非局部特征方向图像插值方法研究

doi:10.3969/j.issn.0372-2112.2016.05.008

电子学报 ›› 2016, Vol. 44 ›› Issue (5): 1064-1070.DOI: 10.3969/j.issn.0372-2112.2016.05.008

非局部特征方向图像插值方法研究

詹毅¹, 李梦²

1. 重庆工商大学数学与统计学院, 重庆 400067;
2. 重庆文理学院群与图的理论及应用重点实验室, 重庆 402160

收稿日期:2014-12-17 修回日期:2015-05-24 出版日期:2016-05-25
- 通讯作者:
- 詹毅
- 作者简介:
- 李梦女,1973年出生,四川开江人,2012年在重庆大学数学与统计学院获得博士学位,现为重庆文理学院副教授,主要研究领域为偏微分方程及其在图像处理中的应用.E-mail:limeng7319@163.com
- 基金资助:
- 国家自然科学基金 (No.61202349); 重庆市基础与前沿研究计划一般项目 (No.cstc2013jcyjA40058,No.cstc2015jcyjA0142)

Research on Image Interpolation with Non-local Feature Directions

ZHAN Yi¹, LI Meng²

1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
2. Key Laboratory of Group & Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing 402160, China

Received:2014-12-17 Revised:2015-05-24 Online:2016-05-25 Published:2016-05-25

摘要/Abstract

摘要：

提出了一种非局部的特征方向图像插值方法,有效地保持了插值图像轮廓的光滑,抑制了图像边缘的模糊.这种方法把非局部Hessian矩阵的特征向量视为图像特征方向,使图像能量泛函沿这个方向进行扩散,其扩散强度由图像局部Hessian矩阵特征值参与控制.它克服了传统方法以梯度方向指示图像特征方向的局部性,使图像能量泛函沿正确方向扩散,避免了对图像特征的模糊.数值实验结果显示,该方法既能很好地重建插值图像的边缘,又不会在插值图像中产生伪影或图像边缘失真.

关键词: 非局部梯度, 非局部曲率, 总变差, 变分方法, 图像插值

Abstract:

A method of image interpolation with non-local feature directions is proposed.This method respectes the smooth of the contour profile of interpolated image and retrains blur edges.The eigenvector of the non-local Hessian matrix is considered as the image featrue direction.The diffusion of image energy functional is controlled by the eigenvalue of image local Hessian along the direction.It overcomes the local limit of gradient pointing image feature and drives image energy functional to diffuse along corrected direction.Thus the blur of image feature is avoids.Numerical experiments on real images show that images interpolated by the proposed method have better interpolated edges and are almost artifact-free.

Key words: non-local gradient, non-local curvature, total variation, variational methods, image interpolation

中图分类号:

TN911

詹毅, 李梦. 非局部特征方向图像插值方法研究[J]. 电子学报, 2016, 44(5): 1064-1070.

ZHAN Yi, LI Meng. Research on Image Interpolation with Non-local Feature Directions[J]. Acta Electronica Sinica, 2016, 44(5): 1064-1070.

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非局部特征方向图像插值方法研究

Research on Image Interpolation with Non-local Feature Directions

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