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) results as well as the visual results show the superiority of the proposed technique over the conventional and alternative image super resolution techniques. For Lena's image, the PSNR is 6.21 dB higher than the bicubic interpolation.

Self-adaptive image scaling method based on bicubic interpolation

Abstract: The invention provides a self-adaptive image scaling method based on bicubic interpolation. The self-adaptive image method based on the bicubic interpolation comprises the following steps: conducting a Gaussian blur operation of a source image so that detail information which can not be displayed under the condition of low resolution is eliminated and distortion of a scaled image is avoided; finding the corresponding pixel location of a target image pixel point on the source image, self-adaptively selecting m sampling pixel points which are corresponding to the periphery of pixel points, obtaining a weighted value which is corresponding to each sampling pixel point according to a bicubic interpolation function, and weighting and summing and to get a pixel value of the scaled image according to the weighted values of the m sampling pixel points and pixel values of the m sampling pixel values; and conducting a sharpening operation of the scaled image so that the edges of an image are clear and a target image is obtained.

Real-time super-resolution for digital zooming using finite kernel-based edge orientation estimation and truncated image restoration

Abstract: This paper presents a novel real-time super-resolution (SR) method using directionally adaptive image interpolation and image restoration. The proposed interpolation method estimates the edge orientation using steerable filters and performs edge refinement along the estimated edge orientation. Bi-linear and bi-cubic interpolation filters are then selectively used according to the estimated edge orientation for reducing jagging artifacts in slanting edge regions. The proposed restoration method can effectively remove image degradation caused by interpolation using the directionally adaptive truncated constrained least-squares (TCLS) filter. The proposed method provides high-quality magnified images which are similar to or better than the result of advanced interpolation or SR methods without high computational load. Experimental results indicate that the proposed system gives higher peak-to-peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) values than the state-of-the-art image interpolation methods.