“…Then, we approximate the first-order and second-order regularization terms by using the forward difference, central difference, mid-point rule, and Dirichlet boundary conditions. For more information and details, the reader is referred to Lajili et al 36 and Zhang et al 37 overcome these limitations by a multilevel technique, which assures the numerical solution serves as a perfect starting point and speeds up the registration process. Indeed, starting with the initial guess U = 0, the idea is to improve this guess by resizing the original images to a sequence of coarser ones where computations are cheap and register these smaller images (see Figure 3).…”
Section: Gauss-newton Methodsmentioning
confidence: 99%
“…Then, we approximate the first‐order and second‐order regularization terms by using the forward difference, central difference, mid‐point rule, and Dirichlet boundary conditions. For more information and details, the reader is referred to Lajili et al 36 and Zhang et al 37 …”
In this paper, we propose new variational model for image registration from tomographic data. First, we employ the topological gradient approach for a tomographic reconstruction that uses the first‐ and the second‐order discontinuities in order to detect important objects of a given observed X‐ray tomographic data (sinograms). Second, we use this geometric information furnished by a high‐order operator in order to define an appropriate fidelity measure for the image registration process. A theoretical study of the proposed model is provided; Gauss–Newton method and multilevel technique are used for its numerical implementation. The performed numerical experiments show the efficiency and effectiveness of our model.
“…Then, we approximate the first-order and second-order regularization terms by using the forward difference, central difference, mid-point rule, and Dirichlet boundary conditions. For more information and details, the reader is referred to Lajili et al 36 and Zhang et al 37 overcome these limitations by a multilevel technique, which assures the numerical solution serves as a perfect starting point and speeds up the registration process. Indeed, starting with the initial guess U = 0, the idea is to improve this guess by resizing the original images to a sequence of coarser ones where computations are cheap and register these smaller images (see Figure 3).…”
Section: Gauss-newton Methodsmentioning
confidence: 99%
“…Then, we approximate the first‐order and second‐order regularization terms by using the forward difference, central difference, mid‐point rule, and Dirichlet boundary conditions. For more information and details, the reader is referred to Lajili et al 36 and Zhang et al 37 …”
In this paper, we propose new variational model for image registration from tomographic data. First, we employ the topological gradient approach for a tomographic reconstruction that uses the first‐ and the second‐order discontinuities in order to detect important objects of a given observed X‐ray tomographic data (sinograms). Second, we use this geometric information furnished by a high‐order operator in order to define an appropriate fidelity measure for the image registration process. A theoretical study of the proposed model is provided; Gauss–Newton method and multilevel technique are used for its numerical implementation. The performed numerical experiments show the efficiency and effectiveness of our model.
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