Adaptive Markov Random Fields for Example-Based Super-resolution of Faces
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Adaptive Markov Random Fields for Example-Based Super-resolution of Faces Todd A. Stephenson1, 2 and Tsuhan Chen1 1 Electrical 2 ReallaeR,
& Computer Engineering Department, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890, USA LLC, P.O. Box 549, Port Republic, 20676 MD, USA
Received 21 December 2004; Revised 1 April 2005; Accepted 5 April 2005 Image enhancement of low-resolution images can be done through methods such as interpolation, super-resolution using multiple video frames, and example-based super-resolution. Example-based super-resolution, in particular, is suited to images that have a strong prior (for those frameworks that work on only a single image, it is more like image restoration than traditional, multiframe super-resolution). For example, hallucination and Markov random field (MRF) methods use examples drawn from the same domain as the image being enhanced to determine what the missing high-frequency information is likely to be. We propose to use even stronger prior information by extending MRF-based super-resolution to use adaptive observation and transition functions, that is, to make these functions region-dependent. We show with face images how we can adapt the modeling for each image patch so as to improve the resolution. Copyright © 2006 T. A. Stephenson and T. Chen. 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.
1.
INTRODUCTION
Early work on enhancing low-resolution images addressed increasing the resolution of the image without any specific outside information related to the image domain. Methods such as linear interpolation [1] first reproduce the existing pixels to produce a magnified image and then smooth the new image. In increasing the resolution of a video frame, however, outside information is available. That is, its neighboring frames typically contain slightly different information that can be used to increase the resolution of the center frame [2]. In contrast to interpolation, this method actually adds information that was lost when the image was taken. This approach is also appropriate when we have neighboring cameras instead of neighboring video frames recording the same scene. The work in [3] expanded multiframe superresolution, in part, by using a Huber-Markov random field (HMRF) to define a simple prior distribution that gives low probabilities for high frequencies. While multiple video frames may not always be available, multiple related images from the same domain may be of use instead. Example-based super-resolution [4] uses the known characteristics of this domain (i.e., the prior distribution) to perform specialized enhancement. They learn the
priors from a database of high-resolution images from the same domain (this is in contrast to priors defined by hand [3]). Statistical pattern recognition methods are then used for example-based super-resolution. Markov random fields (MRF
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