Super Resolution From A Single Image by Gal Graif and Shani Zlotolov Supervised by Anna Oyzerman Abstract Super resolution (SR) are methods that recover a high resolution image from one or more low resolution input images. We'll concentrate on two methods: 1) Classical super resolution- this method uses a set of low resolution images of the same scene to recover a higher resolution image. 2) Example based super resolution- this method uses correspondences between low and high resolution image patches which are learned from a database of low and high resolution image pairs. Our project deals with super resolution from a single image. We'll adjust the two methods to fit a single image and combine the two methods. Patch Redundancy: Small image patches (e.g. 5x5) in a natural image tend to redundantly recur many times inside the image. Patches tend to repeat within the same scale or different scales. Average patch recurrence within and across scales of a single image (averaged over hundreds of natural images). The percent of image patches for which there exist n or more similar patches (n = 1; 2; 3; :::; 9), measured at several different image scales. Classical SR from a single image: In order to perform classical SR from a single image, we'll use patch redundancy within the same scale as a set of low-res images of the same scene. For each patch we will find the k nearest neighbors (KNN). Each repeated patch gives us new information since there are sub-pixel shifts between the repeated patches. Than the information from all low resolution images is fused to a higher resolution image. Example- Based SR from a single image: In order to perform example based SR from a single image we'll use patch redundancy across different scales. The low-res/ high-res patch correspondences which are used in this method can be learned from the redundancy of patches from the original single image in lower scale images. For each patch in the original image (3) its nearest neighbor in a lower scale image (1) is found. Afterwards the parent of the lower scale image patch (2) is copied to the new higher resolution image (4). Combining classical and example based SR: In order to improve the images resolution we combine classical and example-based SR. We explored different combinations of the two algorithms. Combining the two methods by first increasing the resolution using example- based SR and then applying the classical method to improve the resolution even more has been found to deliver the best results. Results: Original image : 70x70 Example Based SR: 110x110 Classical SR: 110x110 Example Based + Classical SR: 137x137 Original image : 70x70 Example Based SR: 110x110 Classical SR: 110x110 Example Based + Classical SR: 137x137 Conclusions: Both classical SR and Example-based SR from a single image generates good results. Classical SR is numerically limited only to small increases in resolution (by factors smaller than 2). Combining classical SR and example-based SR allows reaching a higher resolution image than using one method only. Classical SR algorithm's running time is very long. Downloads: Book Presentation Code Acknowledgment: We would like to thank our project supervisor Anna Oyzerman for supporting us during the learning process and for giving us helpful advice and knowledge which helped us a lot during the project. Bibliography: Daniel Glasner, Shai Bagon, Michal Irani. Super- Resolution from a Single Image. Rehovot, Israel, 2009. Matan Protter, Michael Elad, Hiroyuki Takeda, and Peyman. Generalizing the Nonlocal-Means to Super-Resolution Reconstruction, 2009. Kwang In Kim and Younghee Kwon Example-Based Learning for Single-Image Super-Resolution. Springer Verlag Berlin Heidelberg, 2008.