Morphologie Mathématique: de la Segmentation d'Images à l'Analyse Multivoque

Abstract : The first part of this thesis investigates the watershed line, one of the fundamental tools developed by mathematical morphology to segment images. Characterization of this object for regular functions is given, and a convergence theorem of the associated algorithm is demonstrated. Links between the watershed lines and the Euclidean skeleton by influence zones (or Voronoi diagram), as well as the Eikonal equation used in shape from shading, are then highlighted. Algorithms for geodesic reconstruction and segmentation with anchor points are built on the principle of the watershed. Finally, a hierarchical segmentation algorithm based on a new principle of dynamics of contours, is developed. It provides a single image all the information of the gradient used for segmentation. The second part of this thesis applies the tools from mutational and set-valued analysis to mathematical morphology. Mutational derivative of the dilation tube is calculated, justifying rigorously the intuition that an object expands along its normal at each of its points. The algebraic and continuity properties of applications induced by differential inclusions and acting on closed sets are characterized. Finally, an optimization algorithm (called the Montagne Russe or rollercoaster), of a non-probabilistic nature, guaranteeing the convergence to a global minimum, is proposed.
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Submitted on : Thursday, October 18, 2012 - 11:47:01 AM
Last modification on : Thursday, January 11, 2018 - 6:12:20 AM
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Laurent Najman. Morphologie Mathématique: de la Segmentation d'Images à l'Analyse Multivoque. Systèmes dynamiques [math.DS]. Université Paris Dauphine - Paris IX, 1994. Français. ⟨tel-00742889⟩

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