Abstract
A new rational bi-quartic spline interpolation scheme is constructed in this study. This rational bi-quartic spline has six free parameters that can be used to refine the final interpolating surface. The degree of smoothness attained is C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> continuity. Image interpolation is one of the methods in image processing that is used to rescale the images, either downscaling or upscaling. The proposed rational bi-quartic spline will be used to interpolate the missing pixel in image interpolation. We employ an algorithm that will speed up the process as well as be able to produce the quality upscaling images. We measure the quality of the proposed method by calculating peak-signal-to-noise-ratio (PSNR). Based on numerical comparison, the proposed scheme gives higher PSNR (consequently smaller RMSE) unlike some existing schemes. Thus, the new rational bi-quartic spline with six parameters is better than the existing scheme via an efficient algorithm. All numerical simulations and graphical results are presented using MATLAB.
Highlights
Surface interpolation is important in many aspects of sciences and engineering
EFFICIENT ALGORITHM In order to apply the proposed rational bi-quartic spline scheme for image interpolation, we provide the following algorithm that is a bit modification to the main algorithm presented in Karim and Saaban [11] and Zulkifli et al [23]
In this study, we have constructed a new rational bi-quartic spline interpolation defined on rectangular meshes
Summary
Surface interpolation is important in many aspects of sciences and engineering. The standard approach in surface interpolation is scattered data interpolation and constraint surface modeling on rectangular and triangular meshes. Karim and Saaban [11] have constructed a new rational bi-cubic Ball interpolation (cubic/quadratic) with two parameters From numerical results, they found that, their scheme is better than bicubic spline interpolation. Wang and Tan [18] have utilized rational quartic spline with two parameters for image fusion Their method required the first partial derivatives to be modified if the interpolating curve is not monotonic. As conjectured by Zulkifli et al [23], scheme with more free parameters gives the better quality of image interpolation, in this study, we will propose a new rational bi-quartic spline interpolation (quartic/quadratic) with six free parameters This function is defined on rectangular meshes. Peak-Signal-to-Noise Ratio Red, Green or Blue channels Alpha Beta Gamma Three-Dimensional Genetic Algorithm Transpose of matrix A Image pixels Input pixel in grayscale intensity Interpolating missing pixels
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