Abstract
Image analysis requires an appropriate description of shape. The structure of shape may be determined by a grouping of parts of the image with certain associated characteristics. A coarse-to-fine structure can be determined by an ordered sequence of hierarchical levels. Three methods of generating an ordered sequence are proposed, that is, based on grey-level images, based on shape primitives, and based on symbolic descriptions. The hierarchical representation is based on symbolic descriptions. This paper aims to generalize the hierarchical approach, and to explain the mathematical background.
The author wishes to acknowledge the referees for their helpful comments.
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References
van den Boomgaard, R., Smeulders, A.W.M. (1993). Towards a morphological scale-space theory, this volume, pp. 631–640.
Harary, F. (1972). Graph Theory, Addison Wesley, Reading, MA.
Heijmans, H.J.A.M. (1993). Mathematical morphology as a tool for shape description, this volume,pp. 147–176.
Hummel, R., Moniot, R. (1989). Reconstructions from zero-crossings in scale-space, IEEE Trans. ASSP 37, pp. 2111–2130.
Kent, J.T., Mardia, K.V. (1993). Statistical shape methodology in image analysis, this volume, pp. 443–452.
Kimia, B.B., Tannenbaum, A.R., Zucker, S.W. (1993). Exploring the shape manifold: the role of conservation laws, this volume, pp. 601–620.
Koenderink, J.J. (1984). The structure of images, Biological Cybernetics 50, pp. 363–370.
Kovalevsky, V.A. (1993). A new concept for digital geometry, this volume, pp. 3751.
Kropatsch, W.G., Willersinn, D. (1993). Irregular curve pyramids, this volume, pp. 525–538.
Lindeberg, T.P. (1993). Scale-space for N-dimensional discrete signals, this volume, pp. 571–590.
Lindeberg, T.P. (1993). Scale-space behaviour and invariance properties of differential singularities, this volume, pp. 591–600.
Mattioli, J., Schmitt, M. (1993). On information contained in the erosion curve, this volume, pp. 177–196.
Montanvert, A., Meer, P., Bertolino, P. (1993). Hierarchical shape analysis in grey-level images, this volume, pp. 511–524.
Nacken, P., Toet, A. (1993). Candidate grouping for bottom up segmentation, this volume, pp. 549–558.
Porteous, I.R. (1981). Topological Geometry, Cambridge Univ. Press., Cambridge, UK.
Protter, M.H., Weinberger, H.F. (1967). Maximum Principles in Differential Equations, Prentice-Hall.
Segen, J. (1993). Inference of stochastic graph models for 2-D and 3-D shape, this volume, pp. 493–510.
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© 1994 Springer-Verlag Berlin Heidelberg
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Ying-Lie, O. (1994). Hierarchical Shape Representation for Image Analysis. In: O, YL., Toet, A., Foster, D., Heijmans, H.J.A.M., Meer, P. (eds) Shape in Picture. NATO ASI Series, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03039-4_41
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DOI: https://doi.org/10.1007/978-3-662-03039-4_41
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