Abstract
The aim of image analysis is to provide a symbolic description of the image structure, that can serve to supply information about the image for all kinds of different tasks.
We will give a complete description of the topological structure of images, studied simultaneously at all levels of resolution. This can be achieved through the artifice of embedding an image into a continuous family of images that can be uniquely generated by it. We will show how the representation of the image structure on different levels of resolution may be linked in a logical manner, so that features existing at different levels of resolution get related to each other.
Our method explains the succes of recently introduced ‘pyramid’ algorithms and is of value for the study of image morphology per se. Furthermore, it is not at all limited to two-dimensional images.
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
P.J. Burt, Tsai — Hong Hong and A. Rosenfeld, 1981. Segmentation and estimation of image region properties through cooperative hierarchical computation. IEEE Trans. on Systems, Man and Cybernetics, Vol. SMC-11, no. 12, pp. 802–809.
M. Golubitsky and V. Guillemin, 1973. Stable mappings and their singularities. Springer Verlag; New York — Heidelberg — Berlin.
J. Eells, Jr., 1967. Singularities of smooth maps. Gordon and Breach, New York.
M. Spivak, 1975. A comprehensive introduction to differential geometry. Vol.III. Publish or Perish, Inc., Berkely, Calif., U.S.A.
R. Thorn, 1972. Stabilité structurelle et morphogénèse, essai dfune théorie générale des modèles. W.A. Benjamin Inc., Reading, Massachusetts
T. Poston and I. Stewart, 1978. Catastrophy theory and its applications. Pitman Publ. Ltd., San Fransisco.
J.J. Koenderink and A.J. van Doom, 1979. The structure of two-dimensional scalar fields with applications to vision. Biol. Cybernetics, vol. 33, pp. 151–158.
A. Toet, 1982. Hierarchical image segmentation. M.Sc. Thesis, University of Utrecht, The Netherlands.
J.J. Koenderink, C. Huys and A. Toet, 1983. Resolution dependent structure of images. Submitted for publication to IEEE Trans. on Inf. Theory.
C.N. de Graaf, A. Toet, J.J. Koenderink, P. Zuidema, P.P. van Rijk, 1983. Some applications of hierarchical image processing algorithms. Proc. 8th Conf. Information Processing in Medical Imaging. Ed. F. Deconinck, Brussels, (this book)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Martinus Nijhoff Publishers, The Hague
About this chapter
Cite this chapter
Toet, A., Koenderink, J.J., Zuidema, P., de Graaf, C.N. (1984). Image Analysis -Topological Methods. In: Deconinck, F. (eds) Information Processing in Medical Imaging. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6045-9_19
Download citation
DOI: https://doi.org/10.1007/978-94-009-6045-9_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6047-3
Online ISBN: 978-94-009-6045-9
eBook Packages: Springer Book Archive