Abstract
Multi-Scale Singularity Trees(MSSTs) [10] are multi-scale image descriptors aimed at representing the deep structures of images. Changes in images are directly translated to changes in the deep structures; therefore transitions in MSSTs. Because MSSTs can be used to represent the deep structure of images efficiently, it is important to investigate and understand their transitions and impacts. We present four kinds of MSST transitions and discuss the potential advantages of Saddle-Based MSSTs over Extrema-Based MSSTs. The study of MSST transitions presented in this paper is an important step towards the development of the image matching and indexing algorithms based on MSSTs.
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References
Bille, P.: Report on Known Algorithm for Tree Matching. Technical report, Deliverable No.5, DSSCV, IST-2001-35443 (2003)
Damon, J.: Local Morse Theory for Gaussian Blurred Functions. In: Sporring, et al. (eds.) [11], ch.11, pp. 147–163
Iijima, T.: Basic theory on normalization of a pattern (in case of typical one-dimensional pattern). Bulletin of Electrotechnical Laboratory 26, 368–388 (1962) (in Japanese)
Koenderink, J.J.: The Structure of Images. Biological Cybernetics 50, 363–370 (1984)
Kuijper, A., Olsen, O.F.: Transitions of the Pre-Symmetry Set. In: Proceedings of the 17th Intl Conference on Pattern Recognition, ICPR 2004 (2004)
Lindeberg, T.: Scale-Space Theory in Computer Vision. The Kluwer International Series in Engineering and Computer Science. Kluwer Academic Publishers, Boston (1994)
Loog, M., Duistermaat, J.J., Florack, L.M.J.: On the Behavior of Spatial Critical Points under Gaussian Blurring. A Folklore Theorem and Scale-Space Constraints. In: Kerckhove, M. (ed.) Scale-Space 2001. LNCS, vol. 2106, pp. 183–192. Springer, Heidelberg (2001)
Sethian, J.A.: Fast Marching Methods. SIAM Review 41(2), 199–235 (1999)
Somchaipeng, K., Erleben, K., Sporring, J.: A Multi-Scale Singularity Bounding Volume Hierarchy. In: Proceedings of the 13th Intl Conference in Central Europe (WSCG 2005), January 2005, pp. 179–186 (2005)
Somchaipeng, K., Sporring, J., Kreiborg, S., Johansen, P.: Multi-Scale Singularity Trees: Soft-linked Scale-Space Hierarchies. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 97–106. Springer, Heidelberg (2005)
Sporring, J., Nielsen, M., Florack, L., Johansen, P. (eds.): Gaussian Scale-Space Theory. Kluwer Academic Publishers, Dordrecht (1997)
Weickert, J., Ishikawa, S., Imiya, A.: Om the History of Gaussian Scale-Space Axiomatics. In: Sporring, et al. (eds.) [11], ch. 4, pp. 45–59.
Witkin, A.P.: Scale–space filtering. In: Proc. 8th Int. Joint Conf. on Artificial Intelligence (IJCAI 1983), Karlsruhe, Germany, August 1983, vol. 2, pp. 1019–1022 (1983)
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Somchaipeng, K., Sporring, J., Kreiborg, S., Johansen, P. (2005). Transitions of Multi-scale Singularity Trees. In: Fogh Olsen, O., Florack, L., Kuijper, A. (eds) Deep Structure, Singularities, and Computer Vision. DSSCV 2005. Lecture Notes in Computer Science, vol 3753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11577812_20
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DOI: https://doi.org/10.1007/11577812_20
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