Image Zooming Method based on Data Adapted Moving Least Squares using Non-Local Penalty Function

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. While the classical MLS method uses a fixed approximation space based on algebraic polynomials, the proposed method uses the pproximation space spanned by exponential polynomials. In averaging process, the classical method gives similar penalty to data within a similar distance from the evaluation point so that neighboring data around the evaluation point are heavily weighted even though these data have no similarities. As a result, edges in the magnified images are smoothed. On the purpose of overcoming theses drawbacks, we introduced an adapted MLS method using `non-Local' penalty function such that the weights are determined in a way of depending local data similarities. Moreover, to consider the feature of the data, the linear system is governed by the set of exponential polynomials. We present some numerical examples which demonstrate the advantages of the proposed method for image upsampling.;이 논문은 비선형 보간법을 소개한다. 제안된 방법은 Moving Least Squares (MLS) 기법을 기반으로 하지만, 근본적인 수정안을 제시한다. 기존의 MLS 기법은 algebraic polynomials로 고정된 근사공간을 사용하는데, 여기서는 exponential polynomials 근사공간을 사용한다. 평균화 과정에서 기존방법은 계산하고자 하는 점과의 거리와 관련된 penalty를 부여한다. 즉, 주변 data에 유사성이 없더라도 가중치를 부여한다. 결과적으로 edge가 smooth하게 된다. 여기서는 non-local penalty 함수를 사용한다. Test결과와 수치적인 예들은 이미지를 확대하는 이 학위논문의 이점을 잘 보여준다.