Abstract
Super-resolution is the art of creating nice high-resolution raster images from given low-resolution raster images. Since “nice” is not a well-defined term in mathematics and computer science, we propose a linear model of the world that allows us, under certain conditions, to achieve perfect super-resolution for arbitrarily high resolution. For example, we may now create a larger-than-life picture of Kurt.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Acharya, T., Tsai, P.-S.: Computational foundations of image interpolation algorithms. ACM Ubiquity 8 (2007)
Atkins, C.B., Bouman, C.A., Allebach, J.P.: Optimal image scaling using pixel classification. In: Proceedings of the 2001 International Conference on Image Processing (ICIP 2001), vol. 3, pp. 864–867 (2001)
Baker, S., Kanade, T.: Limits on super-resolution and how to break them. In: Proceedings of the 2000 IEEE Conference on Computer Vision and Pattern Recognition (CPVR 2000), vol. 2, pp. 372–379 (2000)
Blomgren, P., Papanicolaou, G., Zhao, H.: Super-resolution in time reversal acoustics. Journal of the Acoustical Society of America 111, 230–248 (2002)
Blu, T., Thévenaz, P., Unser, M.: Generalized interpolation: higher quality at no additional cost. In: Proceedings of the 1999 International Conference on Image Processing (ICIP 1999), vol. 3, pp. 667–671 (1999)
Candocia, F.M., Principe, J.C.: Superresolution of images with learned multiple reconstruction kernels. In: Guan, L., Kung, S.Y., Larsen, J. (eds.) Multimedia Image and Video Processing, ch. 4, pp. 219–243. CRC Press, New York (2000)
Corduneanu, A., Platt, J.C.: Learning spatially-variable filters for super-resolution of text. In: Proceedings of the 2010 International Conference on Image Processing (ICIP 2010), vol. 1, pp. 849–852 (2005)
Davis, L.: A survey of edge detection techniques. Computer Graphics and Image Processing 4, 248–270 (1975)
Dey, T.K., Mehlhorn, K., Ramos, E.A.: Curve reconstruction: connecting dots with good reason. Computational Geometry: Theory and Applications 10, 289–303 (2000)
Farsiu, S., Elad, M., Milanfar, P.: A practical approach to super-resolution. In: Proceedings of the 40th Asilomar Conference on Signals, Systems and Computers (2006) (invited paper)
Freeman, W.T., Jones, T.R., Pasztor, E.C.: Example-based super-resolution. IEEE Computer Graphics and Applications, 56–65 (2002)
Friedman, T.L.: The World is Flat: A Brief History of the Twenty-First Century. Farrar, Strauss and Giroux (2005)
Irani, M., Peleg, S.: Super resolution from image sequences. In: Proceedings of the 10th International Conference on Pattern Recognition (ICPR 1990), vol. 2, pp. 115–120 (1990)
Jiang, Z., Wong, T.-T., Bao, H.: Practical super-resolution from dynamic video sequences. In: Proceedings of the 2003 IEEE Conference on Computation Vision and Pattern Recognition (CVPR 2003), vol. 2, pp. 549–554 (2003)
Lehmann, T.M., Gönner, C., Spitzer, K.: Survey: interpolation methods in medical image processing. IEEE Transactions on Medical Imaging 18(11), 1049–1075 (1999)
Lengauer, T., Mehlhorn, K.: The HILL system: a design environment for the hierarchical specification, compaction, and simulation of integrated circuit layouts. In: Penfield Jr., P. (ed.) Proceedings of the MIT VLSI Conference, Artech House, Inc. (1984)
Li, X., Orchard, M.T.: New edge-directed interpolation. IEEE Transactions on Image Processing 10(10), 1521–1527 (2001)
Lin, Z., Shum, H.-Y.: Fundamental limits of reconstruction-based superresolution algorithms under local translation. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(1), 83–97 (2004)
Mehlhorn, K.: On the size of sets of computable functions. In: Proceedings of the 14th IEEE Symposium on Automata and Switching Theory, pp. 190–196 (1973)
Mehlhorn, K., Näher, S.: The LEDA Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)
Meijering, E.: A chronology of interpolation: from ancient astronomy to modern signal and image processing. Proceedings of the IEEE 90(3), 319–342 (2002)
Mitra, B.: Gaussian-based edge-detection methods: a survey. IEEE Transactions on Systems, Man, and Cybernetics — Part C: Applications and Reviews 32(3) (2002)
Mueller, N., Lu, Y., Do, M.N.: Image interpolation using multiscale geometric representations. In: Proceedings of the 2007 SPIE Conference on Electronic Imaging (2007)
Price, J.R., Hayes III, M.H.: Optimal prefiltering for improved image interpolation. In: Proceedings of the 32nd Asilomar Conference on Signals, Systems and Computers, vol. 2, pp. 959–963 (1998)
Price, K.: Keith Price Bibliography: evaluation of edge detection algorithms (2009), http://www.visionbib.com/bibliography/edge235.html
Raghupathy, A., Chandrachoodan, N., Liu, K.J.R.: Algorithm and VLSI architecture for high performance adaptive video scaling. IEEE MultiMedia 5(4), 489–502 (2003)
Sajjad, M., Khattak, N., Jafri, N.: Image magnification using adaptive interpolation by pixel level data-dependent geometrical shapes. Proceedings of the World Academy of Science, Engineering and Technology 25, 88–97 (2007)
Shechtman, E.: Space-time super-resolution. Master’s thesis, Faculty of MAthematics and Computer Science, The Weizmann Institute of Science (2003)
Sun, J., Sun, J., Xu, Z., Shum, H.-Y.: Image super-resolution using gradient profile prior. In: Proceedings of the 2007 IEEE Conference on Computation Vision and Pattern Recognition (CVPR 2007) (2007); Poster
Easy Thumbnails User Manual. Fookes Software, Switzerland (2001)
Tsai, R.Y., Huang, T.S.: Multiframe image restoration and registration. In: Advances in Computer Vision and Image Processing, ch. 7, vol. 1, pp. 317–339. JAI Press, Greenwich (1984)
Turkowski, K.: Filters for common resampling tasks. In: Glassner, A.S. (ed.) Graphics Gems I, pp. 147–165. Academic Press, London (1990)
Unser, M.: Sampling — 50 years after Shannon. Proceedings of the IEEE 88(4), 569–587 (2000)
van Ouwerkerk, J.D.: A modular approach to image super-resolution algorithms. Ph.D. thesis, Dept. of Media and Knowledge Eng., Delft Univ. of Technology (2006)
Wittman, T.: Mathematical techniques for image interpolation, Oral exam paper (2005), http://www.math.umn.edu/~wittman/Poral2.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fleischer, R. (2009). Is the World Linear?. In: Albers, S., Alt, H., Näher, S. (eds) Efficient Algorithms. Lecture Notes in Computer Science, vol 5760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03456-5_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-03456-5_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03455-8
Online ISBN: 978-3-642-03456-5
eBook Packages: Computer ScienceComputer Science (R0)