Curvature-driven diffusion-based mathematical image registration models

Creative Commons License

AKINLAR M. A., KURULAY M., SEÇER A., Celenk M.

Advances in Difference Equations, vol.2012, 2012 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 2012
  • Publication Date: 2012
  • Doi Number: 10.1186/1687-1847-2012-193
  • Journal Name: Advances in Difference Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: computational modeling, image registration, inverse problems, Petrov-Galerkin scheme, sum of squared differences
  • Open Archive Collection: AVESIS Open Access Collection
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

This paper introduces several mathematical image registration models. Image registration, an ill-posed optimization problem, is formulated as the minimization of the sum of an image similarity metric and a regularization term. Curvature-driven diffusion-based techniques, in particular Perona-Malik, anisotropic diffusion, mean curvature motion (MCM), affine invariant MCM (AIMCM), are employed as a regularization term in this optimal control formulation. Adopting the steepest-descent marching with an artificial time t, Euler-Lagrange (EL) equations with homogeneous Neumann boundary conditions are obtained. These EL equations are approximately solved by the explicit Petrov-Galerkin scheme. The method is applied to the registration of brain MR images of size [InlineEquation not available: see fulltext.]. Computational results indicate that all these regularization terms produce similarly good registration quality but that the cost associated with the AIMCM approach is, on average, less than that for the others. MSC: 68U10, 65D18, 65J05, 97N40. © 2012 Akinlar et al.; licensee Springer.