Abstract
Singular points in the linear scale space provide fundamental features for the extraction of dominant parts of an image. Employing the geometrical configuration of singular points, it is possible to construct a tree in scale space. This tree expresses a hierarchical structure of dominant parts. In this paper, we clarify the graphical grammar for the construction of this tree in the linear scale space and morphological scale space. Furthermore, we show a combinatorial structure of singular points in the linear scale space and morphological scale space using conformal mapping from Euclidean space to the spherical surface.
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References
Bookstein, F.L.: The line-skeleton. CVGIP 11, 1233–1237 (1979)
Rosenfeld, A.: Axial representations of shapes. CVGIP 33, 156–173 (1986)
Serra, J.: Mathematical Morphology. Academic Press, London (1982)
Iijima, T.: Pattern Recognition, Corona-sha, Tokyo (1974) (in Japanese)
Witkin, A.P.: Scale space filtering. In: Pros. of 8th IJCAI, pp. 1019–1022 (1993)
Lindeberg, T.: Scale-Space Theory in Computer Vision. Kluwer, Boston (1994)
ter Haar Romeny, B.M.: Front-End Vision and Multi-Scale Image Analysis Multi-scale Computer Vision Theory and Applications, written in Mathematica. Springer, Heidelberg (2003)
Lindeberg, T.: Feature detection with automatic selection. International Journal of Computer Vision 30, 79–116 (1998)
Otsu, N.: Mathematical Studies on Feature Extraction in Pattern Recognition. Researches of The Electrotechnical Laboratory 818 (1981) (in Japanese)
Weicker, J.: Anisotropic Diffusion in Image Processing. Teubner (1998)
Imiya, A., Sugiura, T., Sakai, T., Kato, Y.: Temporal structure tree in digital linear scale space. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, pp. 356–371. Springer, Heidelberg (2003)
Zhao, N.-Y., Iijima, T.: Theory on the method of determination of view-point and field of vision during observation and measurement of figure IECE Japan. Trans. D. J68-D, 508–514 (1985) (in Japanese)
Zhao, N.-Y., Iijima, T.: A theory of feature extraction by the tree of stable view-points. IECE Japan, Trans. D. J68-D, 1125–1135 (1985) (in Japanese)
Zhao, N.-Y.: A Study of Feature Extraction by the Tree of Stable View-Points, Dissertation to Doctor of Engineering, Tokyo Institute of Technology (1985) (in Japanese)
Pelillo, M., Siddiqi, K., Zucker, S.W.: Matching hierarchical structures using Association graphs. IEEE Trans. PAMI 21, 1105–1120 (1999)
Yuille, A.L., Poggio, T.: Scale space theory for zero crossings. IEEE PAMI 8, 15–25 (1986)
Kuijper, A., Florack, L.M.J., Viergever, M.A.: Scale Space Hierarchy. Journal of Mathematical Imaging and Vision 18, 169–189 (2003)
Kuijper, A., Florack, L.M.J.: The hierarchical structure of images. IEEE, Trans. Image Processing 12, 1067–1079 (2003)
Imiya, A., Katsuta, R.: Extraction of a structure feature from three-dimensional objects by scale-space analysis. In: ter Haar Romeny, B.M., Florack, L.M.J., Viergever, M.A. (eds.) Scale-Space 1997. LNCS, vol. 1252, pp. 353–356. Springer, Heidelberg (1997)
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Imiya, A., Sakai, T. (2006). Combinatorial Properties of Scale Space Singular Points. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds) Combinatorial Image Analysis. IWCIA 2006. Lecture Notes in Computer Science, vol 4040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11774938_26
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DOI: https://doi.org/10.1007/11774938_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35153-5
Online ISBN: 978-3-540-35154-2
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