Image zooming method using edge-directed moving least squares interpolation based on exponential polynomials

This paper presents a nonlinear image interpolation algorithm. The suggested method is based on the moving least squares (MLS) projection technique, but introduces a fundamental modification. The algebraic polynomial-based MLS methods provide very satisfactory results. However, the associated approximation space is shift-and-scale invariant so that it cannot be adjusted according to the characteristic of a given data. As a result, when upsampling images, it has a limitation in producing sharp edges such that edges are often blurred in the magnified images. To recover sharper edges, we need to reduce smoothing parameter or adapt a new parameter sharpening the edges. Motivated by this observations, we propose a novel MLS method governed by a set of exponential polynomials with tension parameters such that they can be tuned to the characteristic of given data. Moreover, for a better match to the local structures around the edges, the suggested algorithm uses weights which consider the edge orientation. Numerical results are presented and compared, visually and by using some quantitative fidelity measures (PSNR, EPSNR, SSIM and FSIM), to the bicubic spline interpolation and other recently developed nonlinear methods. The results demonstrate the new algorithm's ability to magnify an image while preserving edge features.