An Efficient Numerical Method for Mean Curvature-Based Image Registration Model

Mean curvature-based image registration model firstly proposed by Chumchob-Chen-Brito (2011) offered a better regularizer technique for both smooth and nonsmooth deformation fields. However, it is extremely challenging to solve efficiently this model and the existing methods are slow or become efficient only with strong assumptions on the smoothing parameter β. In this paper, we take a different solution approach. Firstly, we discretize the joint energy functional, following an idea of relaxed fixed point is implemented and combine with Gauss-Newton scheme with Armijo's Linear Search for solving the discretized mean curvature model and further to combine with a multilevel method to achieve fast convergence. Numerical experiments not only confirm that our proposed method is efficient and stable, but also it can give more satisfying registration results according to image quality

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

Functional Liftings of Vectorial Variational Problems with Laplacian Regularization

We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous multilabeling approaches, and makes these approaches amenable for variational problems with vectorial data and higher-order regularization, as is common in image processing applications. We motivate the approach in the function space setting and prove that, in the special case of absolute Laplacian regularization, it encompasses the discretization-first sublabel-accurate continuous multilabeling approach as a special case. We present a mathematical connection between the lifted and original functional and discuss possible interpretations of minimizers in the lifted function space. Finally, we exemplarily apply the proposed approach to 2D image registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and Variational Methods" in Hofgeismar, Germany 201

A novel high-Order functional based image registration model with inequality constraint

In this paper, a novel variational image registration model using a second-order functional as regularizer is presented. The main motivation for the new model stems from the LLT model (see Lysaker, 2003). In order to avoid mesh folding, inequality constraint on the determinant of the Jacobian matrix J of the transformation is also proposed. Furthermore, a fast solver is provided for numerical implementation of registration model with inequality constraints. Numerical experiments are illustrated to show the good performance of our new model according to the registration quality

Weighted Mean Curvature

In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation scheme for its discretization in practical image processing applications. We first demonstrate the favorable properties of WMC, such as sampling invariance, scale invariance, and contrast invariance with Gaussian noise model; and we show the relation of WMC to area regularization. We further propose an efficient computation scheme for discretized WMC, which is demonstrated herein to process over 33.2 giga-pixels/second on GPU. This scheme yields itself to a convolutional neural network representation. Finally, WMC is evaluated on synthetic and real images, showing its superiority quantitatively to total-variation and mean curvature.Comment: 12 page

Image registration in intra-oral radiography

Image registration is one of the image processing methods which is widely used in computer vision, pattern recognition, and medical imaging. In digital subtraction radiography, image registration is one of the important prerequisites to match the reference and subsequent images. In this paper, we propose an automatic non-rigid registration method namely curvature-based registration that relies on a curvature based penalizing term and its application on dental radiography. The regularizing term of this intensity-based registration approach provides affine linear transformation so that pre-registration step is no longer necessary. This leads to faster and more reliable solutions. The implementation of this approach is based on the numerical solution of the underlying Euler-Lagrange equations. In addition, a comparison between this algorithm and Linear Alignment Method (LAM) with 20 image pairs is presented. © 2005 IEEE.published_or_final_versio