The first part of the paper describes the parameterization of the fifth-degree polynomial convolutional interpolation kernel. In this way, a two-parameter interpolation kernel is created. The second part of the paper describes an experiment in which the interpolation of some test images, using the one-parameter and the proposed two-parameter kernel, is performed. Some standard Test images, which are frequently used in digital image processing, were used in the experiment. Interpolation errors were determined using MSE. After that, the results of the experiment are presented using graphs and tables. Finally, a detailed comparative analysis, which shows the higher precision of the interpolation with the proposed two-parameter fifth-degree interpolation kernel, is presented.
The ideal interpolation kernel is described by the sinc function, and its spectral characteristic is the box function. Due to the infinite length of the ideal kernel, it is not achievable. Therefore, convolutional interpolation kernels of finite length, which should better approximate the ideal kernel in a specified interval, are formed. The approximation function should have a small numerical complexity, so as to reduce the interpolation execution time. In the scientific literature, great attention is paid to the polynomial kernel of the third order. However, the time and spectral characteristic of the third-order polynomial kernels differs significantly from the shape of the ideal kernel. Therefore, the accuracy of cubic interpolation is lower. By optimizing the kernel parameters, it is possible to better approximate the ideal kernel. This will increase the accuracy of the interpolation. The first part of the paper describes a three-parameter (3P) Keys interpolation kernel, r. After that, the algorithm for optimizing the parameters of the 3P Keys kernel, is shown. First, the kernel is disassembled into components, and then, over each kernel component, Fourier transform is applied. In this way the spectral characteristic of the 3P Keys kernel, H, was determined. Then the spectral characteristic was developed in the Taylor series, HT. With the condition for the elimination of the members of the Taylor series, which greatly affect the ripple of the spectral characteristic, the optimal kernel parameters (?opt, ?opt, gopt) were determined. The second part of the paper describes an experiment, in which the interpolation accuracy of the 3P Keys kernel, was tested. Parametric cubic convolution (PCC) interpolation, with the 3P kernel, was performed over the images from the Test database. The Test database is created with standard Test images, which are intensively used in Digital Image Processing. By analyzing the interpolation error, which is represented by the Mean Square Error, MSE, the accuracy of the interpolation was determined. The results (?opt, ?opt, gopt, MSEmin) are presented on tables and graphs. Detailed comparative analysis showed higher interpolation accuracy with the proposed 3P Keys interpolation kernel, compared to the interpolation accuracy with, 1P Keys and 2P Keys interpolation kernels. Finally, the numerical values of the optimal kernel parameters, which are determined by the optimization algorithm proposed in this paper, were experimentally verified.
In the first part of the paper, one-parameter (1P), fifth and seventh order polynomial interpolationconvolution kernels, are described. In the second part of the paper an Experiment is described. The precision of theimage interpolation was tested. Interpolation of the Test images from the base, using interpolation kernels, wereperformed. The precision of the interpolation kernels was measured using the mean squared error (MSE). Next,optimum kernel parameter, α, were determined by minimizing MSE. After that, a comparative analysis of theminimum MSE values, for the fifth and seventh order polynomial kernels, was performed. The results are presentedtabularly and graphically.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.