Newton-Thiele Type Continued Fraction Defined on Trapezoidal Mesh in Image Inpainting

Abstract

Digital image in painting, which also called digital image reconstruction, namely, to repair lost data or damaged digital image local area according to the certain rule, to restore the image of integrity. The technology is an important research in many fields such as to restore culture relic, to repair the old films, to incomplete damaged pictures causing by the network transmission, to removal of the object in the image and video and so on. It also has been widely applied in high definition television, high definition multimedia. A new method based on Newton-Thiele type continued fractions has been proposed to make the image in painting. Newton-Thiele type continued fraction is a kind of bivariate rational fraction constructed by means of Newton interpolation polynomial in one variable based on divided differences and Thiele interpolating continued fraction in another variable based on inverse differences, which provides an effective way to interpolate the neighbor points around the damaged pixel and then reconstruct the pixel. But the above algorithm is limited to matrix and ignores these points out of the region covering damaged point, which may cause big accuracy and take unnecessary compute capacity. We propose an improved algorithm based on Newdon-Thiele continued fraction defined on irregular mesh to reconstruct a damaged pixel in this paper, in order to avoid these conditions.