On Geometric Variational Models for Inpainting Surface Holes (PREPRINT)

Abstract

Geometric approaches for filling-in surface holes are introduced and studied in this paper. The basic idea is to represent the surface of interest in implicit form, and fill-in the holes with a scalar, or systems of, geometric partial differential equations often derived from optimization principles. These equations include a system for the joint interpolation of scalar and vector fields, a Laplacian-based minimization, a mean curvature diffusion flow, and an absolutely minimizing Lipschitz extension. The theoretical and computational framework, as well as examples with synthetic and real data, are presented in this paper.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2006
Accession Number
ADA478742

Entities

People

  • Gloria Haro
  • Guillermo Sapiro
  • Joan Verdera
  • Vicent Caselles

Organizations

  • University of Minnesota

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Curvature
  • Differential Equations
  • Diffusion
  • Equations
  • Extrapolation
  • Geometric Forms
  • Geometry
  • Image Processing
  • Image Restoration
  • Image Segmentation
  • Integrals
  • Interpolation
  • Mathematics
  • Partial Differential Equations
  • Three Dimensional

Readers

  • Computer Vision.
  • Graph Algorithms and Convex Optimization.