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Bicubic interpolation

About: Bicubic interpolation is a research topic. Over the lifetime, 3348 publications have been published within this topic receiving 73126 citations.


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Journal ArticleDOI
TL;DR: The theoretical optimal shift that maximizes the quality of the authors' shifted linear interpolation is nonzero and close to 1/5, and this optimal value is similar to that of the computationally more costly "high-quality" cubic convolution.
Abstract: We present a simple, original method to improve piecewise-linear interpolation with uniform knots: we shift the sampling knots by a fixed amount, while enforcing the interpolation property. We determine the theoretical optimal shift that maximizes the quality of our shifted linear interpolation. Surprisingly enough, this optimal value is nonzero and close to 1/5. We confirm our theoretical findings by performing several experiments: a cumulative rotation experiment and a zoom experiment. Both show a significant increase of the quality of the shifted method with respect to the standard one. We also observe that, in these results, we get a quality that is similar to that of the computationally more costly "high-quality" cubic convolution.

432 citations

Journal ArticleDOI
TL;DR: In this paper, the inverse distance weighted (IDW) interpolation method has been expanded to allow users to define the expected degree of surface abruptness along thematic boundaries using a transition matrix.

401 citations

Journal ArticleDOI
TL;DR: In this article, a Gauss-Newton-based digital image correlation (DIC) method was proposed 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.
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.

391 citations

Book ChapterDOI
15 Oct 2000
TL;DR: This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data, and explains why the approximation order inherent in the synthesis function is important to limit these interpolation artifacts.
Abstract: This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as a discrete sum of weighted and shifted synthesis functions—in other words, a mixed convolution equation. An important issue is the choice of adequate synthesis functions that satisfy interpolation properties. Examples of finite-support ones are the square pulse (nearest-neighbor interpolation), the hat function (linear interpolation), the cubic Keys' function, and various truncated or windowed versions of the sinc function. On the other hand, splines provide examples of infinite-support interpolation functions that can be realized exactly at a finite, surprisingly small computational cost. We discuss implementation issues and illustrate the performance of each synthesis function. We also highlight several artifacts that may arise when performing interpolation, such as ringing, aliasing, blocking and blurring. We explain why the approximation order inherent in the synthesis function is important to limit these interpolation artifacts, which motivates the use of splines as a tunable way to keep them in check without any significant cost penalty.

385 citations

Journal ArticleDOI
TL;DR: A parametric implementation of cubic convolution image reconstruction is presented which is generally superior to the standard algorithm and which can be optimized to the frequency content of the image.
Abstract: Cubic convolution, which has been discussed by Rifman and McKinnon (1974), was originally developed for the reconstruction of Landsat digital images. In the present investigation, the reconstruction properties of the one-parameter family of cubic convolution interpolation functions are considered and thee image degradation associated with reasonable choices of this parameter is analyzed. With the aid of an analysis in the frequency domain it is demonstrated that in an image-independent sense there is an optimal value for this parameter. The optimal value is not the standard value commonly referenced in the literature. It is also demonstrated that in an image-dependent sense, cubic convolution can be adapted to any class of images characterized by a common energy spectrum.

349 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202350
2022118
202187
202087
2019122
201892