Coupling Image Restoration and Segmentation: A Generalized Linear Model/Bregman Perspective

  • Authors:

  • Grégory Paul;Janick Cardinale;Ivo F. Sbalzarini

  • Affiliations:

  • MOSAIC Group, ETH Zurich, Zurich, Switzerland 8092 and ETH Zurich, Computer Vision Laboratory, Zurich, Switzerland 8092;MOSAIC Group, ETH Zurich, Zurich, Switzerland 8092;MOSAIC Group, ETH Zurich, Zurich, Switzerland 8092 and MOSAIC Group, Center of Systems Biology, Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany 01307

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 2013

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Abstract

We introduce a new class of data-fitting energies that couple image segmentation with image restoration. These functionals model the image intensity using the statistical framework of generalized linear models. By duality, we establish an information-theoretic interpretation using Bregman divergences. We demonstrate how this formulation couples in a principled way image restoration tasks such as denoising, deblurring (deconvolution), and inpainting with segmentation. We present an alternating minimization algorithm to solve the resulting composite photometric/geometric inverse problem. We use Fisher scoring to solve the photometric problem and to provide asymptotic uncertainty estimates. We derive the shape gradient of our data-fitting energy and investigate convex relaxation for the geometric problem. We introduce a new alternating split-Bregman strategy to solve the resulting convex problem and present experiments and comparisons on both synthetic and real-world images.