Research On The Theory And Application Of Image Interpolation Based On Rational Fractal Function

Image interpolation or image magnification refers to obtain high resolution images with an‘ideal'appearance from low resolution ones.Image interpolation plays an important role in image processing,and it is widely used in various fields,such as aerospace,medical,military,scientific research,communications,remote sensing satellite,television,film production,etc.Various interpolating methods have been proposed,such as nearest point interpolation,bilinear interpolation,bi-cubic interpolation and spline interpolation,etc.Although these traditional methods are effective,they have disadvantages in ringing artifacts,blurred details and so forth.In this article,a class of bivariate rational function and rational fractal function are investigated.By analysizing the shape parameters and its effects,some adaptive image interpolation algorithms are proposed.The main contributions as following:1.A piecewise bivariate rational spline interpolation is presented only based on the values of the interpolate function.C~2 continuous conditions have been given.At the same time,the error estimation formula of bivariate rational interpolation function is presented.Furthermore,two new types of bivariate of rational fractal function are construted,including type of(3,1)and(3,2).As for the type of(3,2)rational fractal function,its proporities such as convergence,stability and quasi-locality.Moreover,the dimension calculation method of fractal interpolation surface is given.2.In order to make up for the deficiency of the polynomial interpolation method in edge structure preservation,we present an interpolation algorithm based on a rational function model with constraint parameters.Firstly,based on the construction principle of the rational function,the detection threshold is selected through contour analysis.The smooth and non-smooth areas are interpolated by bicubic interpolation and general rational interpolation,respectively.In order to enhance the contrast in non-smooth areas and preserve the details,the parameter optimization technique is applied to get optimal shape parameters.The algorithm preserves the edge structure effectively and achieves very competitive result.3.To compensate the deficiency of rational function on the texture detail preserving,a new image interpolation algorithm based on fractal dimension is proposed for the purpose of improving the quality of texture image magnification.For the input image,first of all,median filter and histogram equalization is used to input image preprocessing;Secondly,the image is classified the texture area and smooth area through the blanket method;Thirdly,in the region of the texture using rational fractal interpolation function,adopting rational interpolation function in smooth area.Finally,optimization technique is utilized to further modify the interpolation model,which is proved to be effective.4.As for the disadvantage of single scale of fractal dimension in texture analysis,a new interpolation model is proposed based on the bivariate rational interpolation.This model contains rational fractal interpolation and bivariate rational interpolation,which is identified uniquely by the values of Iterated Function System parameters(scaling factor and shape parameters).Due to efficiency capacity of fractal in description of complex phenomenon,the fractal dimension is employed to texture analysis.Based on the analysis of local fractal dimension(LFD),a new local adaptive threshold method is proposed.And then images can be divided into texture region and non-texture region.As for texture regions,rational fractal interpolation is used to get high resolution images.Similarly,rational interpolation is used in non-texture region.Considering the parameters in rational fractal interpolation model,we propose a new method for calculating the scaling factor.Further,the quality of interpolated image is improved by shape parameters optimization technique.