Composed Segmentation of Tubular Structures by an Anisotropic PDE Model

  • Authors:
  • Elena Franchini;Serena Morigi;Fiorella Sgallari

  • Affiliations:
  • Department of Mathematics-CIRAM, University of Bologna, Bologna, Italy;Department of Mathematics-CIRAM, University of Bologna, Bologna, Italy;Department of Mathematics-CIRAM, University of Bologna, Bologna, Italy

  • Venue:
  • SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
  • Year:
  • 2009

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Abstract

In this work we introduce the composed segmentation (C-segmentation), that is a priori composition of sources to obtain a single one segmentation result according to specific logic combinations. The approach and the segmentation model are general but we apply the C-segmentation technique to the challenging problem of segmenting tubular-like structures. The reconstruction is obtained by continuously deforming an initial distance function following the Partial Differential Equation (PDE)-based diffusion model derived from a minimal volume-like variational formulation. The gradient flow for this functional leads to a nonlinear curvature motion model. An anisotropic variant is provided which includes a diffusion tensor aimed to follow the tube geometry. Numerical examples demonstrate the ability of the proposed method to produce high quality 2D/3D segmentations of complex and eventually incomplete synthetic and real data.