Connection and Image Segmentation
Connexions et Segmentation d’Image
OPEN ACCESS
After some reminders on the notion of a set connection, a formal definition of image segmentation is proposed, that interprets it in terms of set connections. Then the central theorem of the paper identifies segmentation, connective criteria, and induced connections for any family of functions from an arbitrary space E into an arbitrary space T. The soundness of the egmentation approach is explicited by a series of examples. The connections are then used for filtering purposes. Here the main operations are the opening by reconstruction and the leveling. In conclusion, the proposed approach is compared with variational methods and with graph based strategies.
Résumé
Après quelques rappels sur la notion de connexion ensembliste, une définition formelle de la segmentation des images est proposée, qui l'interprète en termes de partition maximale selon un critère donné. Le théorème central du texte identifie alors segmentation, critère connectif et connections induites, pour toute famille de fonctions d'un espace arbitraire E dans un espace arbitraire T. La pertinence de la théorie est illustrée par une série d'exemples. Les connexions sont ensuite utilisées à des fins de filtrage. Ici, les deux opérations de base sont l'ouverture par reconstruction et le nivellement. Le texte se conclut par la comparaison de la démarche proposée avec les méthodes variationnelles et avec les stratégies à base de graphes.
Segmentation, connective criteria, connection, Lipschitz, quasi-flat zones, jump connection, smooth connection, leveling.
Mots clés
Segmentation, critères connectifs, connexion, Lipschitz, zones quasi-plates, connexion par sauts, connexion lisse, nivellement.
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