, Volume 25, Issue 3, pp 353-364
Date: 29 Aug 2006

Edge-Forming Methods for Image Zooming

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Abstract

The article is concerned with edge-forming methods to be applied as a post-process for image zooming. Image zooming via standard interpolation methods often produces the so-called checkerboard effect, in particular, when the magnification factor is large. In order to remove the artifact and to form reliable edges, a nonlinear semi-discrete model and its numerical algorithm are suggested along with anisotropic edge-forming numerical schemes. The algorithm is analyzed for stability and choices of parameters. For image zooming by integer factors, a few iterations of the algorithm can form clear and sharp edges for gray-scale images. Various examples are presented to show effectiveness and efficiency of the newly-suggested edge-forming strategy.

The work of this author is supported in part by NSF grant DMS–0312223.
Youngjoon Cha received his B.Sc. (1988) and M.Sc. (1990) from Mathematics, Seoul National University, Seoul, South Korea; and Ph.D. (1996) from Mathematics, Purdue University, working on mathematical epidemiology, under a guidance of Prof. Fabio Milner.
He was a post-doctoral researcher at Purdue University, and Seoul National University, South Korea, from 1996 to 1997 and from 1997 to 1998, respectively.
He is currently an associate professor in the Department of Applied Mathematics, Sejong University, South Korea. His research interests include image processing, mathematical and numerical modeling for waves, and mathematical epidemiology.
Seongjai Kim received his B.Sc. (1988) and M.Sc. (1990) from Mathematics, Seoul National University, Seoul, South Korea; and Ph.D. (1995) from Mathematics, Purdue University, working on computational fluid dynamics, under a guidance of Prof. Jim Douglas, Jr.
After two years of post-doctoral research on seismic inversion at Rice University, he worked for Shell E&P Tech. Co., Houston, for a year and the Department of Mathematics, University of Kentucky, for seven years. He is currently an associate professor in the Department of Mathematics and Statistics, Mississippi State University. His research interests are in mathematical and numerical modeling for wave propagation in highly heterogeneous media, seismology, and image processing for challenging images.