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Convex Lifting-Type Methods for Curvature Regularization

In: Handbook of Variational Methods for Nonlinear Geometric Data

Author

Listed:
  • Ulrich Böttcher

    (Applied Mathematics Münster, Westfälische Wilhelms-Universität Münster)

  • Benedikt Wirth

    (Applied Mathematics Münster, Westfälische Wilhelms-Universität Münster)

Abstract

Human visual perception is able to complete contours of objects even if they are disrupted or occluded in images. A possible mathematical imitation of this property is to represent object contours in the higher-dimensional space of positions and directions, the so-called roto-translation space, and to use this representation to promote contours with small curvature and separate overlapping objects. Interpreting image level lines as contours then leads to curvature-penalizing regularization functionals for image processing, which become convex through the additional dimension. We present the basic concept, some of its properties, as well as numerical discretization approaches for those functionals.

Suggested Citation

  • Ulrich Böttcher & Benedikt Wirth, 2020. "Convex Lifting-Type Methods for Curvature Regularization," Springer Books, in: Philipp Grohs & Martin Holler & Andreas Weinmann (ed.), Handbook of Variational Methods for Nonlinear Geometric Data, chapter 0, pages 207-233, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-31351-7_7
    DOI: 10.1007/978-3-030-31351-7_7
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