Abstract
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 257 × 257 . 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.
Highlights
The purpose of image registration is to align two or more images of the same scene obtained at different times, perspectives or sensors such as MRI, X-ray, CT, PET, SPECT, and tomography
In order to overcome the illposedness of the optimization problem ( ) and to assure smooth solutions, we introduce additional regularization terms
In [ ] we studied the same optimal control formulation of the image registration problem with different regularization terms and showed the existence and uniqueness of this optimization problem using appropriate theorems
Summary
The purpose of image registration is to align two or more images of the same scene obtained at different times, perspectives or sensors such as MRI, X-ray, CT, PET, SPECT, and tomography. Image registration is a significant and challenging subject which usually involves high storage requirements, high CPU costs and mostly deals with noisy, distorted, and occluded data. In literature several different types of image registration techniques (see, for instance, [ , ] and references therein) were developed. Each of these algorithms was generated based on a specific application, disease or image modality. There is still no general image registration technique which could be used in every sort of data. Based on these facts, finding fast and efficient image registration techniques is a quite useful and still significantly important area of research
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