A novel variational model for image registration using Gaussian curvature

Image registration is one important task in many image processing applications. It aims to align two or more images so that useful information can be extracted through comparison, combination or superposition. This is achieved by constructing an optimal trans- formation which ensures that the template image becomes similar to a given reference image. Although many models exist, designing a model capable of modelling large and smooth deformation field continues to pose a challenge. This paper proposes a novel variational model for image registration using the Gaussian curvature as a regulariser. The model is motivated by the surface restoration work in geometric processing [Elsey and Esedoglu, Multiscale Model. Simul., (2009), pp. 1549-1573]. An effective numerical solver is provided for the model using an augmented Lagrangian method. Numerical experiments can show that the new model outperforms three competing models based on, respectively, a linear curvature [Fischer and Modersitzki, J. Math. Imaging Vis., (2003), pp. 81- 85], the mean curvature [Chumchob, Chen and Brito, Multiscale Model. Simul., (2011), pp. 89-128] and the diffeomorphic demon model [Vercauteren at al., NeuroImage, (2009), pp. 61-72] in terms of robustness and accuracy.Comment: 23 pages, 5 figures. Key words: Image registration, Non-parametric image registration, Regularisation, Gaussian curvature, surface mappin

A robust multigrid approach for variational image registration models

AbstractVariational registration models are non-rigid and deformable imaging techniques for accurate registration of two images. As with other models for inverse problems using the Tikhonov regularization, they must have a suitably chosen regularization term as well as a data fitting term. One distinct feature of registration models is that their fitting term is always highly nonlinear and this nonlinearity restricts the class of numerical methods that are applicable. This paper first reviews the current state-of-the-art numerical methods for such models and observes that the nonlinear fitting term is mostly ‘avoided’ in developing fast multigrid methods. It then proposes a unified approach for designing fixed point type smoothers for multigrid methods. The diffusion registration model (second-order equations) and a curvature model (fourth-order equations) are used to illustrate our robust methodology. Analysis of the proposed smoothers and comparisons to other methods are given. As expected of a multigrid method, being many orders of magnitude faster than the unilevel gradient descent approach, the proposed numerical approach delivers fast and accurate results for a range of synthetic and real test images

3D orientation-preserving variational models for accurate image registration

The Beltrami coefficient from complex analysis has recently been found to provide a robust constraint for obtaining orientation-preserving and diffeomorphic transformations for registration of planar images. There exists no such concept of the Beltrami coefficient in three or higher dimensions, although a generalized theory of quasi-conformal maps in high dimensions exists. In this paper, we first propose a new algebraic measure in three dimensions (3D) that mimics the Beltrami concept in two dimensions (2D) and then propose a corresponding registration model based on it. We then establish the existence of solutions for the proposed model and further propose a converging generalized Gauss--Newton iterative method to solve the resulting nonlinear optimization problem. In addition, we also provide another two possible regularizers in 3D. Numerical experiments show that the new model can produce more accurate orientation-preserving transformations than competing state-of-the-art registration models