TY - JOUR
T1 - Curvature-driven diffusion-based mathematical image registration models
AU - Akinlar, Mehmet Ali
AU - Kurulay, Muhammet
AU - Secer, Aydin
AU - Celenk, Mehmet
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - computational modeling
KW - image registration
KW - inverse problems
KW - Petrov-Galerkin scheme
KW - sum of squared differences
UR - http://www.scopus.com/inward/record.url?scp=84873391894&partnerID=8YFLogxK
U2 - 10.1186/1687-1847-2012-193
DO - 10.1186/1687-1847-2012-193
M3 - Article
AN - SCOPUS:84873391894
SN - 1687-1839
VL - 2012
JO - Advances in Difference Equations
JF - Advances in Difference Equations
M1 - 193
ER -