Research On Image Interpolation Based On Rational Function With Parameters

Image interpolation plays an important role in digital image processing, which aims at reconstructing a high-resolution image from a corresponding low-resolution image. It has been widely used in digital photography, medical imaging, computer vision, and all kinds of consumer electronics. Image interpolation is one of the hot topics in image processing. Although there are some relatively mature methods which are widely used in commercial hardware and software products, it still has some important and difficult problems needed to be solved, such as fitting to edge and detail areas, the tradeoff between algorithm complexity and accuracy etc.In this work, we construct image interpolation model based on a class of rational function by studying the property of a class of rational function with parameters. Through theoretical analysis and experimental verification, the inner relationship between rational function properties and image effects is studied. The primary strategies are as following:First, a new image interpolation algorithm based on C1-continuous rational function model with both smoothing and surface constraints was proposed. The image edge regions can be detected adaptively by using contour analysis. Basically, the detective threshold is selected based on the rational function construction. Selecting different parameters in the rational function model, the edge regions and smooth regions are interpolated by bicubic interpolation and rational interpolation respectively. The optimal rational interpolation parameters can be obtained with based on the contrast sensitivity enhancement of the human eyes. Experimental results demonstrate that the proposed method achieves competitive performance with the state-of-the-art interpolation algorithms, especially in image details features.Second, the main reason of zigzagging artifact comes from asymmetry of original C1-continuous model. A method of eliminating this asymmetry is proposed. It is based on blended and weighted rational function algorithm. Blend aims to eliminate the asymmetry on direction and space through 4 rotated models of original model. Weight coefficients are determined by the edge information from different scale based on point sampling. Experiences show that zigzagging artifact on the edge areas can be removed because of blending and weighting.Third, for the C2-continuous rational function, it is a relatively symmetry model and has an explicit expression with two parameters. A new algorithm of optimization parameters is proposed. The number of parameters is reduced according to the property of the C2-continuous rational function. Then the parameter is modified in order to make the interpolation patch approximate the ideal patch. Experiments show that this method has a high objective image assessment value; besides, it can keep the local texture feature well and can reduce the zigzagging around the edge region. It is very competitive to other state-of-the-art methods.Forth, we analysis the affect of the smooth of rational function, change of parameters based on the methods above. All these methods are easy to implement and have a good visual effect in detail and edge areas. They are comparable to other state-of-the-art methods in image quality. Besides, they can perform zoom with arbitrary scaling factors in one operation. For the class of rational function itself, C2-countinuous rational function has a better image quality no matter in experimental data or in visual effect than C1-countinuous function, so smoothness is the primary factor in this class of rational function interpolation; the effect of parameters to image interpolation is slightly weaker than smoothness. But parameters play a positive role to image interpolation because they can add degree of freedom such that the interpolation can be adjusted by other theories, such as human contrast sensitivity or energy control.