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Mathematical Problems in Engineering
Volume 2013, Article ID 571052, 8 pages
Research Article

A Bidirectional Flow Joint Sobolev Gradient for Image Interpolation

1College of Computer Science, Chongqing University, Chongqing 400030, China
2College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
3College of Mathematics and Science, Chongqing University, Chongqing 400044, China
4Department of Mathematics & KLDAIP, Chongqing University of Arts and Sciences, Yongchuan, Chongqing 402160, China

Received 9 February 2013; Accepted 9 May 2013

Academic Editor: Ezzat G. Bakhoum

Copyright © 2013 Yi Zhan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An energy functional with bidirectional flow is presented to sharpen image by reducing its edge width, which performs a forward diffusion in brighter lateral on edge ramp and backward diffusion that proceeds in darker lateral. We first consider the diffusion equations as gradient flows on integral functionals and then modify the inner product from to a Sobolev inner product. The experimental results demonstrate that our model efficiently reconstructs the real image, leading to a natural interpolation with reduced blurring, staircase artifacts and preserving better the texture features of image.