Abstract
Image compression and manipulation by weighted finite automata exploit similarities in the images in order to obtain notable compression ratios and manipulation tools. The investigations are often based on two-dimensional images. A natural extension is to consider three- or even n-dimensional images which are decomposed in two- dimensional slices, e. g. data produced by tomography. By applying the two-dimensional methods to the slices the volume similarities may be disregarded. Building three-dimensional patterns by merging sequenced images of movie scenes may result in increased similarities. Here we consider transformations of the input strings for weighted finite automata in order to obtain dimension transformations which preserve multidimensional similarities. We focus our investigations on the state complexity and show that a noticeable reduction of the number of states can be achieved.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berstel, J., and Morcrette, M. Compact representation of patterns by finite automata. Pixim’ 89, Computer Graphics in Paris, 2nd Annual Conference on Computer Graphics; Selected Papers (Paris, 1989), pp. 387–401. 208
Berstel, J., and Nait Abdallah, A. Quadtrees generated by finite automata. AFCET-GROPLAN 61/62 (1989), 167–175. 208, 210
CCITT SGVIII Joint Photographics Experts Groupt (JPEG), ISO/IEC JTC1/SC2/WG8. JPEG Technical Specification (Revision 5), January 1992. JPEG 8-R5. 208
Čulik, K., and Dube, S. Affine automata and related techniques for generation of complex images. Theoretical Computer Science 116 (1993), 373–398. 208
Čulik, K., and Karhumäki, J. Finite automata computing real functions. SIAM Journal on Computing 23 (1994), 789–814. 210
Čulik, K., and Kari, J. Image compression using weighted finite automata. Computers and Graphics 17 (1993), 305–313. 209, 210
Culik, K., and Kari, J. Digital images and formal languages. In Handbook of Formal Languages, G. Rozenberg and A. Salomaa, Eds., vol. 3. Springer Verlag, Berlin, 1997, pp. 599–616. 208, 210
Schlesinger, M. I., and Hlavác, V. Ten Lectures on Statistical and Structural Pattern Recognition, vol. 24 of Computational Imaging and Vision. Kluwer Academic Publishers, Dordrecht, 2002. 209
Staiger, L. Quadtrees and the Hausdor. dimension of pictures. Proceedings of the 4 th Workshop on Geometrical Problems of Image Processing (Berlin, 1989), vol. 51 of Mathematical Research, Berlin: Akademie-Verlag, pp. 173–178. 208, 210
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kutrib, M., Jan-Thomas, L. (2002). String Transformation for n-Dimensional Image Compression. In: Grosky, W.I., Plášil, F. (eds) SOFSEM 2002: Theory and Practice of Informatics. SOFSEM 2002. Lecture Notes in Computer Science, vol 2540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36137-5_15
Download citation
DOI: https://doi.org/10.1007/3-540-36137-5_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00145-4
Online ISBN: 978-3-540-36137-4
eBook Packages: Springer Book Archive