TY - JOUR

T1 - Image zooming method using edge-directed moving least squares interpolation based on exponential polynomials

AU - Lee, Yeon Ju

AU - Yoon, Jungho

N1 - Funding Information:
The authors are grateful to the anonymous referee for the valuable suggestions on this paper. Jungho Yoon was supported by NRF grant 2015 R1A5A1009350 (Science Research Center Program) through the National Research Foundation of Korea .
Publisher Copyright:
© 2015 Elsevier Inc.

PY - 2015/7/20

Y1 - 2015/7/20

N2 - Abstract 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.

AB - Abstract 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.

KW - Edge-directed interpolation

KW - Exponential polynomial

KW - Image upsampling

KW - Minimization problem

KW - Moving least squares

KW - Reproducing property

UR - http://www.scopus.com/inward/record.url?scp=84939222629&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2015.07.086

DO - 10.1016/j.amc.2015.07.086

M3 - Article

AN - SCOPUS:84939222629

VL - 269

SP - 569

EP - 583

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

M1 - 21488

ER -