Abstract
Hierarchical data representations in the context of classification and data clustering were put forward during the fifties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satisfied. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing.
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A preliminary version of this paper was presented at the workshop WADGMM 2010 [1] held in conjunction with ICPR 2010, Istanbul, August 2010.
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Soille, P., Najman, L. (2012). On Morphological Hierarchical Representations for Image Processing and Spatial Data Clustering. In: Köthe, U., Montanvert, A., Soille, P. (eds) Applications of Discrete Geometry and Mathematical Morphology. WADGMM 2010. Lecture Notes in Computer Science, vol 7346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32313-3_4
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