On the equivalence between hierarchical segmentations and ultrametric watersheds

We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations. We end this paper by showing how to use the proposed framework in practice in the example of constrained connectivity; in particular it allows to compute such a hierarchy following a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.Comment: 19 pages, double-colum

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. 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 satis ed. 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

Patterns of ash (Fraxinus excelsior L.) colonization in mountain grasslands: the importance of management practices

International audienceWoody colonization of grasslands is often associated with changes in abiotic or biotic conditions or a combination of both. Widely used as fodder and litter in the past traditional agro-pastoral system, ash (Fraxinus excelsior L.) has now become a colonizing species of mountain grasslands in the French Pyrenees. Its present distribution is dependent on past human activities and it is locally controlled by propagule pressure and abiotic conditions. However, even when all favourable conditions are met, all the potentially colonizable grasslands are not invaded. We hypothesize that management practices should play a crucial role in the control of ash colonization. From empirical field surveys we have compared the botanical composition of a set of grasslands (present and former) differing in management practices and level of ash colonization. We have displayed a kind of successional gradient positively linked to both ash cover and height but not to the age of trees. We have tested the relationships between ash presence in grassland and management types i.e. cutting and/or grazing, management intensity and some grassland communities' features i.e. total and local specific richness and species heterogeneity. Mixed use (cutting and grazing) is negatively linked to ash presence in grassland whereas grazing alone positively. Mixed use and high grazing intensity are directly preventing ash seedlings establishment, when low grazing intensity is allowing ash seedlings establishment indirectly through herbaceous vegetation neglected by livestock. Our results show the existence of a limit between grasslands with and without established ashes corresponding to a threshold in the intensity of use. Under this threshold, when ash is established, the colonization process seems to become irreversible. Ash possesses the ability of compensatory growth and therefore under a high grazing intensity develops a subterranean vegetative reproduction. However the question remains at which stage of seedling development and grazing intensity these strategies could occur

In your opinion, what makes a good judge? The study of public opinion through free answers in a survey

Typology, abstract concepts, perception, open-ended questions, textual data,

Taxicab Correspondence Analysis of Contingency Tables with One Heavyweight Column

correspondence analysis, taxicab correspondence analysis, heavyweight, supplementary point, forced classification,