Improved variational image registration model and a fast algorithm for its numerical approximation

Abstract

In a multimodal image registration scenario, where two given images have similar features, but noncomparable intensity variations, the sum of squared differences is not suitable for inferring image similarities. In this article, we first propose a new variational model based on combining intensity and geometric transformations, as an alternative to use mutual information and an improvement to the work by Modersitzki and Wirtz (Modersitzki and Wirtz, Lect Notes Comput Sci 4057 (2006), 257–263), and then develop a fast multigrid (MG) algorithm for solving the underlying system of fourth‐order and nonlinear partial differential equations. We can demonstrate the effective smoothing property of the adopted primal‐dual smoother by a local Fourier analysis. Numerical tests will be presented to show both the improvements achieved in image registration quality and MG efficiency. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011

Vectorial Total Variation-Based Regularization for Variational Image Registration

“…In [14], the main contribution was to highlight the fact that an approximate Jacobian idea (in Taylor's expansion) for all nonlinear terms in the diffusion image registration provides a better MG smoother than linearization of only one term which was the standard way of designing a MG method at that time. Finally, in [15] the authors proposed a new data fitting term based on combining intensity and geometric transformations, as an alternative to use mutual information for a multimodal image registration scenario, and then developed a fast MG algorithm for solving the EL system of coupled fourth-order and nonlinear PDEs.…”

Selective variational image segmentation combined with registration: Models and algorithms

“…It should be remarked that much work on using a mean curvature stems from our success of [9] in solving the curvature equation (or fourth order and highly nonlinear partial differential equations) efficiently. Although there exist many models of variational framework [23], for mono-modality images, we recommend the model of [17]; for multi-modality images, we believe the new model by [16] is much better in terms of robustness than widely used mutual information based models.…”

“…Finally for both segmentation and registration models, one may follow the simple algorithms from [15] to develop fast multigrid algorithms [17], [16], [4], [5].…”

“…The results of 3D local segmentation models following variational model with a new similarity functional and regularization terms is proposed[16] min u,c J α1,α2 (u, c) = D (u, c) + α 1 R 1 (u) + α 2 R 2 (c)…”

Linearized FE Approximations to a Nonlinear Gradient Flow

“…The equation has been involved in many applications, such as minimal surface flow [32], prescribed mean curvature flow [16,24], geometric measure theory [4], and a regularized model in image denoising [11,13,14,19,25,34,35,38,40]. A review article for With these a priori estimates, we establish the L 2 -norm optimal error estimate without any time-step restrictions.…”