Content Aware Image Resizing using Quasi-conformal Mapping




【主 讲 人】陈发来  中国科学技术大学数学系教授


陈发来,中国科学技术大学数学系教授、博士生导师。1982年进入中国科技大学数学系学习,分别于1987年、1989年、1994年获计算数学专业学士、硕士、博士学位。1995年任副教授,1998年晋升教授,1999年受聘博士生导师岗位。从1994年起分别到美国杨伯翰大学、美国Rice大学、香港科技大学、香港大学、新加坡国立大学、奥地利林茨大学等访问。现为中国科学技术大学数学系教授、博士生导师,中国工业应用数学学会常务理事及几何设计与计算分会副主任,计算数学学会常务理事,安徽省数学会秘书长,《Computer Aided Geometric Design》、《Visual Computer》,《数学与系统科学》,《数值计算与计算机应用》,《高校计算数学学报》,《计算机辅助设计与图形学学报》编委。曾两次获国家级教学成果二等奖。2001年获教育部高校青年教师奖。2002年获国家自然科学基金杰出青年基金。2003年获宝钢优秀教师奖特等奖。2008年获中科院优秀导师奖,中国计算机图形学杰出奖。2009年获冯康科学计算奖,新世纪百千万人才工程国家级人选。



Content-aware image resizing is resizing an image such that the prominent feature of the image is intact and the homogenous content of the image is distorted as little as possible. There is a lot of research on this topic, and various approaches have been proposed so far. One problem with previous methods is the lack of a theoretical guarantee of a rigorous bijective map between an image and the target image, which may cause artifacts in the target image. In this paper, we present a new approach to solve the image resizing problem based on quasi-conformal mapping. We apply quasi-conformal mapping to set up a bijective map between an image and the target image such that the salient feature of the image is uniformly scaled, while the homogenous content of the image is distorted as little as possible. The distortion is characterized by a function defined by the Beltrami coefficient of the quasi-conformal mapping, which is minimized by solving a nonconvex optimization problem. Solving the optimization problem is reduced to solving two convex optimization problems alternatingly. We implemented our algorithm with many examples and made comparisons with previous approaches. The examples suggest that our method is comparable with previous approaches while guaranteeing that there are no foldovers. Furthermore, our method can easily preserve line features and handle large changes in the aspect ratios of images.