Abstract
In Mathematical Morphology, the reconstruction of images from markers has proven to be useful in morphological filtering and image segmentation. This work investigates the utilization of a criterion in the reconstruction process, whose utilization in the problem of the image reconstruction from an image marker has been partially treated elsewhere. This work further investigates this idea and extends it to the problem of image reconstruction from labelled markers. In the binary case, this allows us to compute the modified influence zones associated to the set of labelled markers. A significant difference with the usual case (i.e., the ”normal” influence zones) is that we generally do not obtain a whole partition of the space, because the criterion added to the reconstruction process causes that some points or pixels are not recovered. In addition, in this paper we consider the gray-level case, and we use the reconstruction with criterion to separate regions from a non-binary input image. This input image is considered as a topographic relief (similarly as in a normal watershed); however, the flooding mechanism is modified by the reconstruction criterion. The benefit is that we can control to some extent how the flooding proceeds and, therefore, how image region shapes are recovered.
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Beucher, S., Meyer, F.: The morphological approach to segmentation: the watershed transformation. In: Dougherty, E. (ed.) Book Mathematical morphology in image processing, pp. 433–481. Marcel Dekker, New York (1993)
Crespo, J., Serra, J., Schafer, R.: Theoretical aspects of morphological filters by reconstruction. Signal Process 47(2), 201–225 (1995)
Crespo, J., Schafer, R.: Locality and adjacency stability constraints for morphological connected operators. Journal of Mathematical Imaging and Vision 7, 85–102 (1997)
Crespo, J., Maojo, V.: New Results on the Theory of Morphological Filters by Reconstruction. Journal Pattern Recognition 31(4), 419–429 (1998)
Digabel, H., Lantuéjoul, C.: C. Iterative algorithms. In: Caen, J.-L., Chermant, E. (eds.) Second Symposium Européen d’Analyse Quantitative des Microstructures en Sciences des Matériaux, Biologie et Médecine, pp. 85–99. Riederer Verlag, Stuttgart (1977)
Heijmans, H.: Morphological Image Operators (Advances in Electronics and Electron Physics, Series Editor: P. Hawkes). Academic Press, London (1994)
Meyer, F., Beucher, S.: Morphological segmentation. J. Visual Commun. Image Repres 1(1), 21–45 (1990)
Salembier, P., Serra, J.: Flat zones filtering, connected operators, and filters by reconstruction. J. of IEEE Transactions on Image Processing 4, 1153–1160 (1995)
Schmitt, M., Mattioli, J.: Morphologie Mathematique, Masson (1993)
Serra, J.: Image Analysis and Mathematical Morphology, vol. 1. Academic Press, London (1982)
Serra, J. (ed.): Image Analysis and Mathematical Morphology, vol. 2. Academic Press, London (1988)
Serra, J., Salembier, P.: Connected operators and pyramids. In: SPIE (ed.) FOSSACS 2001, vol. 2030, pp. 85–76 (1993)
Serra, J.: Connectivity on complete lattices. Journal of Mathematical Imaging and Vision 9, 231–251 (1998)
Soille, P.: Morphological Image Analysis: Principles and Applications, 2nd edn. Springer, Heidelberg (2003)
Terol, R., Vargas, D.: A study of openings and closings with reconstruction criteria. In: Talbot, H., Beare, R. (eds.) Mathematical Morphology, Proc. of the VIth International Symposium (2002)
Vincent, L., Soille, P.: Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations. J. IEEE Trans. Pattern Anal. Machine Intell 13, 583–598 (1991)
Vargas, D., Crespo, J., Maojo, V., Terol, I.R.: Medical Image Segmentation Using Openings and Closings with Reconstruction Criteria. In: Proceedings of the International Conference on Image Processing ICIP (September 2003) (to be published)
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Vargas-Vazquez, D., Crespo, J., Maojo, V. (2003). Morphological Image Reconstruction with Criterion from Labelled Markers. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds) Discrete Geometry for Computer Imagery. DGCI 2003. Lecture Notes in Computer Science, vol 2886. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39966-7_45
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DOI: https://doi.org/10.1007/978-3-540-39966-7_45
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